diff --git a/algorithms/mcts-pw-algorithm-part2.tex b/algorithms/mcts-pw-algorithm-part2.tex new file mode 100644 index 0000000..a711e26 --- /dev/null +++ b/algorithms/mcts-pw-algorithm-part2.tex @@ -0,0 +1,89 @@ +% \vspace{-2.5mm} +\begin{algorithm}[!ht] + \caption{Monte Carlo tree search simulation.} + \label{alg:mcts-pw-simulate} + \begin{algorithmic} + \Function{Simulate$(s, d)$}{} + \If {$d=0$} + \State \Return $0$ + \EndIf + \If {$s \not\in \mathcal{T}$} + \State $\mathcal{T} \leftarrow \mathcal{T} \cup \{s\}$ + \State $N(s) \leftarrow N_0(s)$ + \State \Return \textproc{Rollout}$(s,d)$ + \EndIf + \State $N(s) \leftarrow N(s) + 1$ + \State $\bar{a} \leftarrow \textproc{SelectAction}(s)$ \algorithmiccomment{selection} + \State $(s^\prime, r) \leftarrow \textproc{DeterministicStep}(s,\bar{a})$ \algorithmiccomment{expansion} + \State $q \leftarrow r + \gamma \textproc{Simulate}(s^\prime, d-1)$ \algorithmiccomment{simulation/rollout} + \State $N(s,\bar{a}) \leftarrow N(s,\bar{a})+1$ + \State $Q(s,\bar{a}) \leftarrow Q(s,\bar{a})+\frac{q-Q(s,\bar{a})}{N(s,\bar{a})}$ \algorithmiccomment{backpropagation} + \State \Return $q$ + \EndFunction + \end{algorithmic} +\end{algorithm} +% +% \vspace{-2.5mm} +\begin{algorithm}[!ht] + \caption{Modified rollout with end-of-depth evaluation.} + \label{alg:mcts-pw-rollout} + \begin{algorithmic} + \Function{Rollout$(s,d)$}{} + \If {$d = 0$} + \State $(p, e, d) \leftarrow \textproc{Evaluate}(s)$ + \State $\tau \leftarrow \textproc{IsTerminal}(s)$ + % \State $(\bar{a},s^\prime) \leftarrow \textproc{Evaluate}(s)$ + \State $\bar{a}^* \leftarrow \textproc{UpdateBestAction}(s,Q)$ + \State \Return $R(p,e,d,\tau)$ + % \State \Return $R(s,\bar{a},s^\prime)$ + \ElsIf {$d = \floor{d_\text{max}/2}$} + \State $\bar{a} \leftarrow \bar{a}^*$ \algorithmiccomment{feed best action} + \Else + % \State $\bar{a} \sim \mathbb{U}$ \algorithmiccomment{sample seed uniformly} + \State $\bar{a} \leftarrow \textproc{SampleAction}(s,Q)$ + \EndIf + \State $(s^\prime, r) \sim G(s,\bar{a})$ + \State \Return $r + \gamma$ \textproc{Rollout}$(s^\prime,d-1)$ + \EndFunction + \end{algorithmic} +\end{algorithm} +% +\begin{algorithm}[!ht] + \caption{Action selection with progressive widening.} + \label{alg:mcts-pw-action-widen} + \begin{algorithmic} + \Function{SelectAction$(s)$}{} + \If {$| A(s) | \le kN(s)^\alpha$} + \State $\bar{a} \leftarrow \textproc{SampleAction}(s,Q)$ + % \State $\bar{a} \sim \mathbb{U}$ \algorithmiccomment{sample seed uniformly} + \State $(N(s,\bar{a}), Q(s,\bar{a})) \leftarrow (N_0(s,\bar{a}), Q_0(s,\bar{a}))$ + \State $A(s) \leftarrow A(s) \cup \{\bar{a}\}$ + \EndIf + \State \Return $\argmax_{\bar{a} \in A(s)} Q(s,\bar{a}) + c\sqrt{\frac{\log N(s)}{N(s,\bar{a})}}$ + \EndFunction + \end{algorithmic} +\end{algorithm} +% +\begin{algorithm}[!ht] + \caption{Single deterministic next state.} + \label{alg:mcts-pw-deterministic-state} + \begin{algorithmic} + \Function{DeterministicStep$(s,\bar{a})$}{} + \If {$N(s,\bar{a},\cdot) = \emptyset$} + \State $(s^\prime, r) \sim G(s,\bar{a})$ + % \State $R(s,\bar{a},s^\prime) \leftarrow r$ + \State $\textproc{SetCache}(s, \bar{a}, s^\prime, r)$ + \State $N(s,\bar{a},s^\prime) \leftarrow N_0(s,\bar{a},s^\prime)$ + \Else + % \State $s^\prime \leftarrow \arg_{s^\prime} N(s,\bar{a},\cdot)$ + % \State $(s^\prime, r) \leftarrow (\textproc{CachedNextState}(s,\bar{a}), R(s,\bar{a},s^\prime))$ + % \State $(s^\prime, r) \leftarrow \textproc{CachedNextState}(s,\bar{a})$ + \State $(s^\prime, r) \leftarrow \textproc{GetCache}(s,\bar{a})$ + % \State $s^\prime \leftarrow (\cdot)$ + % \State $r \leftarrow R(s,\bar{a},s^\prime)$ + \State $N(s,\bar{a},s^\prime) \leftarrow N(s,\bar{a},s^\prime)+1$ + \EndIf + \State \Return $(s^\prime,r)$ + \EndFunction + \end{algorithmic} +\end{algorithm} \ No newline at end of file diff --git a/algorithms/mcts-pw-algorithm.tex b/algorithms/mcts-pw-algorithm.tex new file mode 100644 index 0000000..cfe85a4 --- /dev/null +++ b/algorithms/mcts-pw-algorithm.tex @@ -0,0 +1,13 @@ +% +\begin{algorithm}[!ht] + \caption{Top-level Monte Carlo tree search algorithm.} + \label{alg:mcts-pw} + \begin{algorithmic} + \Function{MonteCarloTreeSearch$(s, d)$}{} + \Loop {} + \State \textproc{Simulate}$(s,d)$ + \EndLoop + \State \Return $\argmax_{\bar{a} \in A(s)} Q(s, \bar{a})$ + \EndFunction + \end{algorithmic} +\end{algorithm} diff --git a/algorithms/monte-carlo-algorithm.tex b/algorithms/monte-carlo-algorithm.tex new file mode 100644 index 0000000..13edac4 --- /dev/null +++ b/algorithms/monte-carlo-algorithm.tex @@ -0,0 +1,16 @@ +\algtext*{EndLoop}% Remove "end _X_" text +\algtext*{EndIf} +\algtext*{EndFor} +\algtext*{EndFunction} +\begin{algorithm}[th!] + \caption{Direct Monte Carlo simulation.} + \label{alg:mc} + \begin{algorithmic} + \Function{DirectMonteCarlo$(s_0,n,d)$}{} + \For {$1 \to n$} + \State \textproc{Initialize}$(\bar{\mathcal{S}})$ + \State \textproc{Rollout}$(s_0, d)$ \algorithmiccomment{without action feeding} + \EndFor + \EndFunction + \end{algorithmic} +\end{algorithm} \ No newline at end of file diff --git a/appendices/episodic_ast_appendix.tex b/appendices/episodic_ast_appendix.tex new file mode 100644 index 0000000..ae7e285 --- /dev/null +++ b/appendices/episodic_ast_appendix.tex @@ -0,0 +1,88 @@ +% "and Miss Distances" +\chapter{Alternative FMS Failure Events}\label{sec:application_events} +This section details alternative failure events investigated and their associated miss distance calculations. +Ultimately, analysis of these failure events showed their inadequacy and arc length failures were selected as the primary event. + +\section{Tangency Kinks} +Tangency kinks arise when a small angle threshold is exceeded between the inbound straight segment and the tangent of the turn segment at a given waypoint. The failure event occurs when this angle difference $\theta$ is above the threshold $\tau_k = 0.001$ \si{\radian}. + +\begin{figure}[!ht] +\centering +\resizebox{0.6\columnwidth}{!}{\input{diagrams/tangent-angle.tex}} +\caption{Tangency kink failure event and miss distance.} +\label{fig:tangency_kink} +\end{figure} + +Miss distance for the tangency kinks is calculated by first determining the azimuth angle $z$ between the start point of the arc $s$ and the center point $c$. The azimuth is calculated using a WGS84 Earth flattening leveraging the Geodesic.jl\footnote{\url{https://github.com/anowacki/Geodesics.jl}} package which implements Vincenty's formula \cite{vincenty}. The tangency angle $\theta$ is then calculated for each $\ell \in L$ where $L$ is the set of lateral packets that each have a straight segment and a turn arc with radius $r$. The sign of the radius $r$ indicates the direction of turn, where left is negative and right is positive. The course-in angle of the straight segment $\ell$ is denoted $\angle \ell$, +% \begin{align*} +% U(\phi) &= \arctan((1 - f) \tan \phi))\\ +% (U_s, U_c) &= (U(\phi_s),\, U(\phi_c)) +% \end{align*} +% +% \begin{align*} +% \lambda = \Lambda(L, f) +% \end{align*} +% https://github.com/anowacki/Geodesics.jl +% +% \begin{align*} +% % https://en.wikipedia.org/wiki/Vincenty%27s_formulae#Inverse_problem +% % Inverse problem +% % 1. Vincenty, T. (1975). "Direct and Inverse Solutions of Geodesics on the Ellipsoid with application of nested equations" (PDF). Survey Review. XXIII (176): 88–93. doi:10.1179/sre.1975.23.176.88 +% z = \arctan(\cos U_c \sin \lambda,\, \cos U_s \sin U_c - \sin U_s \cos U_c \cos \lambda) +% % \alpha_c = \arctan(\cos U_s \sin \lambda,\, -\sin U_s \cos U_c + \cos U_s \sin U_c \cos \lambda) +% \end{align*} +% +\begin{equation*} + % d = \tau_k - \max\left\{ \abs{z - \angle \ell + \sign(r)\frac{\pi}{2}} : (\ell,r) \in L \right\}. + d = \tau_k - \max\limits_{(\ell,r) \in L} \abs{z - \angle \ell + \sign(r)\frac{\pi}{2}}. +\end{equation*} + + +\section{Course Directions} +In-bound and out-bound course directions may deviate from one another and can be classified as a failure event. +Closely related to the \textit{disconnection} failure event, the course direction failures can arise when two sequential lateral packets are disconnected. This failure specifically looks for angle differences between the course-out $\theta_{\text{out}}$ and course-in $\theta_\text{in}$ directions of the sequential lateral packets. If this angle difference $\omega = \abs{\theta_\text{out} - \theta_\text{in}}$ is above the threshold $\tau_c = 1\si{\degree}$ then it is classified as a failure. + +\begin{figure}[!ht] +\centering +\resizebox{0.6\columnwidth}{!}{\input{diagrams/course-direction.tex}} +\caption{Course direction failure event and miss distance.} +\label{fig:course_direction} +\end{figure} + +Miss distance is calculated as how close to the threshold $\tau_c$ is the maximum wrapped angle difference between the course-out angle and course-in angle denoted by $\omega$, namely +\begin{equation*} + % d = \tau_c - \max\left\{ \abs{\theta_\text{out} - \theta_\text{in}} : \theta_\text{out} \in L_i, \theta_\text{in} \in L_{i+1} \right\}. + % d = \tau_c - \max\limits_{\theta_\text{out} \in L_i, \theta_\text{in} \in L_{i+1}}\abs{\theta_\text{out} - \theta_\text{in}}. + d = \tau_c - \max\limits_{\substack{\theta_\text{out} \in L_i\\\theta_\text{in} \in L_{i+1}}}\abs{\theta_\text{out} - \theta_\text{in}}. +\end{equation*} + +% \begin{itemize} +% \item Explain how tangent angle is calculated +% \item Talk about WGS84 flattening +% \item Mention Vincenty's inverse formula, Karney's inverse formula, and cite comparison paper (get papers, \textit{GEODESIC ALGORITHMS: AN EXPERIMENTAL STUDY}) +% \item Describe all variables used ($r = \text{radius}$, etc) +% \item Update how the angle is calculated based on Nick's adjustments +% \end{itemize} + + +\section{Disconnections} +Disconnected lateral packets occur when two sequential lateral packets are not connected end-to-start, thus leaving a distance $\delta$ between them. If this geodesic distance $\delta = \lVert e_i - p_{i+1} \rVert$ is above the threshold $\tau_d = 10$ \si{ft} then a failure occurred. + +\begin{figure}[!ht] +\centering +\resizebox{0.6\columnwidth}{!}{\input{diagrams/disconnection.tex}} +\caption{Disconnected failure event and miss distance.} +\label{fig:disconnection} +\end{figure} + +Miss distance is calculated as the threshold $\tau_d$ minus the maximum distance between the end points $e_i$ (or $s_i$ if no arc is provided) and the initial point $p_{i+1}$ of the next lateral packet: +\begin{equation*} + % d = \tau_d - \max\left\{ \lVert e_i - p_{i+1} \rVert : (e_i,p_{i+1}) \in L \right\}. + % d = \tau_d - \max\limits_{(e_i,p_{i+1}) \in L}\lVert e_i - p_{i+1} \rVert. + % d = \tau_d - \max\limits_{e_i \in L_i, p_{i+1} \in L_{i+1}}\lVert e_i - p_{i+1} \rVert. + d = \tau_d - \max\limits_{\substack{e_i \in L_i\\p_{i+1} \in L_{i+1}}}\lVert e_i - p_{i+1} \rVert +\end{equation*} + + +% We use the modified reward function that incorporates severity based on the miss distance at the time of an event. +% For our four miss distances described above, we want to reward egregious miss distances, thus finding events that are more severe. diff --git a/chapters/cem_variants.tex b/chapters/cem_variants.tex new file mode 100644 index 0000000..32226f7 --- /dev/null +++ b/chapters/cem_variants.tex @@ -0,0 +1,616 @@ +% \begin{abstract} +% The cross-entropy (CE) method is a popular stochastic method for optimization due to its simplicity and effectiveness. +% Designed for rare-event simulations where the probability of a target event occurring is relatively small, +% the CE-method relies on enough objective function calls to accurately estimate the optimal parameters of the underlying distribution. +% Certain objective functions may be computationally expensive to evaluate, and the CE-method could potentially get stuck in local minima. +% This is compounded with the need to have an initial covariance wide enough to cover the design space of interest. +% We introduce novel variants of the CE-method to address these concerns. +% To mitigate expensive function calls, during optimization we use every sample to build a surrogate model to approximate the objective function. +% The surrogate model augments the belief of the objective function with less expensive evaluations. +% We use a Gaussian process for our surrogate model to incorporate uncertainty in the predictions which is especially helpful when dealing with sparse data. +% To address local minima convergence, we use Gaussian mixture models to encourage exploration of the design space. +% We experiment with evaluation scheduling techniques to reallocate true objective function calls earlier in the optimization when the covariance is the largest. +% To test our approach, we created a parameterized test objective function with many local minima and a single global minimum. Our test function can be adjusted to control the spread and distinction of the minima. +% Experiments were run to stress the cross-entropy method variants and results indicate that the surrogate model-based approach reduces local minima convergence using the same number of function evaluations. +% \end{abstract} + + +\section{Introduction} +The cross-entropy (CE) method is a probabilistic optimization approach that attempts to iteratively fit a distribution to elite samples from an initial input distribution \cite{rubinstein2004cross,rubinstein1999cross}. +The goal is to estimate a rare-event probability by minimizing the \textit{cross-entropy} between the two distributions \cite{de2005tutorial}. +The CE-method has gained popularity in part due to its simplicity in implementation and straightforward derivation. +The technique uses \textit{importance sampling} which introduces a proposal distribution over the rare-events to sample from then re-weights the posterior likelihood by the \textit{likelihood ratio} of the true distribution over the proposal distribution. + +There are a few key assumptions that make the CE-method work effectively. +Through random sampling, the CE-method assumes that there are enough objective function evaluations to accurately represent the objective. +This may not be a problem for simple applications, but can be an issue for computationally expensive objective functions. +Another assumption is that the initial parameters of the input distribution are wide enough to cover the design space of interest. For the case with a multivariate Gaussian distribution, this corresponds to an appropriate mean and wide covariance. +In rare-event simulations with many local minima, the CE-method can fail to find a global minima especially with sparse objective function evaluations. + +This work aims to address the key assumptions of the CE-method. +We introduce variants of the CE-method that use surrogate modeling to approximate the objective function, thus updating the belief of the underlying objective through estimation. +As part of this approach, we introduce evaluation scheduling techniques to reallocate true objective function calls earlier in the optimization when we know the covariance will be large. +The evaluation schedules can be based on a distribution (e.g., the Geometric distribution) or can be prescribed manually depending on the problem. +We also use a Gaussian mixture model representation of the prior distribution as a method to explore competing local optima. +While the use of Gaussian mixture models in the CE-method is not novel, we connect the use of mixture models and surrogate modeling in the CE-method. +This connection uses each elite sample as the mean of a component distribution in the mixture, optimized through a subroutine call to the standard CE-method using the learned surrogate model. +To test our approach, we introduce a parameterized test objective function called \textit{sierra}. +The sierra function is built from a multivariate Gaussian mixture model with many local minima and a single global minimum. +Parameters for the sierra function allow control over both the spread and distinction of the minima. +Lastly, we provide an analysis of the weak areas of the CE-method compared to our proposed variants. + + +\section{Related Work} \label{sec:related_work} +The cross-entropy method is popular in the fields of operations research, machine learning, and optimization \cite{kochenderfer2015decision,Kochenderfer2019}. +The combination of the cross-entropy method, surrogate modeling, and mixture models has been explored in other work \cite{bardenet2010surrogating}. +The work in \cite{bardenet2010surrogating} proposed an adaptive grid approach to accelerate Gaussian-process-based surrogate modeling using mixture models as the prior in the cross-entropy method. They showed that a mixture model performs better than a single Gaussian when the objective function is multimodal. +Our work differs in that we augment the ``elite'' samples both by an approximate surrogate model and by a subroutine call to the CE-method using the learned surrogate model. +Other related work use Gaussian processes and a modified cross-entropy method for receding-horizon trajectory optimization \cite{tan2018gaussian}. +Their cross-entropy method variant also incorporates the notion of exploration in the context of path finding applications. +An approach based on \textit{relative entropy}, described in \cref{sec:background_ce}, proposed a model-based stochastic search that seeks to minimize the relative entropy \cite{NIPS2015_5672}. They also explore the use of a simple quadratic surrogate model to approximate the objective function. +Prior work that relate cross-entropy-based adaptive importance sampling with Gaussian mixture models show that a mixture model require less objective function calls than a na\"ive Monte Carlo or standard unimodal cross-entropy-based importance sampling method \cite{kurtz2013cross,wang2016cross}. + + +\section{Background} \label{sec:background} +This section provides necessary background on techniques used in this work. We provide introductions to cross-entropy and the cross-entropy method, surrogate modeling using Gaussian processes, and multivariate Gaussian mixture models. + +\subsection{Cross-Entropy} \label{sec:background_ce} +Before understanding the cross-entropy method, we first must understand the notion of \textit{cross-entropy}. +Cross-entropy is a metric used to measure the distance between two probability distributions, where the distance may not be symmetric \cite{de2005tutorial}. +The distance used to define cross-entropy is called the \textit{Kullback-Leibler (KL) distance} or \textit{KL divergence}. +The KL distance is also called the \textit{relative entropy}, and we can use this to derive the cross-entropy. +Formally, for a random variable $\mat{X} = (X_1, \ldots, X_n)$ with a support of $\mathcal{X}$, the KL distance between two continuous probability density functions $f$ and $g$ is defined to be: +\begin{align*} + \mathcal{D}(f, g) &= \E_f\left[\log \frac{f(\vec{X})}{g(\vec{X})} \right]\\ + &= \int\limits_{\vec{x} \in \mathcal{X}} f(\vec{x}) \log f(\vec{x}) d\vec{x} - \int\limits_{\vec{x} \in \mathcal{X}} f(\vec{x}) \log g(\vec{x}) d\vec{x} +\end{align*} +We denote the expectation of some function with respect to a distribution $f$ as $\E_f$. +Minimizing the KL distance $\mathcal{D}$ between our true distribution $f$ and our proposal distribution $g$ parameterized by $\vec{\theta}$, is equivalent to choosing $\vec\theta$ that minimizes the following, called the \textit{cross-entropy}: +\begin{align*} + H(f,g) &= H(f) + \mathcal{D}(f,g)\\ + &= -\E_f[\log g(\vec{X})] \tag{using KL distance}\\ + &= - \int\limits_{\vec{x} \in \mathcal{X}} f(\vec{x}) \log g(\vec{x} \mid \vec{\theta}) d\vec{x} +\end{align*} +where $H(f)$ denotes the entropy of the distribution $f$ (where we conflate entropy and continuous entropy for convenience). +This assumes that $f$ and $g$ share the support $\mathcal{X}$ and are continuous with respect to $\vec{x}$. +The minimization problem then becomes: +\begin{equation} \label{eq:min} +\begin{aligned} + \minimize_{\vec{\theta}} & & - \int\limits_{\vec{x} \in \mathcal{X}} f(\vec{x}) \log g(\vec{x} \mid \vec{\theta}) d\vec{x} +\end{aligned} +\end{equation} +Efficiently finding this minimum is the goal of the cross-entropy method algorithm. + + +\subsection{Cross-Entropy Method} \label{sec:background_cem} +Using the definition of cross-entropy, intuitively the \textit{cross-entropy method} (CEM or CE-method) aims to minimize the cross-entropy between the unknown true distribution $f$ and a proposal distribution $g$ parameterized by $\vec\theta$. +This technique reformulates the minimization problem as a probability estimation problem, and uses adaptive importance sampling to estimate the unknown expectation \cite{de2005tutorial}. +The cross-entropy method has been applied in the context of both discrete and continuous optimization problems \cite{rubinstein1999cross,kroese2006cross}. + + +The initial goal is to estimate the probability +\begin{align*} + \ell = P_{\vec{\theta}}(S(\vec{x}) \ge \gamma) +\end{align*} +where $S$ can the thought of as an objective function of $\vec{x}$, and $\vec{x}$ follows a distribution defined by $g(\vec{x} \mid \vec{\theta})$. +We want to find events where our objective function $S$ is above some threshold $\gamma$. +We can express this unknown probability as the expectation +\begin{align} \label{eq:expect} + \ell = \E_{\vec{\theta}}[\mathbbm{1}_{(S(\vec{x}) \ge \gamma)}] +\end{align} +where $\mathbbm{1}$ denotes the indicator function. +A straightforward way to estimate \cref{eq:expect} can be done through Monte Carlo sampling. +But for rare-event simulations where the probability of a target event occurring is relatively small, this estimate becomes inadequate. +The challenge of the minimization in \cref{eq:min} then becomes choosing the density function for the true distribution $f(\vec{x})$. +Importance sampling tells us that the optimal importance sampling density can be reduced to +\begin{align*} + f^*(\vec{x}) = \frac{\mathbbm{1}_{(S(\vec{x}) \ge \gamma)}g(\vec{x} \mid \vec{\theta})}{\ell} +\end{align*} +thus resulting in the optimization problem: +\begin{align*} + \vec{\theta}_g^* &= \argmin_{\vec{\theta}_g} - \int\limits_{\vec{x} \in \mathcal{X}} f^*(\vec{x})\log g(\vec{x} \mid \vec{\theta}_g) d\vec{x}\\ + &= \argmin_{\vec{\theta}_g} - \int\limits_{\vec{x} \in \mathcal{X}} \frac{\mathbbm{1}_{(S(\vec{x}) \ge \gamma)}g(\vec{x} \mid \vec{\theta})}{\ell}\log g(\vec{x} \mid \vec{\theta}_g) d\vec{x} +\end{align*} +Note that since we assume $f$ and $g$ belong to the same family of distributions, we get that $f(\vec{x}) = g(\vec{x} \mid \vec{\theta}_g)$. +Now notice that $\ell$ is independent of $\vec{\theta}_g$, thus we can drop $\ell$ and get the final optimization problem of: +\begin{align} \label{eq:opt} + \vec{\theta}_g^* &= \argmin_{\vec{\theta}_g} - \int\limits_{\vec{x} \in \mathcal{X}} \mathbbm{1}_{(S(\vec{x}) \ge \gamma)}g(\vec{x} \mid \vec{\theta}) \log g(\vec{x} \mid \vec{\theta}_g) d\vec{x}\\\nonumber + &= \argmin_{\vec{\theta}_g} - \E_{\vec{\theta}}[ \mathbbm{1}_{(S(\vec{x}) \ge \gamma)} \log g(\vec{x} \mid \vec{\theta}_g)] +\end{align} + +The CE-method uses a multi-level algorithm to estimate $\vec{\theta}_g^*$ iteratively. +The parameter $\vec{\theta}_k$ at iteration $k$ is used to find new parameters $\vec{\theta}_{k^\prime}$ at the next iteration $k^\prime$. +The threshold $\gamma_k$ becomes smaller that its initial value, thus artificially making events \textit{less rare} under $\vec{X} \sim g(\vec{x} \mid \vec{\theta}_k)$. + +In practice, the CE-method algorithm requires the user to specify a number of \textit{elite} samples $m_\text{elite}$ which are used when fitting the new parameters for iteration $k^\prime$. +Conveniently, if our distribution $g$ belongs to the \textit{natural exponential family} then the optimal parameters can be found analytically \cite{Kochenderfer2019}. For a multivariate Gaussian distribution parameterized by $\vec{\mu}$ and $\mat{\Sigma}$, the optimal parameters for the next iteration $k^\prime$ correspond to the maximum likelihood estimate (MLE): +\begin{align*} + \vec{\mu}_{k^\prime} &= \frac{1}{m_\text{elite}} \sum_{i=1}^{m_\text{elite}} \vec{x}_i\\ + \vec{\Sigma}_{k^\prime} &= \frac{1}{m_\text{elite}} \sum_{i=1}^{m_\text{elite}} (\vec{x}_i - \vec{\mu}_{k^\prime})(\vec{x}_i - \vec{\mu}_{k^\prime})^\top +\end{align*} + +The cross-entropy method algorithm is shown in \cref{alg:cem}. +For an objective function $S$ and input distribution $g$, the CE-method algorithm will run for $k_\text{max}$ iterations. +At each iteration, $m$ inputs are sampled from $g$ and evaluated using the objective function $S$. +The sampled inputs are denoted by $\mat{X}$ and the evaluated values are denoted by $\mat{Y}$. +Next, the top $m_\text{elite}$ samples are stored in the elite set $\e$, and the distribution $g$ is fit to the elites. +This process is repeated for $k_\text{max}$ iterations and the resulting parameters $\vec{\theta}_{k_\text{max}}$ are returned. +Note that a variety of input distributions for $g$ are supported, but we focus on the multivariate Gaussian distribution and the Gaussian mixture model in this work. + +%% CE-method +\begin{algorithm}[ht] + \begin{algorithmic} + \Function{CrossEntropyMethod}{}($S, g, m, m_\text{elite}, k_\text{max}$) + \For {$k \in [1,\ldots,k_\text{max}]$} + \State $\mat{X} \sim g(\;\cdot \mid \vec{\theta}_k)$ where $\mat{X} \in \R^m$ + \State $\mat{Y} \leftarrow S(\vec{x})$ for $\vec{x} \in \mat{X}$ + \State $\e \leftarrow$ store top $m_\text{elite}$ from $\mat{Y}$ + \State $\vec{\theta}_{k^\prime} \leftarrow \textproc{Fit}(g(\;\cdot \mid \vec{\theta}_k), \e)$ + \EndFor + \State \Return $g(\;\cdot \mid \vec{\theta}_{k_\text{max}})$ + \EndFunction + \end{algorithmic} + \caption{\label{alg:cem} Cross-entropy method.} +\end{algorithm} + + +\subsection{Mixture Models} +A standard Gaussian distribution is \textit{unimodal} and can have trouble generalizing over data that is \textit{multimodal}. +A \textit{mixture model} is a weighted mixture of component distributions used to represent continuous multimodal distributions \cite{kochenderfer2015decision}. +Formally, a Gaussian mixture model (GMM) is defined by its parameters $\vec{\mu}$ and $\mat{\Sigma}$ and associated weights $\w$ where $\sum_{i=1}^n w_i = 1$. We denote that a random variable $\mat{X}$ is distributed according to a mixture model as $\mat{X} \sim \operatorname{Mixture}(\vec{\mu}, \vec{\Sigma}, \vec{w})$. +The probability density of the GMM then becomes: +%% Mixture model PDF +\begin{gather*} + P( \mat{X} = \vec{x} \mid \vec{\mu}, \mat{\Sigma}, \vec{w}) = \sum_{i=1}^n w_i \Normal(\vec{x} \mid \vec{\mu}_i, \mat{\Sigma}_i) +\end{gather*} + +To fit the parameters of a Gaussian mixture model, it is well known that the \textit{expectation-maximization (EM)} algorithm can be used \cite{dempster1977maximum,aitkin1980mixture}. +The EM algorithm seeks to find the maximum likelihood estimate of the hidden variable $H$ using the observed data defined by $E$. +Intuitively, the algorithm alternates between an expectation step (E-step) and a maximization step (M-step) to guarantee convergence to a local minima. +A simplified EM algorithm is provide in \cref{alg:em} for reference and we refer to \cite{dempster1977maximum,aitkin1980mixture} for further reading. + +%% Expectation Maximization +\begin{algorithm}[ht] + \begin{algorithmic} + \Function{ExpectationMaximization}{$H, E, \vec{\theta}$} + \For{\textbf{E-step}} + \State Compute $Q(h) = P(H=h \mid E=e, \vec{\theta})$ for each $h$ % (use any probabilistic inference algorithm) + \State Create weighted points: $(h,e)$ with weight $Q(h)$ + \EndFor + \For{\textbf{M-step}} + \State Compute $\mathbf{\hat{\vec{\theta}}}_{\text{MLE}}$ + \EndFor + \State Repeat until convergence. + \State \Return $\mathbf{\hat{\vec{\theta}}}_{\text{MLE}}$ + \EndFunction + \end{algorithmic} + \caption{\label{alg:em} Expectation-maximization.} +\end{algorithm} + + + +\subsection{Surrogate Models} +In the context of optimization, a surrogate model $\hat{S}$ is used to estimate the true objective function and provide less expensive evaluations. +Surrogate models are a popular approach and have been used to evaluate rare-event probabilities in computationally expensive systems \cite{li2010evaluation,li2011efficient}. +The simplest example of a surrogate model is linear regression. +In this work, we focus on the \textit{Gaussian process} surrogate model. +A Gaussian process (GP) is a distribution over functions that predicts the underlying objective function $S$ and captures the uncertainty of the prediction using a probability distribution \cite{Kochenderfer2019}. +This means a GP can be sampled to generate random functions, which can then be fit to our given data $\mat{X}$. +A Gaussian process is parameterized by a mean function $\m(\mat{X})$ and kernel function $\mat{K}(\mat{X},\mat{X})$, which captures the relationship between data points as covariance values. +We denote a Gaussian process that produces estimates $\hat{\vec{y}}$ as: +\begin{align*} +\hat{\vec{y}} &\sim\mathcal{N}\left(\vec{m}(\mat{X}),\vec{K}(\mat{X},\mat{X})\right)\\ + &= \begin{bmatrix} % Changed `m` to `n` + \hat{S}(\vec{x}_1), \ldots, \hat{S}(\vec{x}_n) + \end{bmatrix} +\end{align*} +where +\begin{gather*} +\vec{m}(\mat{X}) = \begin{bmatrix} m(\vec{x}_1), \ldots, m(\vec{x}_n) \end{bmatrix}\\ +\vec{K}(\mat{X}, \mat{X}) = \begin{bmatrix} + k(\vec{x}_1, \vec{x}_1) & \cdots & k(\vec{x}_1, \vec{x}_n)\\ + \vdots & \ddots & \vdots\\ + k(\vec{x}_n, \vec{x}_1) & \cdots & k(\vec{x}_n, \vec{x}_n) + \end{bmatrix} +\end{gather*} +We use the commonly used zero-mean function $m(\vec{x}_i) = \vec{0}$. +For the kernel function $k(\vec{x}_i, \vec{x}_i)$, we use the squared exponential kernel with variance $\sigma^2$ and characteristic scale-length $\ell$, where larger $\ell$ values increase the correlation between successive data points, thus smoothing out the generated functions. The squared exponential kernel is defined as: +% Isotropic Squared Exponential kernel (covariance): \exp(-\frac{r^2}{2\ell^2}) +\begin{align*} +k(\vec{x},\vec{x}^\prime) = \sigma^2\exp\left(- \frac{(\vec{x} - \vec{x}^\prime)^\top(\vec{x} - \vec{x}^\prime)}{2\ell^2}\right) +\end{align*} +We refer to \cite{Kochenderfer2019} for a detailed overview of Gaussian processes and different kernel functions. + + + +\section{Algorithms} \label{sec:algorithms} +We can now describe the cross-entropy method variants introduced in this work.\footnote{Code available at \href{https://github.com/mossr/CrossEntropyVariants.jl}{https://github.com/mossr/CrossEntropyVariants.jl}} +This section will first cover the main algorithm introduced, the cross-entropy surrogate method (CE-surrogate). +Then we introduce a modification to the CE-surrogate method, namely the cross-entropy mixture method (CE-mixture). +Lastly, we describe various evaluation schedules for redistributing objective function calls over the iterations. + +\subsection{Cross-Entropy Surrogate Method} \label{sec:alg_ce_surrogate} +The main CE-method variant we introduce is the cross-entropy surrogate method (CE-surrogate). +The CE-surrogate method is a superset of the CE-method, where the differences lie in the evaluation scheduling and modeling of the elite set using a surrogate model. +The goal of the CE-surrogate algorithm is to address the shortcomings of the CE-method when the number of objective function calls is sparse and the underlying objective function $S$ has multiple local minima. + +The CE-surrogate algorithm is shown in \cref{alg:ce_surrogate}. +It takes as input the objective function $S$, the distribution $\M$ parameterized by $\vec{\theta}$, the number of samples $m$, the number of elite samples $m_\text{elite}$, and the maximum iterations $k_\text{max}$. +For each iteration $k$, the number of samples $m$ are redistributed through a call to \smallcaps{EvaluationSchedule}, where $m$ controls the number of true objective function evaluations of $S$. % EvaluationSchedule. +Then, the algorithm samples from $\M$ parameterized by the current $\vec{\theta}_k$ given the adjusted number of samples $m$. % and clamped $m_\text{elite}$. +For each sample in $\mat{X}$, the objective function $S$ is evaluated and the results are stored in $\mat{Y}$. +The top $m_\text{elite}$ evaluations from $\mat{Y}$ are stored in $\e$. +Using all of the current function evaluations $\mat{Y}$ from sampled inputs $\mat{X}$, a modeled elite set $\bfE$ is created to augment the sparse information provided by a low number of true objective function evaluations. +Finally, the distribution $\M$ is fit to the elite set $\bfE$ and the distribution with the final parameters $\vec{\theta}_{k_\text{max}}$ is returned. + +%% CE-surrogate +\begin{algorithm}[ht] + \begin{algorithmic} + \Function{CE-Surrogate}{$S$, $\M$, $m$, $m_\text{elite}$, $k_\text{max}$} + \For {$k \in [1,\ldots,k_\text{max}]$} + \State $m, m_\text{elite} \leftarrow \textproc{EvaluationSchedule}(k, k_\text{max})$ + \State $\mat{X} \sim \M(\;\cdot \mid \vec{\theta}_k)$ where $\mat{X} \in \R^m$ + \State $\mat{Y} \leftarrow S(\vec{x})$ for $\vec{x} \in \mat{X}$ + \State $\e \leftarrow$ store top $m_\text{elite}$ from $\mat{Y}$ + \State $\bfE \leftarrow \textproc{ModelEliteSet}(\mat{X}, \mat{Y}, \M, \e, m, m_\text{elite})$ + \State $\vec{\theta}_{k^\prime} \leftarrow \textproc{Fit}(\M(\;\cdot \mid \vec{\theta}_k), \bfE)$ + \EndFor + \State \Return $\M(\;\cdot \mid \vec{\theta}_{k_\text{max}})$ + \EndFunction + \end{algorithmic} + \caption{\label{alg:ce_surrogate} Cross-entropy surrogate method.} +\end{algorithm} + + +The main difference between the standard CE-method and the CE-surrogate variant lies in the call to \smallcaps{ModelEliteSet}. +The motivation is to use \textit{all} of the already evaluated objective function values $\mat{Y}$ from a set of sampled inputs $\mat{X}$. +This way the expensive function evaluations---otherwise discarded---can be used to build a surrogate model of the underlying objective function. +First, a surrogate model $\surrogate$ is constructed from the samples $\mat{X}$ and true objective function values $\mat{Y}$. +We used a Gaussian process with a specified kernel and optimizer, but other surrogate modeling techniques such as regression with basis functions can be used. +We chose a Gaussian process because it incorporates probabilistic uncertainty in the predictions, which may more accurately represent our objective function, or at least be sensitive to over-fitting to sparse data. +Now we have an approximated objective function $\surrogate$ that we can inexpensively call. +We sample $10m$ values from the distribution $\M$ and evaluate them using the surrogate model. +We then store the top $10m_\text{elite}$ values from the estimates $\mathbf{\hat{\mat{Y}}}_\text{m}$. +We call these estimated elite values $\e_\text{model}$ the \textit{model-elites}. +The surrogate model is then passed to \smallcaps{SubEliteSet}, which returns more estimates for elite values. +Finally, the elite set $\bfE$ is built from the true-elites $\e$, the model-elites $\e_\text{model}$, and the subcomponent-elites $\e_\text{sub}$. +The resulting concatenated elite set $\bfE$ is returned. + +\begin{algorithm}[ht] + \begin{algorithmic} + \Function{ModelEliteSet}{$\mat{X}, \mat{Y}, \M, \e, m, m_\text{elite}$} + % Fit to entire population! + \State $\surrogate \leftarrow \textproc{GaussianProcess}(\mat{X}, \mat{Y}, \text{kernel}, \text{optimizer})$ % Squared exponential, NelderMead + \State $\mat{X}_\text{m} \sim \M(\;\cdot \mid \vec{\theta}_k)$ where $\mat{X}_\text{m} \in \R^{10m}$ + \State $\mathbf{\hat{\mat{Y}}}_\text{m} \leftarrow \surrogate(\vec{x}_\text{m})$ for $\vec{x}_\text{m} \in \mat{X}_\text{m}$ + \State $\e_\text{model} \leftarrow$ store top $10m_\text{elite}$ from $\mathbf{\hat{\mat{Y}}}_\text{m}$ + \State $\e_\text{sub} \leftarrow \textproc{SubEliteSet}(\surrogate, \M, \e)$ + \State $\bfE \leftarrow \{ \e \} \cup \{ \e_\text{model} \} \cup \{ \e_\text{sub} \}$ \algorithmiccomment{elite set} + \State \Return $\bfE$ + \EndFunction + \end{algorithmic} + \caption{\label{alg:model_elite_set} Modeling elite set.} +\end{algorithm} + +To encourage exploration of promising areas of the design space, the algorithm \smallcaps{SubEliteSet} focuses on the already marked true-elites $\e$. +Each elite $e_x \in \e$ is used as the mean of a new multivariate Gaussian distribution with covariance inherited from the distribution $\M$. +The collection of subcomponent distributions is stored in $\m$. +The idea is to use the information given to us by the true-elites to emphasize areas of the design space that look promising. +For each distribution $\m_i \in \m$ we run a subroutine call to the standard CE-method to fit the distribution $\m_i$ using the surrogate model $\surrogate$. +Then the best objective function value is added to the subcomponent-elite set $\e_\text{sub}$, and after iterating the full set is returned. +Note that we use $\theta_\text{CE}$ to denote the parameters for the CE-method algorithm. +In our case, we recommend using a small $k_\text{max}$ of around $2$ so the subcomponent-elites do not over-fit to the surrogate model but have enough CE-method iterations to tend towards optimal. + +\begin{algorithm}[ht] + \begin{algorithmic} + \Function{SubEliteSet}{$\surrogate, \M, \e$} + \State $\e_\text{sub} \leftarrow \emptyset$ + \State $\m \leftarrow \{ e_x \in \e \mid \Normal(e_x, \M.\Sigma) \}$ + \For {$\m_i \in \m$} + \State $\m_i \leftarrow \textproc{CrossEntropyMethod}(\surrogate, \m_i \mid \theta_{\text{CE}})$ + \State $\e_\text{sub} \leftarrow \{\e_\text{sub}\} \cup \{\textproc{Best}(\m_i)\}$ + \EndFor + \State \Return $\e_\text{sub}$ + \EndFunction + \end{algorithmic} + \caption{\label{alg:sub_elite_set} Subcomponent elite set.} +\end{algorithm} + + +\subsection{Cross-Entropy Mixture Method} \label{sec:alg_ce_mixture} +We refer to the variant of our CE-surrogate method that takes an input \textit{mixture model} $\M$ as the cross-entropy mixture method (CE-mixture). +The CE-mixture algorithm is identical to the CE-surrogate algorithm, but calls a custom \smallcaps{Fit} function to fit a mixture model to the elite set $\bfE$. +The input distribution $\M$ is cast to a mixture model using the subcomponent distributions $\m$ as the components of the mixture. +We use the default uniform weighting for each mixture component. +The mixture model $\M$ is then fit using the expectation-maximization algorithm shown in \cref{alg:em}, and the resulting distribution is returned. +The idea is to use the distributions in $\m$ that are centered around each true-elite as the components of the casted mixture model. +Therefore, we would expect better performance of the CE-mixture method when the objective function has many competing local minima. +Results in \cref{sec:results} aim to show this behavior. + +%% CE-mixture (fit) +\begin{algorithm}[ht] + \begin{algorithmic} + \Function{Fit}{$\M, \m, \bfE$} + \State $\M \leftarrow \operatorname{Mixture}( \m )$ + \State $\mathbf{\hat{\vec{\theta}}} \leftarrow \textproc{ExpectationMaximization}(\M, \bfE)$ + \State \Return $\M(\;\cdot \mid \mathbf{\hat{\vec{\theta}}})$ + \EndFunction + \end{algorithmic} + \caption{\label{alg:ce_mixture_fit} Fitting mixture models (used by CE-mixture).} +\end{algorithm} + + +\subsection{Evaluation Scheduling} \label{sec:alg_eval_schedule} +Given the nature of the CE-method, we expect the covariance to shrink over time, thus resulting in a solution with higher confidence. +Yet if each iteration is given the same number of objective function evaluations $m$, there is the potential for elite samples from early iterations dominating the convergence. +Therefore, we would like to redistribute the objective function evaluations throughout the iterations to use more truth information early in the process. +We call these heuristics \textit{evaluation schedules}. +One way to achieve this is to reallocate the evaluations according to a Geometric distribution. +Evaluation schedules can also be ad-hoc and manually prescribed based on the current iteration. + +We provide the evaluation schedule we use that follows a Geometric distribution with parameter $p$ in \cref{alg:evaluation_schedule}. +We denote $G \sim \Geo(p)$ to be a random variable that follows a truncated Geometric distribution with the probability mass function $p_G(k) = p(1 - p)^k$ for $k \in \{0, 1, 2, \ldots, k_\text{max}\}$. % Geo(p) PMF +Note the use of the integer rounding function (e.g., $\round{x}$), which we later have to compensate for towards the final iterations. +Results in \cref{sec:results} compare values of $p$ that control the redistribution of evaluations. + + +%% EvaluationSchedule +\begin{algorithm}[ht] + \begin{algorithmic} + \Function{EvaluationSchedule}{$k, k_\text{max}$} + \State $G \sim \Geo(p)$ + \State $N_\text{max} \leftarrow k_\text{max} \cdot m$ + \State $m \leftarrow \round{N_\text{max} \cdot p_G(k)}$ + \If{$k = k_\text{max}$} + \State $s \leftarrow \displaystyle\sum_{i=1}^{k_\text{max}-1} \round{N_\text{max} \cdot p_G(i)}$ + \State $m \leftarrow \min(N_\text{max} - s, N_\text{max} - m)$ + \EndIf + \State $m_\text{elite} \leftarrow \min(m_\text{elite}, m)$ + \State \Return ($m, m_\text{elite}$) + \EndFunction + \end{algorithmic} + \caption{\label{alg:evaluation_schedule} Evaluation schedule using a Geometric distr.} +\end{algorithm} + + +\section{Experiments} \label{sec:experiments} +In this section, we detail the experiments we ran to compare the CE-method variants and evaluation schedules. +We first introduce a test objective function we created to stress the issue of converging to local minima. +We then describe the experimental setup for each of our experiments and provide an analysis and results. + + +\subsection{Test Objective Function Generation} +\begin{figure*}[!t] + \centering + \resizebox{0.8\textwidth}{!}{\input{figures/cem_variants/sierra_group.tex}} + \caption{ + \label{fig:sierra} + Example test objective functions generated using the sierra function. + } +\end{figure*} +To stress the cross-entropy method and its variants, we created a test objective function called \textit{sierra} that is generated from a mixture model comprised of $49$ multivariate Gaussian distributions. +We chose this construction so that we can use the negative peeks of the component distributions as local minima and can force a global minimum centered at our desired $\mathbf{\tilde{\vec{\mu}}}$. +The construction of the sierra test function can be controlled by parameters that define the spread of the local minima. +We first start with the center defined by a mean vector $\mathbf{\tilde{\vec{\mu}}}$ and we use a common covariance $\mathbf{\tilde{\mat{\Sigma}}}$: +\begin{align*} + \mathbf{\tilde{\vec{\mu}}} &= [\mu_1, \mu_2], \quad \mathbf{\tilde{\mat{\Sigma}}} = \begin{bmatrix}\sigma & 0\\ 0 & \sigma \end{bmatrix} +\end{align*} +Next, we use the parameter $\delta$ that controls the clustered distance between symmetric points: +\begin{align*} + \mat{G} &= \left\{[+\delta, +\delta], [+\delta, -\delta], [-\delta, +\delta], [-\delta, -\delta]\right\} +\end{align*} +We chose points $\mat{P}$ to fan out the clustered minima relative to the center defined by $\mathbf{\tilde{\vec{\mu}}}$: +\begin{align*} + \mat{P} &= \left\{[0, 0], [1, 1], [2, 0], [3, 1], [0, 2], [1, 3]\right\} +\end{align*} +The vector $\vec{s}$ is used to control the $\pm$ distance to create an `s' shape comprised of minima, using the standard deviation $\sigma$: +$\vec{s} = \begin{bmatrix}+\sigma, -\sigma \end{bmatrix}$. +We set the following default parameters: standard deviation $\sigma=3$, spread rate $\eta=6$, and cluster distance $\delta=2$. +We can also control if the local minima clusters ``decay'', thus making those local minima less distinct (where $\text{decay} \in \{0, 1\})$. +The parameters that define the sierra function are collected into $\vec{\theta} = \langle \mathbf{\tilde{\vec{\mu}}}, \mathbf{\tilde{\mat{\Sigma}}}, \mat{G}, \mat{P}, \vec{s} \rangle$. +Using these parameters, we can define the mixture model used by the sierra function as: +\begin{gather*} + \Sierra \sim \operatorname{Mixture}\left(\left\{ \vec{\theta} ~\Big|~ \Normal\left(\vec{g} + s\vec{p}_i + \mathbf{\tilde{\vec{\mu}}},\; \mathbf{\tilde{\mat{\Sigma}}} \cdot i^{\text{decay}}/\eta \right) \right\} \right)\\ + \text{for } (\vec{g}, \vec{p}_i, s) \in (\mat{G}, \mat{P}, \vec{s}) +\end{gather*} +We add a final component to be our global minimum centered at $\mathbf{\tilde{\vec{\mu}}}$ and with a covariance scaled by $\sigma\eta$. Namely, the global minimum is $\vec{x}^* = \E[\Normal(\mathbf{\tilde{\vec{\mu}}}, \mathbf{\tilde{\mat{\Sigma}}}/(\sigma\eta))] = \mathbf{\tilde{\vec{\mu}}}$. +We can now use this constant mixture model with $49$ components and define the sierra objective function $\mathcal{S}(\vec{x})$ to be the negative probability density of the mixture at input $\vec{x}$ with uniform weights: + +\begin{align*} + \mathcal{S}(\vec{x}) &= -P(\Sierra = \vec{x}) = -\frac{1}{|\Sierra|}\sum_{j=1}^{n}\Normal(\vec{x} \mid \vec{\mu}_j, \mat{\Sigma}_j) +\end{align*} +An example of six different objective functions generated using the sierra function are shown in \cref{fig:sierra}, sweeping over the spread rate $\eta$, with and without decay. + +\subsection{Experimental Setup} \label{sec:experiment_setup} +Experiments were run to stress a variety of behaviors of each CE-method variant. +The experiments are split into two categories: algorithmic and scheduling. +The algorithmic category aims to compare features of each CE-method variant while holding common parameters constant (for a better comparison). +While the scheduling category experiments with evaluation scheduling heuristics. + +\begin{figure*}[!t] + \centering + \subfloat[The cross-entropy method.]{% + \resizebox{0.3\textwidth}{!}{\input{figures/cem_variants/k5_ce_method.pgf}} + } + \subfloat[The cross-entropy surrogate method.]{% + \resizebox{0.3\textwidth}{!}{\input{figures/cem_variants/k5_ce_surrogate.pgf}} + } + \subfloat[The cross-entropy mixture method.]{% + \resizebox{0.3\textwidth}{!}{\input{figures/cem_variants/k5_ce_mixture.pgf}} + } + \caption{ + \label{fig:k5} Iteration $k=5$ illustrated for each algorithm. The covariance is shown by the contours. + } +\end{figure*} + +Because the algorithms are stochastic, we run each experiment with 50 different random number generator seed values. +To evaluate the performance of the algorithms in their respective experiments, we define three metrics. +First, we define the average ``optimal'' value $\bar{b}_v$ to be the average of the best so-far objective function value (termed ``optimal'' in the context of each algorithm). Again, we emphasize that we average over the 50 seed values to gather meaningful statistics. +Another metric we monitor is the average distance to the true global optimal $\bar{b}_d = \norm{\vec{b}_{\vec{x}} - \vec{x}^*}$, where $\vec{b}_{\vec{x}}$ denotes the $\vec{x}$-value associated with the ``optimal''. +We make the distinction between these metrics to show both ``closeness'' in \textit{value} to the global minimum and ``closeness'' in the \textit{design space} to the global minimum. +Our final metric looks at the average runtime of each algorithm, noting that our goal is to off-load computationally expensive objective function calls to the surrogate model. + +For all of the experiments, we use a common setting of the following parameters for the sierra test function (shown in the top-right plot in \cref{fig:sierra}): +\begin{equation*} + (\mathbf{\tilde{\vec{\mu}}} =[0,0],\; \sigma=3,\; \delta=2,\; \eta=6,\; \text{decay} = 1) +\end{equation*} + + +\subsubsection{Algorithmic Experiments} \label{sec:alg_experiments} +We run three separate algorithmic experiments, each to test a specific feature. +For our first algorithmic experiment (1A), we want to test each algorithm when the user-defined mean is centered at the global minimum and the covariance is arbitrarily wide enough to cover the design space. +Let $\M$ be a distribution parameterized by $\vec{\theta} = (\vec{\mu}, \mat{\Sigma})$, and for experiment (1A) we set the following: +% CE-mixture mean and covariance (1A) +\begin{equation*} + \vec\mu^{(\text{1A})} = [0, 0] \qquad + \mat\Sigma^{(\text{1A})} = \begin{bmatrix} + 200 & 0\\ + 0 & 200 + \end{bmatrix} +\end{equation*} + +For our second algorithmic experiment (1B), we test a mean that is far off-centered with a wider covariance: +% CE-mixture mean and covariance (1B) +\begin{equation*} + \vec\mu^{(\text{1B})} = [-50, -50] \qquad + \mat\Sigma^{(\text{1B})} = \begin{bmatrix} + 2000 & 0\\ + 0 & 2000 + \end{bmatrix} +\end{equation*} +This experiment is used to test the ``exploration'' of the CE-method variants introduced in this work. +In experiments (1A) and (1B), we set the following common parameters across each CE-method variant: +%% CE-mixture hyperparameter settings +\begin{equation*} + (k_\text{max} = 10,\; m=10,\; m_\text{elite}=5)^{(\text{1A,1B})} +\end{equation*} +This results in $m\cdot k_\text{max} = 100$ objective function evaluations, which we define to be \textit{relatively} low. + +For our third algorithmic experiment (1C), we want to test how each variant responds to an extremely low number of function evaluations. +This sparse experiment sets the common CE-method parameters to: +% CE-method params (1C) +\begin{equation*} + (k_\text{max} = 10,\; m=5,\; m_\text{elite}=3)^{(\text{1C})} +\end{equation*} +This results in $m\cdot k_\text{max} = 50$ objective function evaluations, which we defined to be \textit{extremely} low. +We use the same mean and covariance defined for experiment (1A): +\begin{equation*} + \vec\mu^{(\text{1C})} = [0, 0] \qquad + \mat\Sigma^{(\text{1C})} = \begin{bmatrix} + 200 & 0\\ + 0 & 200 + \end{bmatrix} +\end{equation*} + + +\subsubsection{Scheduling Experiments} \label{sec:schedule_experiments} +In our final experiment (2), we test the evaluation scheduling heuristics which are based on the Geometric distribution. +We sweep over the parameter $p$ that determines the Geometric distribution which controls the redistribution of objective function evaluations. +In this experiment, we compare the CE-surrogate methods using the same setup as experiment (1B), namely the far off-centered mean. +We chose this setup to analyze exploration schemes when given very little information about the true objective function. + + + +\subsection{Results and Analysis} \label{sec:results} + +\begin{figure}[!hb] + % \centering + \resizebox{0.9\columnwidth}{!}{\input{figures/cem_variants/experiment1a.tex}} + \caption{ + \label{fig:experiment_1a} + Average optimal value for experiment (1A) when the initial mean is centered at the global minimum and the covariance sufficiently covers the design space. + } +\end{figure} + +\Cref{fig:experiment_1a} shows the average value of the current optimal $\bar{b}_v$ for the three algorithms for experiment (1A). +One standard deviation is plotted in the shaded region. +Notice that the standard CE-method converges to a local minima before $k_\text{max}$ is reached. +Both CE-surrogate method and CE-mixture stay below the standard CE-method curve, highlighting the mitigation of convergence to local minima. +Minor differences can be seen between CE-surrogate and CE-mixture, differing slightly towards the tail in favor of CE-surrogate. +The average runtime of the algorithms along with the performance metrics are shown together for each experiment in \cref{tab:results}. + + +\begin{table}[!ht] + \centering + \caption{\label{tab:results} Experimental results.} + \begin{tabular}{cllll} % p{3cm} + \toprule + \textbf{Exper.} & \textbf{Algorithm} & \textbf{Runtime} & $\bar{b}_v$ & $\bar{b}_d$\\ + \midrule + \multirow{3}{*}{1A} & CE-method & \textbf{0.029 $\operatorname{s}$} & $-$0.0134 & 23.48\\ + &CE-surrogate & 1.47 $\operatorname{s}$ & \textbf{\boldmath$-$0.0179} & \textbf{12.23}\\ + &CE-mixture & 9.17 $\operatorname{s}$ & $-$0.0169 & 16.87\\ + \midrule + \multirow{3}{*}{1B} & CE-method & \textbf{0.046 $\operatorname{s}$} & $-$0.0032 & 138.87\\ + &CE-surrogate & 11.82 $\operatorname{s}$ & \textbf{\boldmath$-$0.0156} & \textbf{18.24}\\ + &CE-mixture & 28.10 $\operatorname{s}$ & $-$0.0146 & 33.30\\ + \midrule + \multirow{3}{*}{1C} & CE-method & \textbf{0.052 $\operatorname{s}$} & $-$0.0065 & 43.14\\ + &CE-surrogate & 0.474 $\operatorname{s}$ & \textbf{\boldmath$-$0.0156} & \textbf{17.23}\\ + &CE-mixture & 2.57 $\operatorname{s}$ & $-$0.0146 & 22.17\\ + \midrule + \multirow{3}{*}{2} & CE-surrogate, $\operatorname{Uniform}$ & --- & \textbf{\boldmath$-$0.0193} & \textbf{8.53}\\ + &CE-surrogate, $\Geo(0.1)$ & {\color{gray}---} & $-$0.0115 & 25.35\\ + &CE-surrogate, $\Geo(0.2)$ & {\color{gray}---} & $-$0.0099 & 27.59\\ + &CE-surrogate, $\Geo(0.3)$ & {\color{gray}---} & $-$0.0089 & 30.88\\ + \bottomrule + & & & \multicolumn{2}{l}{$-\text{0.0220} \approx\vec{x}^*$}\\ + \end{tabular} +\end{table} + +An apparent benefit of the standard CE-method is in its simplicity and speed. +As shown in \cref{tab:results}, the CE-method is the fastest approach by about 2-3 orders of magnitude compared to CE-surrogate and CE-mixture. +The CE-mixture method is notably the slowest approach. +Although the runtime is also based on the objective function being tested, recall that we are using the same number of true objective function calls in each algorithm, and the metrics we are concerned with in optimization are to minimize $\bar{b}_v$ and $\bar{b}_d$. +We can see that the CE-surrogate method consistently out performs the other methods. +Surprisingly, a uniform evaluation schedule performs the best even in the sparse scenario where the initial mean is far away from the global optimal. + +\begin{figure}[!ht] + % \centering + \resizebox{0.9\columnwidth}{!}{\input{figures/cem_variants/experiment1b.tex}} + \caption{ + \label{fig:experiment_1b} + Average optimal value for experiment (1B) when the initial mean is far from the global minimum with a wide covariance. + } +\end{figure} + +When the initial mean of the input distribution is placed far away from the global optimal, the CE-method tends to converge prematurely as shown in \cref{fig:experiment_1b}. +This scenario is illustrated in \cref{fig:example_1b}. +We can see that both CE-surrogate and CE-mixture perform well in this case. + +\begin{figure}[!h] + \centering + \resizebox{0.7\columnwidth}{!}{\input{figures/cem_variants/example1b.pgf}} + \caption{ + \label{fig:example_1b} + First iteration of the scenario in experiment (1B) where the initial distribution is far away form the global optimal. The red dots indicate the true-elites, the black dots with white outlines indicate the ``non-elites'' evaluated from the true objective function, and the white dots with black outlines indicate the samples evaluated using the surrogate model. + } +\end{figure} + + + +\begin{figure}[!ht] + % \centering + \resizebox{0.9\columnwidth}{!}{\input{figures/cem_variants/experiment1c.tex}} + \caption{ + \label{fig:experiment_1c} + Average optimal value for experiment (1C) when we restrict the number of objective function calls. + } +\end{figure} + + +Given the same centered mean as before, when we restrict the number of objective function calls even further to just 50 we see interesting behavior. +Notice that the results of experiment (1C) shown in \cref{fig:experiment_1c} follow a curve closer to the far away mean from experiment (1B) than from the same setup as experiment (1A). Also notice that the CE-surrogate results cap out at iteration 9 due to the evaluation schedule front-loading the objective function calls, thus leaving none for the final iteration (while still maintaining the same total number of evaluations of 50). + + + + +\section{Conclusion} \label{sec:conclusion} +We presented variants of the popular cross-entropy method for optimization of objective functions with multiple local minima. +Using a Gaussian processes-based surrogate model, we can use the same number of true objective function evaluations and achieve better performance than the standard CE-method on average. +We also explored the use of a Gaussian mixture model to help find global minimum in multimodal objective functions. +We introduce a parameterized test objective function with a controllable global minimum and spread of local minima. +Using this test function, we showed that the CE-surrogate algorithm achieves the best performance relative to the standard CE-method, each using the same number of true objective function evaluations. + + +% \printbibliography \ No newline at end of file diff --git a/chapters/episodic_ast.tex b/chapters/episodic_ast.tex new file mode 100644 index 0000000..bb1bb24 --- /dev/null +++ b/chapters/episodic_ast.tex @@ -0,0 +1,603 @@ +% \begin{abstract} +% To find failure events and their likelihoods in flight-critical systems, we investigate the use of an advanced black-box stress testing approach called adaptive stress testing. +% We analyze a trajectory predictor from a developmental commercial flight management system which takes as input a collection of lateral waypoints and en-route environmental conditions. +% Our aim is to search for failure events relating to inconsistencies in the predicted lateral trajectories. +% The intention of this work is to find likely failures and report them back to the developers so they can address and potentially resolve shortcomings of the system before deployment. +% To improve search performance, this work extends the adaptive stress testing formulation to be applied more generally to sequential decision-making problems with episodic reward by collecting the state transitions during the search and evaluating at the end of the simulated rollout. +% We use a modified Monte Carlo tree search algorithm with progressive widening as our adversarial reinforcement learner. +% The performance is compared to direct Monte Carlo simulations and to the cross-entropy method as an alternative importance sampling baseline. +% The goal is to find potential problems otherwise not found by traditional requirements-based testing. +% Results indicate that our adaptive stress testing approach finds more failures and finds failures with higher likelihood relative to the baseline approaches. +% \end{abstract} + +% \begin{IEEEkeywords} +% cyber-physical systems, adaptive stress testing, black-box, Markov decision process, Monte Carlo tree search, flight management systems. +% \end{IEEEkeywords} + + +\section{Introduction} +\label{sec:introduction} + +A primary function of aircraft flight management systems (FMS) is to provide guidance in the form of navigational waypoints between origin and destination airports. +A trajectory predictor is the subsystem that provides trajectories to the guidance subsystem that commands the autopilot. +Failures within the trajectory prediction system can occur if the output waypoints are unreachable given the physical limitations of the aircraft, or if there are problems with the implementation or design of the software. % (e.g., edge cases leading to software crashes). +The goal of this work is to find likely failure cases before system deployment so that the engineers can resolve or address potential problems in the system. + +Traditionally, large-scale Monte Carlo testing is used to generate these failure cases \cite{monte_carlo}. However, Monte Carlo testing can be inadequate for large input spaces with rare failure events \cite{mc_limitations}. +We investigate the use of adaptive stress testing (AST), an advanced black-box stress testing approach that has been successfully applied to find failures in safety-critical systems \cite{ast_acasx,ast_av,lee2018differential,ast_safety}. Adaptive stress testing is a method that uses reinforcement learning to adversarially search for rare failure events in sequential decision-making systems \cite{lee_thesis}. This work applies the AST approach to trajectory prediction systems to efficiently find failure events and their likelihoods. + +The trajectory prediction system is treated as a black-box simulator and AST controls the selection of waypoints and other environmental input parameters. +Monte Carlo tree search (MCTS) with progressive widening is used to explore the possible trajectories and a notion of ``miss distance'' to a failure event is used to help guide the search. +Transition probabilities between states are also used to guide the search towards the most likely failures. +% +In traditional AST formulations, a sequential decision-making problem is assumed, but our open-looped trajectory predictor does not provide a sequence of decisions, but rather generates trajectories based on complete flight plans. +We regard each waypoint in the flight plan as a step in the sequence. +Although we can forcibly fit the problem to a strict sequential framework by calling the system with partial flight plans, this is prohibitively expensive and unnecessary. +Instead, we collect the intermediate states and actions and only evaluate the system at the end of a simulated rollout, then back-propagate the reward to unevaluated parts of the tree. +We can do this due to the structure of the AST reward function. +Therefore, this work extends the AST approach to be applied more generally to sequential decision-making problems with episodic reward (i.e. rewards accumulated at the end of an episode with intermediate rewards of zero). + + +We analyze a trajectory predictor from a developmental commercial FMS which takes as input winds aloft, origin and destination airports, and a collection the lateral waypoints. +The trajectory predictor outputs the discrete-time controls that determine translational motion which would be input to the FMS. +Within the FMS, the trajectories are passed to the guidance subsystem which determines how to command the autopilot. +Although we focus on arc length discrepancies as the primary failure mode (described in \Cref{sec:application}), this work can be easily extended to other failure events. +The performance of AST is compared to two baselines: direct Monte Carlo simulation and the cross-entropy method. +Current failure assessment is performed exhaustively over a navigational database of predefined aircraft routes defined by lateral waypoints. +This testing method is used during development while requirement-based testing is used for final system certification following RTCA DO-178C \cite{do178c}. +The intention of testing during development is to find failures otherwise not covered by requirements-based tests. +As a comparison of developmental testing approaches, we sample routes from the navigational database as another baseline to relate the simulation-based approach to the standard navigational database approach. +Experiments were run to generate likely failure events that are provided to the developers of the trajectory predictor to analyze and resolve potential shortcomings of the system. + + +% \section{Prior Work} \label{sec:prior_work} +AST has been successfully applied to safety-critical systems such as aircraft collision avoidance systems \cite{ast_acasx,lee2018differential} and autonomous vehicles \cite{ast_av}. +\citeauthor*{ast_traj_plan} applied AST to trajectory planning systems, but as will be discussed further in \Cref{sec:approach_ast}, that problem had access to the full FMS, thus fitting the model of traditional AST. +They looked at runtime behavior of the FMS on a simulated aircraft, where the disturbances were added as sensor noise. +In our work, we do not rely on simulating aircraft dynamics and use input waypoints as the disturbances. + +% TODO \citefull + +Other work has been proposed to efficiently search for failures in black-box cyber-physical systems \cite{corso2020survey}. \citeauthor*{trustworthy_ai} propose an importance sampling approach to find rare failure events to assess autonomous vehicle safety. +Their work is similar to AST but relies on an accurate importance distribution. +Other approaches formulate the problem of falsification as an optimization problem and solve it using Bayesian optimization \cite{bayes_opt}, simulated annealing \cite{abbas2013probabilistic,aerts2018temporal}, or rapidly-exploring random trees \cite{rrts}. +Each of these approaches are formulated as a classical optimization problem and use different techniques to search the input space for failures---although there is no likelihood estimation for a given falsifying input. +A different approach altogether uses an existing set of falsifying inputs to bootstrap the search for neighboring failures \cite{bootstrap}. +That work relies on existing counterexamples to base the neighboring search upon. +Our work addresses falsification of sequential systems with episodic reward and includes most likely failure analysis. + + + + +This paper is organized as follows. +% Section \ref{sec:prior_work} reviews prior work of safety-critical applications of AST and reviews alternative approaches to falsification of cyber-physical systems. +Section \ref{sec:background} provides necessary background of AST and commercial aircraft FMS. Section \ref{sec:approach} describes how this work extends existing AST approaches and modifications made to the MCTS algorithm. Section \ref{sec:implementation} details the implementation of this work using the Julia programming language and provides a description of the interface for AST to interact with black-box systems. Section \ref{sec:application} describes the simulation environment constructed for the FMS application and the failure events we are searching for. Section \ref{sec:experiments} describes the experiments and discusses the analysis of the results. Lastly, \Cref{sec:conclusion} provides a discussion on the conclusions from this work. + + + + +\section{Background} \label{sec:background} +This section describes background of the adaptive stress testing approach and flight management systems. + +\subsection{Adaptive Stress Testing} \label{sec:background_ast} +Adaptive stress testing (AST) is a black-box approach to find rare failure events in cyber-physical systems \cite{ast_acasx,lee2018adaptive}. +The AST problem is formulated as a Markov decision process (MDP) and can be solved using reinforcement learning algorithms to guide the search towards likely failure events. +AST can also be formulated more generally as other sequential decision-making processes, such as a partially observable Markov decision process (POMDP) \cite{ast_acasx,ast_av,ast_traj_plan}. + +% AST formulation (MDP) +\begin{figure}[!ht] +\centering +\resizebox{0.85\columnwidth}{!}{\input{diagrams/standard-ast-formulation.tex}} +\caption{Adaptive stress testing formulation.} +\label{fig:ast_mdp} +\end{figure} + +\Cref{fig:ast_mdp} illustrates how the AST concept is formulated. +The system under test is treated as a black box while the simulator $\mathcal{\bar{S}}$ is treated as a gray box that passes the transition probability $p$, event indicator $e$, miss distance $d$, and termination state indicator $\tau$ to the reward function. +The AST problem is solved using an adversarial reinforcement learner that selects a random number generator seed $\bar{a}$ to indirectly control the SUT through the simulator. +In other types of simulators, AST could directly control input disturbances rather than seeds. +In prior work, Monte Carlo tree search and deep reinforcement learning have been used to solve the MDP \cite{ast_acasx, ast_av}. +The output of the AST process is a set of state trajectories deterministically controlled by a set of seeds. +These seeds are used to deterministically playback the simulation starting from an initial state. + +A necessary clarification is differentiating what is black-box with respect to the AST problem. +Given that the simulator must provide $\langle p, e, d, \tau \rangle$ to the AST reward function, the output needs access to the transition probabilities $p$ and terminal indication $\tau$ from the environment, but can determine the event indication $e$ and miss distance $d$ from the output of the SUT. +Thus, depending on the problem, the environment may be required to be white-box but the SUT is strictly black-box. + + + + +The standard AST reward function is designed to guide the search towards failure events and to maximize the likelihoods of those events. It is also affected by the notion of miss distance $d$: a measure of ``closeness'' to a particular event. The miss distance helps guide the search towards failures to search efficiently. The standard reward function is given by: +\begin{equation}\label{eq:standard_reward} + R(p,e,d,\tau)=\begin{cases} + R_E & \text{if } \tau \wedge e \\ + -d & \text{if } \tau \wedge \neg e\\ + \log(p) & \text{otherwise} + % R(s,a,s^\prime)=\begin{cases} + % R_E & \text{if } s \in E \\ + % -d & \text{if } s \not\in E \wedge t \ge T \\ + % \log(p) & \text{if } s \not\in E \wedge t < T + \end{cases} +\end{equation} +The non-negative constant reward for finding an event is given by $R_E$ and is generally set to $0$. +The boolean $e$ indicates when an event has been found and the boolean $\tau$ indicates that the simulation is in a terminal state. +% The notation $e \in E$ is used to describe when an event $e$ has been found. +% The simulation is in a terminal state when the current time $t \ge T$, where $T$ is the maximum time allowed. +If the simulation terminates without finding an event, then the negative miss distance $-d$ is awarded to guide the search towards failure. +Otherwise, the log-likelihood of each state transition is used, denoted by $\log(p)$. +This term is used to maximize the likelihood of the overall trajectory and is designed to guide the search towards likely failures. +Recall that the goal of reinforcement learning is to maximize the expected sum of rewards \cite{sutton2018reinforcement}. +Using log-likelihood means we can maximize the summations, which is equivalent to maximizing the product of the likelihoods. + + + +\subsection{Flight Management Systems} +Aircraft flight management systems (FMS) have been a critical part in reducing workload of pilots in commercial aircraft by contributing to in-flight automation \cite{fms_workload}. +Major components of FMS include flight planning, navigation, guidance, performance optimization, and trajectory prediction \cite{fms}. +This work focuses on the subsystem of the FMS that generates the aircraft trajectory given a flight plan. +This subsystem, called the trajectory predictor, provides deterministic trajectories based on an operator-defined input flight plan and estimates of environmental conditions. +Inputs include winds aloft, origin and destination airports, aircraft weight, cost index (a balance between cost of fuel and time of arrival), and a set of navigational waypoints that define the lateral route. +For our purposes, we focus on the winds aloft, origin and destination airports, and the placement of the lateral waypoints. +The trajectory predictor outputs the discrete-time controls that determine translational motion (i.e. both vertical and horizontal motion) which become input to the guidance subsystem of the FMS. +The trajectories may be processed before being passed to the guidance in the cases where a change in the lateral or vertical trajectory needs to be anticipated and controlled towards. +Therefore, the trajectory predictor is not a strictly sequential decision-making problem because the full sequence of lateral paths are deterministically constructed based solely on the inputs. +The outputs of the trajectory predictor are illustrated in \Cref{fig:lateral_packets}. + +\begin{figure*}[!t] +% Lateral packet diagram +\centering +\resizebox{0.78\textwidth}{!}{\input{diagrams/lateral-packet.tex}} +\caption{Lateral packets output by the trajectory predictor. Lateral packets consist of latitude and longitude points that describe straight line segments $\ell_i$ and turning arc segments starting at $s_i$. Straight segments are optional which can result in multiple turn segments sequenced together, as seen at $s_3$ and $s_4$.} +\label{fig:lateral_packets} +\end{figure*} + + + +\section{Approach} +\label{sec:approach} + +Several modifications were made to adapt AST for sequential decision-making systems with episodic reward. +Modifications to the standard reward function were made to guide the search towards severe failures as well as likely failures. +Modifications to the Monte Carlo tree search algorithm are also described; adapting the search algorithm for efficient SUT evaluations and to use progressive widening with a single deterministic next state.% (given the nature of controlling seeds). + + +\subsection{Adaptive Stress Testing for Episodic Reward Problems} \label{sec:approach_ast} + +% Modified AST formulation (MDP) +\begin{figure*}[!b] + \centering + \resizebox{0.95\textwidth}{!}{\input{diagrams/ast-formulation.tex}} + \caption{ + \label{fig:ast_mdp_modified} + Modified adaptive stress testing formulation for the trajectory predictor with episodic reward. The simulation environment samples waypoints from a distribution and passes those waypoints as input to the SUT at the end of the rollout. + The modified reward function is guided by both the severity and likelihood of the failure event. Information on the dashed lines is only provided to the reward function when the SUT is evaluated. + } +\end{figure*} + +Traditionally, AST is used to steer sequential decision-making systems towards likely failures by controlling the seed used to sample environmental variables within the simulator at each time step (as seen in \Cref{fig:ast_mdp}). +The issue with applying this formulation directly to the trajectory predictor is that this system does not rely on sequential feedback to generate the trajectory and solely relies on its set of inputs. +Therefore, we propose a modification to the AST formulation to abstract the sequential nature of the problem to the simulation environment. +In other words, we collect the state transitions during the search and evaluate the system at the end of the rollout. +This distinction can be seen in \Cref{fig:ast_mdp_modified}. +The transition probability $p$ is output from the environment and the event indication $e$, miss distance $d$, and terminal state indication $\tau$ are output from the black-box SUT, i.e. the trajectory predictor. +% The terminal state indication $\tau$ can be determined either by the simulation environment or the SUT, depending on the application. +The 4-tuple $\langle p, e, d, \tau \rangle$ is passed as input to the reward function and the transition probability $p$ and miss distance $d$ are used to guide the search. + + +The standard AST reward function described in \Cref{eq:standard_reward} was modified to collect all rewards at the termination state and to incorporate a severity measurement when a failure event occurs. +Both the log-likelihood and miss distance $d$ are used throughout the search. +A multiplicative bonus $R_E$ is applied when a failure event occurs and we set $R_E=100$ for our experiments. +The modified reward function becomes: +\begin{equation}\label{eq:modified_reward} + R(p,e,d,\tau) = \begin{cases} + (\log(p) - d)R_E & \text{if } \tau \wedge e \\ + \log(p) - d & \text{if } \tau \wedge \neg e \\ + 0 & \text{otherwise} + \end{cases} +\end{equation} +The transition probability $p$ is given by the probability of sampling a set of waypoints from a multivariate Gaussian distribution $\vec{w} \overset{\bar{a}}{\sim} \Normal(\vec{\mu},\mat{\Sigma})$ composed of waypoint direction and distance (relative to the previous waypoint) and wind direction and magnitude with mean vector $\vec\mu$ and covariance $\mat\Sigma$, deterministically controlled by the seed $\bar{a}$. +If an event is found, then the reward is the negative miss distance combined with the log-likelihood and adjusted by the multiplicative bonus $R_E$. +This modification is used to incorporate severity of an event gauged by the miss distance when an event is found. +If the simulation terminates without finding an event, no multiplicative bonus is applied. +This reward function may not be suitable for certain AST problem formulations, but in \Cref{sec:application} we discuss how these modifications are applicable for the failure event and miss distance we investigate. + + +% MCTS algorithm pseudocode +\subsection{Modified Monte Carlo Tree Search} \label{sec:mcts} +Monte Carlo tree search (MCTS) is an anytime algorithm that uses rollouts of a random policy to estimate the value of each state-action node in the tree \cite{coulom2006efficient,dmubook}. +MCTS has found success in recent years in the reinforcement learning field, notably playing games such as Go \cite{silver2016mastering}. +There are four main stages in each simulation: \textit{selection}, \textit{expansion}, \textit{rollout} (or \textit{simulation}), and \textit{backpropagation}. +\Cref{fig:mcts} illustrates these four steps. +The algorithm is ``anytime'' because a policy can be constructed after any single iteration, but the state-action value estimates become increasingly accurate as more simulations are performed and the tree depth is expanded. +The tree $\mathcal{T}$ is iteratively expanded and the policy improves over time as the algorithm balances exploration with exploitation of the state and action spaces. + +% MCTS 4-step figure +\begin{figure*}[!t] +\centering +\resizebox{\textwidth}{!}{\input{diagrams/mcts-diagram.tex}} +\caption{The four steps of the Monte Carlo tree search algorithm.} +\label{fig:mcts} +\end{figure*} + +% MCTS-PW figure +% \begin{wrapfigure}{r}{0.4\textwidth} +\begin{figure}[!b] +\centering +\resizebox{0.5\textwidth}{!}{\input{diagrams/mcts-pw.tex}} +\caption{MCTS-PW with a single deterministic state and system evaluations at the end of the rollout.} +\label{fig:mcts_pw} +% \end{wrapfigure} +\end{figure} +A commonly used extension of MCTS for large or continuous spaces is progressive widening (PW) \cite{chaslot2007progressive,mcts_ucb,ll_wildfire,mcts_wildfire}. +% We apply PW on the action space of seeds, because the seed forces deterministic state transitions. +We apply PW on the action space of seeds because there are an infinite number of seeds. +There is no need to apply PW to the state transitions, since a seed uniquely determines the next state. +This notion can be seen in \Cref{fig:mcts_pw} where each action $\bar{a}_i$ leads to a single deterministic state $s_j$ as its child node. +The states are deterministically sampled from the generative model $G$ given the current state and action. +We define the state $s$ as a collection of all preceding actions deterministically leading to that point in the simulation. +Note that because the state $s$ is a sequence of seeds that uniquely determines the state of the simulator $\bar{S}$, we may overload the notation when calling $\smallcaps{Evaluate}$ and $\smallcaps{IsTerminal}$ for convenience. +In our formulation, the generative model samples state transitions and does not evaluate the underlying system (unlike standard MCTS). +This difference is in \Cref{alg:mcts-pw-rollout}, $\smallcaps{Rollout}$, where new state transitions are generated during the rollout and the system is only evaluated at the end. +By default, actions are uniformly selected from a random policy. +However, to encourage exploration of promising actions, the current best action $\bar{a}^*$ is used mid-rollout. +The best action is updated at the end of the rollout based on updated $Q$-values. + + +These modifications were made to MCTS-PW specifically for episodic reward problems. +The evaluation of our SUT is expensive so we limit the evaluations to the end of the rollout (rather than at node creation and throughout the rollout). +This way, we can reduce the number of external system executions but still provide the search with information during tree expansion, namely using back-propagated values of the transition probabilities and the miss distance from previously finished rollouts. +Choosing to evaluate at the end of the rollout provides the SUT with an expanded set of waypoints which it evaluates once the rollout has reached its maximum depth. +Generally for AST problem formulations, the discount factor $\gamma$ is set to $1$. +Algorithm \ref{alg:mcts-pw} is the entry point of MCTS-PW. + +\input{algorithms/mcts-pw-algorithm.tex} +\input{algorithms/mcts-pw-algorithm-part2.tex} + + +\section{Implementation} +\label{sec:implementation} +The AST implementation was written in the Julia programming language \cite{julia}. +% Julia is an open-source, high-level, dynamically-typed, scientific computing language that can achieve speeds comparable to C \cite{julia}. +Implementation of the simulation environment around the SUT was also written in Julia, but this section will focus on the algorithms required for AST and MCTS-PW. +Modifications to MCTS were implemented and merged into the existing MCTS.jl\footnote{\url{https://github.com/JuliaPOMDP/MCTS.jl}} Julia package. + + +\subsection{Interface}\label{sec:implementation_interface} +To apply AST to a general black-box system, a user has to provide the interface defined in \Cref{tab:interface}. +% +The simulation object $\bar{\mathcal{S}}$ is the user-defined data structure that holds parameters for their simulation. +All of the following functions take the simulation object $\bar{\mathcal{S}}$ as input and can modify the object in place. +The {\sc Initialize} function resets the simulation and the SUT to an initial state. +The {\sc Evaluate} function executes the SUT and returns the transition probability $p$, a boolean indicating an event occurred $e$, and the miss distance $d$. +% Three subroutines determine these output values: {\sc Transition} returns the transition probability $p$, {\sc MissDistance} returns the miss distance $d$, and {\sc IsEvent} returns the event indication $e$ (where all three subroutines are used by the {\sc Evaluate} function, but may also be called individually). +Three subroutines determine these output values: {\sc Transition}, {\sc MissDistance}, and {\sc IsEvent} (where all three subroutines are used by the {\sc Evaluate} function, but may also be called individually). +Finally, the {\sc IsTerminal} function returns a boolean $\tau$ to indicate if the simulation is in a terminal state. + +% Interface definition +\begin{table}[!h] + \centering + \caption{\label{tab:interface} Adaptive Stress Testing Interface} + \begin{threeparttable} + \begin{tabular}{@{}p{6cm}l@{}} % wrap with @{} to remove spaces. + \toprule + \textbf{Function} & \textbf{$\bm{\text{Input}\mapsto\text{Output}}$} \\ + \midrule + \textsc{Initialize} & $\bar{S} \mapsto \emptyset$ \\ + \textsc{Evaluate} & $\bar{S} \mapsto \langle p, e, d \rangle$ \\ + $\quad$\textsc{Transition} & $\bar{S} \mapsto p \in \mathbb{R}$ \\ + $\quad$\textsc{MissDistance} & $\bar{S} \mapsto d \in \mathbb{R}$ \\ + $\quad$\textsc{IsEvent} & $\bar{S} \mapsto e \in \mathbb{B}$ \\ + \textsc{IsTerminal} & $\bar{S} \mapsto \tau \in \mathbb{B}$ \\ + \bottomrule + \end{tabular} + \end{threeparttable} +\end{table} + + +As an example, the functions in the above interface can either be implemented directly in Julia or can call out to C++, Python, MATLAB\textsuperscript{\textregistered} or run an executable on the command line. Typically, implementing the {\sc MissDistance} and {\sc IsEvent} functions rely solely on the output of the SUT, thus keeping in accordance with the black-box formulation. + +% TODO. POMDPStressTesting.jl transferred to github.com/sisl + +\subsection{Stress Testing Julia Framework} +We have implemented the AST interface written in Julia as part of a new package called POMDPStressTesting.jl.\footnote{\url{https://github.com/sisl/POMDPStressTesting.jl}} +This package is inspired by work originally done in the AdaptiveStressTesting.jl\footnote{\url{https://github.com/sisl/AdaptiveStressTesting.jl}} package, but POMDPStressTesting.jl adheres to the \texttt{MDP} interface defined by the POMDPs.jl\footnote{\url{https://github.com/JuliaPOMDP/POMDPs.jl}} package \cite{pomdps_jl}. +Thus, POMDPStressTesting.jl fits into the POMDPs.jl ecosystem, which is why it can use the MCTS.jl package as an off-the-shelf solver. +This design choice allows other Julia packages within the POMDPs.jl ecosystem to be used; this includes solvers, simulation tools, policies, and visualizations. + + +The intention of the POMDPStressTesting.jl package is to provide the user with a virtual black-box interface they must define, and provide the necessary AST algorithms to run the search. Future modifications will focus on inclusion of benchmark falsification problems from the literature \cite{arch_comp}. + + + +\section{Application} +\label{sec:application} + +The primary goal of this work is applying the modified AST formulation to a trajectory predictor in a developmental commercial FMS. +The following sections will describe the input and output specification of the trajectory predictor and detail the investigated failure event and the associated miss distance. +We will also describe the simulation environment constructed to run the SUT. + + + + +\subsection{Trajectory Predictor} +The inputs of the trajectory predictor controlled by AST are the origin and destination airports, a set of intermediate waypoints, and the wind direction and magnitude at each waypoint. +The output of the trajectory predictor is a detailed flight path which provides predicted vertical data, predicted lateral data (i.e. lateral packets, illustrated in \Cref{fig:lateral_packets}), and other flight path information currently unused in this application. +The following failure event and miss distance is calculated by parsing the SUT output after each evaluation. + + +% \input{failure-tangency-kink} % Non-DASC + + +\begin{figure}[!hb] +\centering +\resizebox{0.6\columnwidth}{!}{\input{diagrams/arc-length.tex}} +\caption{Arc length $\beta$ and calculated arc length $\alpha r$, showing a failure in red.} +\label{fig:arc_length} +\end{figure} + +\subsubsection{Arc Length Failure} +Arc length is defined as the distance traveled across the arc from the starting point $s$ and ending point $e$, shown in \Cref{fig:arc_length}. +Failures can arise when the arc length $\beta$ does not agree with the arc length computed using the angular extent $\alpha$ and arc radius $r$. +Angular extent is computed as +% \vspace{-2mm} +\begin{equation} + \alpha = \sign(r) \cdot |z_s - z_e| + 2\pi +\end{equation} +where $z_s$ is the azimuth from the center waypoint $c$ to the starting waypoint $s$, and $z_e$ is the azimuth from the center waypoint $c$ to the ending waypoint $e$. +The sign of $r$ determines the turn direction, where negative values represent left turns. +A failure occurs when the calculated difference $\abs{\beta - \alpha r}$ is above the threshold $h=10$ \si{ft}. + + + +The arc length miss distance is how close the arc length difference comes to the threshold $h$. +We transform this difference by scaling the log-ratio of the threshold $h$ and the maximum miss distance from that trajectory. +This way, non-positive values indicate an event. +Namely, we define miss distance to be: +\begin{equation} \label{eq:miss} + d = \rho\log\left(\frac{h}{\max\,\abs{\beta - \alpha r}}\right) +\end{equation} +We use a scale of $\rho=100$ to match the expected range of the log-likelihood in our problem so that the log-likelihood does not dominate the miss distance in the reward function. + +% \input{failure-disconnection} % Non-DASC +% \input{failure-course-direction} % Non-DASC + +\subsection{Simulation Environment} +A simulator was constructed to sample waypoint trajectories and evaluate the SUT. +Starting from an origin airport, waypoints were sampled from a multivariate Gaussian distribution of independent normals that encodes waypoint direction and distance (relative to the previous waypoint) and wind direction and magnitude, deterministically controlled by the seed $\bar{a}$: +\begin{equation} + \vec{w} \overset{\bar{a}}{\sim} \Normal(\vec{\mu}, \vec{\Sigma}) +\end{equation} +Mean and variance values for the waypoint direction and distance were set by a domain expert and the values for winds aloft were learned from observational weather data. +\begin{gather*} +\vec{\mu} = \left[180\,\si{\degree},\; 50\,\si{nmi},\; -88.5\si{\degree},\; 66.8\,\si{kts}\right]\\ +\mat{\Sigma} = \begin{bmatrix} +45\si{\degree} & 0 & 0 & 0\\ +0 & 30\,\si{nmi} & 0 & 0\\ +0 & 0 & 39.5\si{\degree} & 0\\ +0 & 0 & 0 & 24.4\,\si{kts} +\end{bmatrix} +\end{gather*} + +The simulator implements the interface defined in \Cref{sec:implementation_interface} for the trajectory predictor. +The failure event and miss distance calculations described in \Cref{sec:application} were also implemented within the simulator. + +\subsection{Navigational Database} +In addition to the simulator, we have access to a navigational database of aircraft routing procedures. +The routes are encoded as collections of waypoints describing departure, arrival, and en-route airways. +Exhaustively searching all combinations of the waypoints in the navigational database is the current approach to finding failures during development. +We employ the navigational database as a baseline by sampling the same allotted number of SUT evaluations to assess the miss distance distribution and search for failures. + + + +\section{Experiments} +\label{sec:experiments} +Experiments were run to test the AST approach using MCTS-PW against direct Monte Carlo (MC) simulations as a na\"ive baseline and the cross-entropy method as an importance sampling baseline. +We also perform Monte Carlo sampling over the routes in the navigational database as another baseline. +Algorithm \ref{alg:mc} describes the direct Monte Carlo simulation approach for $n$ episodes, starting at an initial state $s_0$, with a rollout depth $d$. Note the rollout function does not use the action feeding procedure described in \Cref{sec:mcts}. + +\input{algorithms/monte-carlo-algorithm.tex} + + + +The cross-entropy method (CEM) is a probabilistic optimization technique that iteratively fits an initial distribution to elite samples \cite{rubinstein1999cross,rubinstein2004cross}. +The method uses importance sampling, which introduces a proposal distribution over rare events to sample from then re-weights the posterior likelihood by the \textit{likelihood ratio} of the true distribution ($\vec w$ in our case) over the proposal distribution. +The idea is to artificially make failure events less rare under the newly fit proposal distribution. +We set the proposal distribution to be the same as the true distribution $\vec w$, with the exception that the waypoint distance was reduced to $\mu=1\,\si{nmi}$ and $\sigma=3\,\si{nmi}$ to encourage smaller distances between the waypoints. + + + +For the experiments, the San Francisco International Airport (KSFO) was used as an origin airport and the Los Angeles International Airport (KLAX) was used as a destination airport. +Comparisons were run to assess the effectiveness of AST against CEM and direct MC in finding high-likely severe failure events. +Metrics include the number of failure events found $N_E$, iteration of first failure $i_{FF}$, and statistics about the miss distance. +We also report the mean log-likelihood of failures found by each algorithm relative to the mean log-likelihood of failures found by the direct MC approach. +For a given algorithm, this is computed as: +\begin{equation} + \operatorname{rel-log}(p) = \frac{\log(p_{\text{alg}})}{\log(p_\text{MC})} +\end{equation} +Values larger than one indicate a higher relative likelihood. +% + +\begin{table}[!ht] + \centering + \caption{\label{tab:mcts_params} Algorithm Hyperparameters} + \begin{threeparttable} + \begin{tabular}{@{}p{10cm}r@{}} + \toprule + \textbf{Hyperparameter} & \textbf{Value} \\ + \midrule + episodes \tnote{*} & $5000$ \\ + maximum tree depth $d_\text{max}$ (i.e. number of waypoints) \tnote{*} & $12$ \\ + rollout depth $d$ \tnote{$\dagger$} & $12$ \\ + exploration constant $c$ & $10$ \\ + progressive widening $k$ & $10$ \\ + progressive widening $\alpha$ & $0.3$ \\ + \bottomrule + \end{tabular} + \begin{tablenotes} + \item[*] {Used by all algorithms.} + \item[$\dagger$] {Used by MCTS and direct Monte Carlo.} + \end{tablenotes} + \end{threeparttable} +\end{table} + + +All experiments were run with the MCTS hyperparameters listed in \Cref{tab:mcts_params}. +Sensitivity analysis of the various hyperparameter values has been omitted from this paper for brevity. +When controlling the parameters for progressive widening, to encourage widening let $k \to \infty$ and $\alpha \to 1$. To discourage widening, let $k \to 1$ and $\alpha \to 0$. + + +\subsection{Results and Analysis} + +We first look at the performance of each approach over all episodes. +An initial seed is set across each experiment and we run each algorithm for 5000 episodes. +For each of these approaches, the number of episodes also corresponds to the number of SUT evaluation calls. + +\begin{figure}[!ht] +\centering +\resizebox{0.8\columnwidth}{!}{\input{figures/episodic_ast/episode-figures.pgf}} +\caption{Running miss distance mean, minimum miss distance, and log-scaled cumulative number of failure events across episodes. One standard deviation is reported in the shaded regions.} +\label{fig:episodes} +\end{figure} + +The first two plots in \Cref{fig:episodes} show the running mean and minimum miss distance over each episode. +Notice that the direct Monte Carlo approach applied to the navigational database baseline converges quickly to a minimum miss distance that remains above the rest, and a running mean that only outperforms the CEM approach. +% +Evident from \Cref{fig:episodes} is the initial behavior that MCTS and direct Monte Carlo share. +Recall that MCTS balances exploration and exploitation, and initially acts similar to direct Monte Carlo. +This similarity is based on the choice of exploration hyperparameters and the miss distance in the reward function. +This behavior suggests that the miss distance for this problem is a noisy measurement of the actual distance to a failure event. +At about episode 500, the MCTS approach starts to exploit found failures which can be seen as the descent of the running mean passing the origin (i.e. the event horizon). + + +One goal of the AST approach using MCTS is to exploit known failures to maximize their likelihood. +The bottom plot in \Cref{fig:episodes} shows the cumulative number of failure events which highlights this behavior. +Notice that each approach finds failures relatively early in the search, suggesting that failure events may be common given the choice of simulation environment. + + +\begin{figure}[ht!] +\centering +\resizebox{0.79\columnwidth}{!}{\input{figures/episodic_ast/distribution-figures.pgf}} +\caption{Distribution of negative miss distances for all episodes (where values to the right of the origin are events) and distribution of log-likelihoods filtered by failure events.} +\label{fig:distributions} +\end{figure} + +We are also interested in the distribution of the miss distances collected from each approach. +Recall that the miss distance $d$ is a transformation of the arc length discrepancy relative to a threshold, detailed in \Cref{eq:miss}. +Thus, the value for $d$ is unitless and non-positive values indicate an event. +The top plot of \Cref{fig:distributions} shows the miss distance distributions, indicating the event horizon at the origin. +The miss distance distribution from the navigational database is used as a proxy for miss distance distributions we would expect in the real-world. +The CEM approach converges to a local minima and stays there, which is evident in the concentration of the CEM miss distance distribution. +MCTS and the direct MC approach share similar distributions to the left of the event horizon (indicating non-failure events), further suggesting that the miss distance is a noisy measurement of the true distance to a failure. +The spike to the right of the origin is the distribution of failure events found by our AST approach using MCTS. +The bottom plot in \Cref{fig:distributions} shows the distribution of log-likelihoods filtered for the failure events, suggesting that AST finds failures with higher likelihood than the CEM approach. + + + +The collected aggregate results are shown in \Cref{tab:results}. +AST finds failures with relative likelihood about an order of magnitude greater than that of direct Monte Carlo. +The CEM approach finds a small number of failures with very low relative likelihood. +This is because CEM is using importance sampling and after re-weighting the samples using the true distribution, we would expect to get these extremely small likelihood values. +% This emphasizes the case of CEM strictly for falsification and not for most likely failure analysis. +AST has the lowest mean miss distance $\bar{X}_d$, noting the large standard deviation which is a result of large differences between miss distances from failure and non-failure events. +Each approach finds their first failure early in the experiment, with AST finding failures the earliest. +The effect of feeding the best action midway through the rollout accelerates finding these failures. +Once found, AST will exploit the failures to maximize their likelihood. +We see that AST finds failures in about $88\%$ of episodes (i.e. system executions), where as standard MC and CEM find failures in about $0.1\%$ and $0.48\%$ of episodes, respectively. +% This suggests that these failures can be found randomly, but AST will try to exploit the failures to maximize their likelihood. + + + + +\begin{table}[!ht] + \centering + \caption{\label{tab:results} Experimental Results} + \begin{threeparttable} + \begin{tabular}{@{}lrrrrr@{}} + \toprule + Algorithm\tnote{*} & $N_E$ & $i_{FF}$ & $\bar{X}_d$ & $\min(d)$ & $\operatorname{rel-log}(p)$\tnote{$\dagger$}\\ + \midrule + $\text{MC}_\text{NavDB}$ & $0$ & --- & $560.21 \pm75.09$ & $410.98$ & ---\\ + MC & $5$ & $128$ & $407.44 \pm64.85$ & $-1127.7$ & $1.0$\\ + CEM & $24$ & $249$ & $625.65 \pm97.80$ & $-1077.3$ & $4.5\times 10^{-161}$\\ + $\text{AST}_\text{MCTS}$ & $\bm{4394}$ & $\bm{61}$ & $\bm{-923.49 \pm497.4}$ & $\bm{-1147.9}$ & $\bm{13.1}$\\ + \bottomrule + \end{tabular} + \begin{tablenotes} + \item[*] {Hyperparameters listed in \Cref{tab:mcts_params}.} + \item[$\dagger$] {Mean log-likelihood relative to direct Monte Carlo.} + \end{tablenotes} + \end{threeparttable} +\end{table} + + + + +\subsection{Example Failure} +Many of the failures are a result of two duplicate waypoints being generated in sequence. +Based on the defined environmental distributions, this is possible, but unlikely. +We observed that duplicate waypoints do not always cause failures and that certain assemblages of neighboring waypoints affect whether a failure is caused by the duplicates. +Despite failures arising from these duplicate waypoints, certain failures found only by AST have waypoints close in range to each other---not necessarily identical---which can also result in arc length failures. +\Cref{fig:example_failure} shows an example failure trajectory and \Cref{fig:example_failure_zoomed} zooms in on the specific arc length failure. +Refer to the figure captions for further descriptions. +A set of failure trajectories was generated and provided to the engineers of the trajectory predictor. +These failures are encoded in input files than can be deterministically played back through the system. + + +\begin{figure}[t!] +\noindent\makebox[\columnwidth][c]{% +\begin{minipage}{1.25\columnwidth} +\centering +\resizebox{0.55\columnwidth}{!}{\input{figures/episodic_ast/dasc-failure.pgf}} +\end{minipage}} +\caption{Full trajectory of an example arc length failure originating from KSFO. Red diamonds indicate the input waypoints selected by MCTS and the yellow circles indicate the output lateral packets from the SUT. The red box shows where the failure occurs, shown in more detail in \Cref{fig:example_failure_zoomed}.} +\label{fig:example_failure} +\end{figure} + +\begin{figure}[b!] +\noindent\makebox[\columnwidth][c]{% +\begin{minipage}{1.25\columnwidth} +\centering +\resizebox{0.55\columnwidth}{!}{\input{figures/episodic_ast/dasc-failure-zoomed.pgf}} +\end{minipage}} +\caption{Example arc length failure, zoomed in from \Cref{fig:example_failure}. Notice two almost identical red waypoint diamonds, which are separated by about 0.08 \si{nmi} or about 486 \si{ft} (zoom in further for more detail). The arc length failure is shown as the extending arc after the center yellow waypoint, which extends about 3 \si{nmi} past its intended end waypoint. This extension is the negative miss distance.} +\label{fig:example_failure_zoomed} +\end{figure} + +% \section{Future Work} +% \label{sec:future_work} +% Incorporating a search over origin/destination airports, winds aloft, aircraft weight, and cost index will be explored. +% Updates to the developmental trajectory predictor will need to be made for these inputs to be registered. +% An extension of this work would include failure events for predicted altitude constraints. +% An interesting research question to be explored is how to incorporate the notion of multi-event search balancing into a single search. +% Standard AST can be applied to the full FMS as well, without having to target the trajectory predictor itself, similar to work done previously \cite{ast_traj_plan}. + + + +Due to the nature of exploiting known failures, certain failure cases may only have minor differences between them. +To assess the impact of the trajectory predictor failures on broader flight operations, each failure case would have to be evaluated on the full FMS in simulation. +This would include modeling aircraft dynamics, guidance systems, and control feedback. +Full assessment of the trajectory predictor failures would help inform the system developers in their decision to mitigate issues before deployment. +Further extensions of this work include searching for other failure events and stress testing other components of the FMS. + + +\pagebreak + + +\section{Conclusion} +\label{sec:conclusion} +Adaptive stress testing was extended for sequential systems with episodic reward to find likely failures in FMS trajectory predictors. +To improve search performance, we used Monte Carlo tree search with progressive widening and modified the rollout with end-of-depth evaluations. +We feed the best action midway through the rollout to encourage exploration of promising actions, resulting in exploiting failures to maximize their likelihood. +A simulation environment was constructed to evaluate the trajectory predictor, and a navigational database was sampled to compare to existing methods of finding failures during development. +Performance of AST using MCTS-PW was compared against direct Monte Carlo simulations and the cross-entropy method. +Results suggest that the AST approach finds more failures with both higher severity and higher relative likelihood. +The failure cases are provided to the system engineers to address unwanted behaviors before system deployment. +In addition to requirements-based tests, we show that AST can be used for confidence testing during development. + + +\section*{Acknowledgments} +The authors would like to thank GE's Global Research Center and GE Aviation for supporting this work through the Stanford Center for AI Safety. +We also thank the NASA AOSP System-Wide Safety Project for partially supporting this work. +The authors will also like to thank Nicholas Visser and Joachim Hochwarth for their contributions. +We thank Anthony Corso and Mark Koren for their feedback and the Stanford Intelligent Systems Laboratory for their development of the POMDPs.jl ecosystem and the MCTS.jl package. +We would also like to thank Mark Darnell, Scott Edwards, and Andrew Foster for their technical support. diff --git a/chapters/introduction.tex b/chapters/introduction.tex new file mode 100644 index 0000000..2c42f58 --- /dev/null +++ b/chapters/introduction.tex @@ -0,0 +1,6 @@ + +\subsection{Motivation} + +\subsection{Black-Box Systems Definition} + +\subsection{Safety-Critical Applications} diff --git a/chapters/pomdpstresstesting.tex b/chapters/pomdpstresstesting.tex new file mode 100644 index 0000000..d80b497 --- /dev/null +++ b/chapters/pomdpstresstesting.tex @@ -0,0 +1,64 @@ +\section{Summary} + +\href{https://github.com/sisl/POMDPStressTesting.jl}{POMDPStressTesting.jl} is a package that uses reinforcement learning and stochastic optimization to find likely failures in black-box systems through a technique called adaptive stress testing \cite{ast}. +Adaptive stress testing (AST) has been used to find failures in safety-critical systems such as aircraft collision avoidance systems \cite{ast_acasx}, flight management systems \cite{ast_fms}, and autonomous vehicles \cite{ast_av}. +The POMDPStressTesting.jl package is written in Julia \cite{julia} and is part of the wider POMDPs.jl ecosystem \cite{pomdps_jl}, which provides access to simulation tools, policies, visualizations, and---most importantly---solvers. +We provide different solver variants including online planning algorithms such as Monte Carlo tree search \cite{mcts} and deep reinforcement learning algorithms such as trust region policy optimization (TRPO) \cite{trpo} and proximal policy optimization (PPO) \cite{ppo}. +Stochastic optimization solvers such as the cross-entropy method \cite{cem} are also available and random search is provided as a baseline. +Additional solvers can easily be added by adhering to the POMDPs.jl interface. + +\begin{lstlisting}[language=Julia] +# GrayBox simulator and environment +abstract type GrayBox.Simulation end +function GrayBox.environment(sim::Simulation)::GrayBox.Environment end +function GrayBox.transition!(sim::Simulation)::Real end + +# BlackBox.interface(input::InputType)::OutputType +function BlackBox.initialize!(sim::Simulation)::Nothing end +function BlackBox.evaluate!(sim::Simulation)::Tuple{Real, Real, Bool} end +function BlackBox.distance(sim::Simulation)::Real end +function BlackBox.isevent(sim::Simulation)::Bool end +function BlackBox.isterminal(sim::Simulation)::Bool end +\end{lstlisting} + +The AST formulation treats the falsification problem (i.e. finding failures) as a Markov decision process (MDP) with a reward function that uses a measure of distance to a failure event to guide the search towards failure. +The reward function also uses the state transition probabilities to guide towards \textit{likely} failures. +Reinforcement learning aims to maximize the discounted sum of expected rewards, therefore maximizing the sum of log-likelihoods is equivalent to maximizing the likelihood of a trajectory. +A gray-box simulation environment steps the simulation and outputs the state transition probabilities, and the black-box system under test is evaluated in the simulator and outputs an event indication and the real-valued distance metric (i.e. how close we are to failure). +To apply AST to a general black-box system, a user has to implement the following Julia interface: + +% NOTE: Interface WAS here. + +Our package builds off work originally done in the AdaptiveStressTesting.jl package \cite{ast}, but POMDPStressTesting.jl adheres to the interface defined by POMDPs.jl and provides different action modes and solver types. +Related falsification tools (i.e. tools that do not include most-likely failure analysis) are \textsc{S-TaLiRo} \cite{staliro}, Breach \cite{breach}, and \textsc{FalStar} \cite{falstar}. +These packages use a combination of optimization, path planning, and reinforcement learning techniques to solve the falsification problem. +The tool most closely related to POMDPStressTesting.jl is the AST Toolbox in Python \cite{ast_av}, which wraps around the gym reinforcement learning environment \cite{gym}. +The author has contributed to the AST Toolbox and found the need to create a similar package in pure Julia for better performance and to interface with the POMDPs.jl ecosystem. + + +\section{Statement of Need} + +Validating autonomous systems is a crucial requirement before their deployment into real-world environments. +Searching for likely failures using automated tools enable engineers to address potential problems during development. +Because many autonomous systems are in environments with rare failure events, it is especially important to incorporate likelihood of failure within the search to help inform the potential problem mitigation. +This tool provides a simple interface for general black-box systems to fit into the adaptive stress testing problem formulation and gain access to solvers. +Due to varying simulation environment complexities, random seeds can be used as the AST action when the user does not have direct access to the environmental probability distributions or when the environment is complex. +Alternatively, directly sampling from the distributions allows for finer control over the search. +The interface is designed to easily extend to other autonomous system applications and explicitly separating the simulation environment from the system under test allows for wider validation of complex black-box systems. + + + +\section{Research and Industrial Usage} + +POMDPStressTesting.jl has been used to find likely failures in aircraft trajectory prediction systems \cite{ast_fms}, which are flight-critical subsystems used to aid in-flight automation. +A developmental commercial flight management system was stress tested so the system engineers could mitigate potential issues before system deployment \cite{ast_fms}. +In addition to traditional requirements-based testing for avionics certification \cite{do178c}, this work is being used to find potential problems during development. +There is also ongoing research on the use of POMDPStressTesting.jl for assessing the risk of autonomous vehicles and determining failure scenarios of autonomous lunar rovers. + + +\section{Acknowledgments} + +We acknowledge Ritchie Lee for his guidance and original work on adaptive stress testing and the AdaptiveStressTesting.jl package and Mark Koren, Xiaobai Ma, and Anthony Corso for their work on the AST Toolbox Python package and the CrossEntropyMethod.jl package. +We also acknowledge Shreyas Kowshik for his initial implementation of the TRPO and PPO algorithms in Julia. +We want to thank the Stanford Intelligent Systems Laboratory for their development of the POMDPs.jl ecosystem and the MCTS.jl package; particular thanks to Zachary Sunberg. +We also want to thank Mykel J. Kochenderfer for his support and research input and for advancing the Julia community. diff --git a/chapters/weakness_rec.tex b/chapters/weakness_rec.tex new file mode 100644 index 0000000..1b254e8 --- /dev/null +++ b/chapters/weakness_rec.tex @@ -0,0 +1,330 @@ +% \title{Adversarial Weakness Recognition\\ for Efficient Black-Box Validation} + +% \begin{abstract} +% When validating a black-box system, exhaustively evaluating over the entire validation dataset may be computationally intractable. +% The challenge then becomes to intelligently automate selective validation given knowledge of the system failures experienced so far. +% We propose an adaptive black-box validation framework that will learn system weaknesses over time and exploit this knowledge to propose validation samples that will likely result in a failure. +% We use a low-dimensional encoded representation of inputs to train an adversarial failure classifier to intelligently select candidate failures to evaluate. +% Experiments were run to test our approach against a random candidate selection process and we also compare against full knowledge of the true system failures. +% We stress test a black-box neural network classifier trained on the MNIST dataset. +% Results show that using our framework, the adversarial failure classifier selects failures about $3$ times more often than random. + +% \end{abstract} + + +\section{Introduction} +Finding failures in a validation dataset may be computationally expensive if we search over the entire dataset. +Then the challenge becomes how to intelligently select candidate inputs that are likely to lead to failures. +We are also interested in finding failures in black-box systems, i.e. systems where we can only pass inputs and observe outputs---without any knowledge of the inner-workings of the system. +The motivation to find such candidate failure inputs is to reduce the need to exhaustively evaluate an entire validation dataset, especially for black-box systems that may be computationally expensive to call. +Each input sample in the dataset may also be high-dimensional, therefore we also want to learn a low-dimensional representation of the dataset and use that representation to learn features that caused failures. +An adversarial failure classifier will input the low-dimensional representation and determine if a sampled input will likely result in a failure. +Our proposed framework combines the components of a dataset encoder, an adversarial failure classifier, and a candidate failure selector to propose dataset inputs that will likely result in failure, all to reduce the computational cost of evaluating the system under test and to focus only on evaluating predicted failures. +The framework is available online.\footnote{\url{https://github.com/sisl/FailureRepresentation.jl}} + +\subsection{Related Work} +Current approaches to validate black-box systems focus their search over input disturbances to find failures \citep{corso2020survey}. +A black-box reinforcement learning approach known as adaptive stress testing (AST) has recently been used to find the most likely failures in aircraft collision avoidance systems \citep{lee2015adaptive, lee2018adaptive}, aircraft flight management systems \citep{moss2020adaptive}, and autonomous vehicles \citep{koren2018adaptive, koren2019efficient}. +An underlying assumption of the AST problem formulation is that the system under test can be modeled as a sequential decision making process with explicitly defined states. +This assumption limits the application of AST for validation over a dataset and ultimately creates \textit{more} data to validate due to applying input disturbances. +Other approaches use model-based clustering to efficiently sample large datasets, but rely on tuned initialization parameters for good performance \citep{wehrens2004model}. +Bayesian methods have been used to efficiently sample data from large hierarchical datasets using techniques to fit clusters over randomly partitioned subsets of the data \citep{huang2005sampling}. +To be effective, these techniques assume hierarchical structure in the data. +Compression-based approaches have also been applied to reduce data size without loss of useful information \citep{ferrari2013handling}, but are generally domain specific. +The most straightforward approach is to evaluate the system exhaustively over the entire validation dataset, which may be expensive and is the main motivation of our proposed framework. + + + +\section{Dataset and Features} +We are using the MNIST handwritten digit dataset \citep{lecun2010mnist} as our collection of inputs we want to selectively sample. +We chose MNIST because it is a well-known machine learning dataset with many benchmarks, and is small enough to quickly iterate our framework without worrying about computational concerns. +The MNIST training data contains $60{,}000$ gray-scale images of handwritten digits, each represented as $28\times28$ pixels. The test dataset contains $10{,}000$ gray-scale images with the same $28\times28$ pixel dimensions. For feature extraction, we left that up to the autoencoder described in \Cref{sec:autoencoder}. + + + +\subsection{Black-Box System Under Test} +\begin{wrapfigure}{r}{0.2\textwidth} + \vspace{-30pt} + \centering + \centerline{\includegraphics[width=0.15\textwidth]{figures/weakness_rec/MNIST-failure-7(1).png}} + \caption{Example failure (i.e. misclassification) which classified this image as a $1$ instead of a $7$.} + \label{fig:mnist_nn_failure} +\end{wrapfigure} +To test our framework, we trained an MNIST classifier to be our black-box system under test $\mathcal{S}$. +We are using the Julia machine learning package \texttt{Flux.jl} \citep{Flux.jl-2018} for building the neural network model and training. +The black-box classifier $\mathcal{S}$ consists of two dense layers and a $\ReLU$ activation, mapping the input size of $28\times28=784$ to $32$ activations, and then an output layer of size $10$ (for each digit class). +We use the logit cross-entropy loss, which is equivalent to the cross-entropy loss after applying the $\softmax$ function to the predicted output $\mathbf{\hat y}$: +\begin{equation*} +\mathcal{L}_\mathcal{S}(\softmax(\mathbf{\hat y}), \mathbf{y}) = -\frac{1}{m} \sum_{i=1}^m y_i \log(\hat y_i) +\end{equation*} +We trained the system over $20$ epochs, with a mini-batch size of $1024$, and using the Adam optimizer \citep{kingma2017adam} with a learning rate of $\alpha=3e^{-4}$. This classifier achieves around $93.2\%$ accuracy, so there is room to find weaknesses to exploit failures, where we define a failure as a misclassification. +\Cref{fig:mnist_nn_failure} shows an example failure where the system misclassified a particular digit. + + + + +\section{Method} +Our proposed framework consists of two major components: a dataset autoencoder, and an adversarial failure selector. These components are iteratively called within a \textit{sampled validation loop}. The dataset autoencoder is used to sample $m$ low-dimensional representations of the encoded input samples $\tilde{\mathbf{x}}$. We encode inputs into a lower-dimensional space for two reasons: 1) to reduce the potential high-dimensionality of the inputs $\mathbf{x}$ and 2) to learn features in this low-dimensional space that likely caused failures. +We then split the $m$ low-dimensional samples into a training set $\tilde{\mathcal{D}}_\text{train}$ and test set $\tilde{\mathcal{D}}_\text{test}$. +The training set $\tilde{\mathcal{D}}_\text{train}$ is passed to an adversarial agent that learns characteristics of the low-dimensional feature representation that led to failures. +We use a failure classifier as our adversary, and then predict which inputs led to failures over the test data $\tilde{\mathcal{D}}_\text{test}$, then map the predicted failures from the low-dimensional space back to the original representation, and then run the candidate inputs expected to result in a failure through the system under test. \Cref{fig:framework} illustrates each step of the validation framework. + +% \newpage % TODO: remove + +\begin{figure}[t] +\centering +\resizebox{0.9\textwidth}{!}{% + \includegraphics[page=1]{figures/weakness_rec/validation_diagram.pdf} + % \input{figures/weakness_rec/validation_diagram.tex} % TOO INTENSE. +} +\caption{Validation framework---a dataset autoencoder $\mathcal{E}$ is trained on the entire validation dataset $\mathcal{D}_\text{test}$ consisting of input samples $\mathbf{x}$. Then $m$ samples of encoded low-dimensional representations of the inputs $\tilde{\mathbf{x}}$ are selected for this iteration $t$, denoted $\tilde{\mathbf{x}}_t^{(1:m)}$ for all $m$ samples. The low-dimensional representations are then split into a training and test dataset. The training dataset $\tilde{\mathcal{D}}_\text{train}$ is used to train an adversarial failure classifier $\mathcal{A}$ on the encoded representations. Then the test dataset $\tilde{\mathcal{D}}_\text{test}$ is used to select candidate failures $\tilde{\mathbf{x}}_c$ as predicted by the adversary. Finally, the candidate failures from the adversary $\tilde{\mathbf{x}}_c$ are mapped back to the original inputs $\mathbf{x}_c \subseteq \mathbf{x}$ and evaluated by the system under test $\mathcal{S}$.} +\label{fig:framework} +\end{figure} + + +\subsection{Dataset Autoencoder}\label{sec:autoencoder} +To get a low-dimensional representation of the inputs $\mathbf{x}$, we used an autoencoder network \citep{kramer1991nonlinear}. +We trained the autoencoder $\mathcal{E}$ on the MNIST test dataset $\mathcal{D}_\text{test}$ and sample from the low-dimensional representation $\tilde{\mathbf{x}}$ as inputs into our adversarial failure classifier. +We use the MNIST test set because this is our input validation set---thus, we want our autoencoder to only have information about the validation set, without the need to have access to the training set used by the system under test. +The autoencoder network maps the $28\times28$ input image $\mathbf x$ into a low-dimensional latent space of size $64$ using a $\LeakyReLU$ activation. +Then the decoder will take the $64$-dimensional representation $\mathbf{\tilde x}$, again using a $\LeakyReLU$ activation layer, and attempt to recover the original input $\mathbf x'$. +We pre-trained the autoencoder over $20$ epochs, with a mini-batch size of $1000$, and tuned the network parameters using the Adam optimizer with a learning rate of $\alpha=1e^{-3}$. +Training is unsupervised and we use the mean squared error loss function: +\begin{equation*} +\mathcal{L}_\mathcal{E}(\mathbf{x}', \mathbf{x}) = \frac{1}{m} \sum_{i=1}^m \left( x'_i - x_i \right)^2 +\end{equation*} +\Cref{fig:autoencoder_nn} illustrates the autoencoder network architecture and \Cref{fig:mnist_autoencoder} shows samples of the true inputs and their output after encoding/decoding. + + +\begin{figure*}[!t] + \centering + \subfloat[Dataset autoencoder architecture, with inputs $\mathbf{x} \in \mathbb{R}^{28\times28}$, encoded through a dense $\LeakyReLU$ layer of size $\frac{28\times28}{2}$ to a low-dimensional representation $\tilde{\mathbf{x}} \in \mathbb{R}^{64}$, then decoded through a $\LeakyReLU$ layer of size $\frac{28\times28}{2}$, outputting $\mathbf{x}' \in \mathbb{R}^{28\times28}$.]{% + \resizebox{0.45\textwidth}{!}{ + \includegraphics[page=1]{figures/weakness_rec/autoencoder-nn.pdf} + % \input{figures/weakness_rec/autoencoder-nn.tex} % Needs lualatex + } + \label{fig:autoencoder_nn} + } + \hspace{5mm} + \subfloat[Sampled output from the MNIST autoencoder: true input is on top and the recovered input on bottom.]{% + \resizebox{0.45\textwidth}{!}{ + \centerline{\includegraphics[width=0.6\textwidth]{figures/weakness_rec/sample-MNIST-autoencoder-5.png}} + } + \label{fig:mnist_autoencoder} + } + \caption{Dataset autoencoder architecture and sample decoded output.} +\end{figure*} + + +\subsection{Adversarial Failure Classifier} +To learn the low-dimensional features that are likely to cause failures, we train an adversary $\mathcal{A}$ in the validation loop to classify failures. +The supervised adversary is trained on the partition $\tilde{\mathcal{D}}_\text{train}$ of the low-dimensional samples $\tilde{\mathbf{x}}$ and outputs a prediction that a given input would lead to a system failure. +In order to get the target classifications $\mathbf{y}$, we use the system $\mathcal{S}$ to run the true inputs associated to the encoded inputs which are part of the training data $\tilde{\mathcal{D}}_\text{train}$. This gives us the targets we can now train our adversary on. +Our adversarial loss function is the binary cross-entropy loss: +\[ +\mathcal L_\mathcal{A}(\mathbf{\hat y}, \mathbf{y}) = -\frac{1}{m}\sum_{i=1}^m y_i\log(\hat y_i) - (1 - y_i)\log(1 - \hat y_i) +\] +The adversarial network architecture consists of $3$ dense layers which map the low-dimensional representation of $\tilde{\mathbf{x}} \in \mathbb{R}^{64}$ through a $\ReLU$ layer of size $128$, another $\ReLU$ layer of size $64$, and finally an output sigmoid layer to map the predictions to a probability. +For each sampled validation iteration $t$ (shown in \Cref{fig:framework}), we retrain the adversary $\mathcal{A}$ for $20$ epochs using the Adam optimizer with learning rate $\alpha=3e^{-5}$. Notice that our learning rate is very small, this is so we do not overfit to early iterations in $t$ and can generalize across different samples of the low-dimensional space. The adversary will use the test data partition $\tilde{\mathcal{D}}_\text{test}$ to select the encoded input that it predicted would lead to a failure. +We use the threshold of $\mathcal{A}(\tilde{x}) \ge 0.5$ to indicate the input $\tilde{x} \in \tilde{\mathcal{D}}_\text{test} \subset (\tilde{\mathbf{x}}, \mathbf{y})$ led to a failure. +All encoded inputs in the test dataset that led to a failure are considered candidate failure scenarios, and we denote them as $\tilde{\mathbf{x}}_c$. +We use a mapping from the encoded inputs $\tilde{\mathbf{x}}_c$ to the original inputs $\mathbf{x}_c \subseteq \mathbf{x}$, and finally pass the failure candidates to the true system $\mathcal{S}$ for actual evaluation. + +%%% TODO: Change Loss function m to n ??? + +% We use the binary cross-entropy loss with an added factor $\Delta\softmax$ which is used as a distance metric to indicate the severity of a misclassification. +% The $\Delta\softmax$ metric is defined as the difference between the $\softmax$ probability of the prediction $\mathbf{\hat y}$ and the $\softmax$ probability of the \textit{true target} as indicated by the prediction: +% \[ +% \Delta\operatorname{softmax}(\mathbf y, \mathbf{\hat y}) = +% \max\left(\operatorname{softmax}(\mathbf{\hat y})\right) - +% \operatorname{softmax}(\mathbf{\hat y})^{\left[ \operatorname{argmax} \mathbf y \right]} +% \] + + +% \subsection{Hyperparameters} +% % Table with all hyperparams for E, A, and S (in separate tables) +% % Describe the sensitivity of adversarial learning rate +% \lipsum[13] + + +\section{Experiments and Results} +\begin{table}[b] + \centering + \caption{Evaluation Metrics}\label{tab:metrics} + \begin{threeparttable} + \begin{tabular}{@{}lrr|rr@{}} + \toprule + \textbf{Failure Selector} & \textbf{Precision}\tnote{*} & \textbf{Recall}\tnote{*} & \textbf{Sampled Precision}\tnote{$\dagger$} & \textbf{Sampled Recall}\tnote{$\dagger$}\\ + \midrule + Adversary $\mathcal{A}$ & $0.2441$ & $0.2260$ & $0.2374 \pm 0.11$ & $0.3244 \pm 0.17$ \\ + Random & $0.0647$ & $0.4712$ & $0.0618 \pm 0.04$ & $0.0910 \pm 0.07$ \\ + \bottomrule + \end{tabular} + \begin{tablenotes} + \item[*] {Run over $\mathcal{D}_\text{test}$ only calculated for the ``failure'' class.} + \item[$\dagger$] {Calculated from $T=10$ iterations of the \textit{sampled validation loop}.} + \end{tablenotes} + \end{threeparttable} +\end{table} +To evaluate our approach, we ran $T=10$ sampled validation iterations, sampling $m=500$ random encodings and partitioning these samples in half into $\tilde{\mathcal{D}}_\text{train}$ and $\tilde{\mathcal{D}}_\text{test}$ for the adversary. +Because the failure rate for our system under test $\mathcal{S}$ is about $0.0677$, we augment the training dataset by duplicating the known failures $10$ times after running each training set through the system $\mathcal{S}$ to get the true outputs $\mathbf{y}_\text{train}$. +We use two main metrics to evaluate the performance of the adversary: \textit{precision} and \textit{recall}. During each iteration $t$, we save off the current adversary $\mathcal{A}_t$ and evaluate the \textit{area under the ROC curve} (AUC) as shown in \Cref{fig:roc}. The ROC curve highlights incremental improvement of the adversary after each iteration. Note that we retrain the new adversary $\mathcal{A}_{t}$ starting from the network weights learning by the previous adversary $\mathcal{A}_{t-1}$. +To balance between precision and recall, we swept over the prediction threshold to determine which threshold value to select (see \Cref{fig:sweep}). +Based on this tuning sweep, we chose a threshold of $\hat y \ge 0.5$ to indicate a positive failure prediction by the adversary. + +During each iteration $t$, the adversary selects $k$ candidate inputs predicted to be failures. +For comparison, we employ a random selection of $k$ candidates and evaluate the precision and recall metrics of the random scheme. +This allows us to compare our adversarial learning approach to a baseline. \Cref{tab:metrics} quantifies the evaluation metrics for the adversary and random candidate selector. + + +%% subfigure version. +% \begin{figure}[ht] +% \centering +% \begin{subfigure}[t]{0.59\textwidth} +% \centering +% % \resizebox{\columnwidth}{!}{\input{figures/weakness_rec/roc.pgf}} +% \caption{ROC curve and AUC for each adversary $\mathcal{A}_t$.} +% \label{fig:roc} +% \end{subfigure} +% \hfill +% \begin{subfigure}[t]{0.4\textwidth} +% \centering +% % \resizebox{\textwidth}{!}{\input{figures/weakness_rec/threshold_sweep.pgf}} +% \caption{Tuning prediction threshold.} +% \label{fig:sweep} +% \end{subfigure} +% \caption{ROC curve and evaluation metrics.} +% \label{fig:roc_and_metrics} +% \end{figure} + +\begin{figure*}[t] + \centering + \subfloat[ROC curve and AUC for each adversary $\mathcal{A}_t$.]{% + \resizebox{0.54\textwidth}{!}{\input{figures/weakness_rec/roc.pgf}} + \label{fig:roc} + } + \hspace{5mm} + \subfloat[Tuning prediction threshold.]{% + \resizebox{0.36\textwidth}{!}{\input{figures/weakness_rec/threshold_sweep.pgf}} + \label{fig:sweep} + } + \caption{ROC curve and evaluation metrics.} + \label{fig:roc_and_metrics} +\end{figure*} + + +% \begin{figure}[ht] +% \centering +% \begin{subfigure}[t]{0.49\textwidth} +% \centering +% \resizebox{\columnwidth}{!}{\input{figures/weakness_rec/confusion_sut.pgf}} +% \caption{TODO.} +% \label{fig:confusion_sut} +% \end{subfigure} +% \hfill +% \begin{subfigure}[t]{0.49\textwidth} +% \centering +% \resizebox{\columnwidth}{!}{\input{figures/weakness_rec/confusion_adversary.pgf}} +% \caption{TODO.} +% \label{fig:confusion_adversary} +% \end{subfigure} +% \caption{Confusion matrices TODO} +% \label{fig:confusion} +% \end{figure} + +\section{Analysis and Discussion} +\begin{wrapfigure}{r}{0.3\textwidth} + \vspace{-30pt} + \centering + \resizebox{0.3\textwidth}{!}{\input{figures/weakness_rec/confusion_adversary.pgf}} + \caption{Confusion matrix.} + \label{fig:confusion_adversary} +\end{wrapfigure} +Shown by the confusion matrix in \Cref{fig:confusion_adversary}, the adversarial failure classifier achieves about $0.24$ in precision and $0.23$ in recall. +Compared to random, the precision rate is about $3$ times better using the adversary. Random recall---as expected---is around $0.5$. +These results show that our approach learned the low-dimensional representation of a failure over the validation set, and based on this information it selected candidate failures to be evaluated. +To see which element of the low-dimensional feature vector contributed the most to a likely failure as predicted by the adversary, we encoded a one-hot vector over $\mathbb{R}^{28\times28}$ (i.e. the input space) and plotted the output likelihood of failure for each of the pixels, shown in \Cref{fig:failure_likelihood}. + +% THIS TAKES A WHILE TO COMPILE.... +\begin{wrapfigure}{l}{0.3\textwidth} + \centering + \resizebox{0.3\textwidth}{!}{\input{figures/weakness_rec/failure-likelihood.pgf}} + \caption{Failure likelihood.} + \label{fig:failure_likelihood} +\end{wrapfigure} + +\Cref{fig:predictions} compares the failures classified by the adversary. +For the true positives in \Cref{fig:true_positives}, the top row of digits are the $10$ digits with the highest predicted failure likelihood that were true failures, the middle row shows the feature that had the strongest influence on the failure classification (decoding a one-hot vector representation of the maximum of a $\softmax$ over low-dimensional inputs), and the bottom row shows the reconstructed digits after passing through the autoencoder. +Similarly for the false negatives in \Cref{fig:false_negatives}, the top row are the $10$ digits with the lowest predicted failure likelihood that were true failures, the middle row shows the strongest influential feature, and the bottom row shows the output of the autoencoder. Notice that certain features in the middle row are shared among the other digits, indicating features that play a larger role in classifying failures. + +%%% TODO +% \begin{figure}[ht] +% \centering +% \begin{subfigure}[t]{0.49\textwidth} +% \centering +% % \resizebox{\columnwidth}{!}{\input{figures/weakness_rec/feature-likelihood.pgf}} +% \resizebox{\columnwidth}{!}{\input{figures/weakness_rec/failure-likelihood.pgf}} +% \caption{TODO.} +% \label{fig:feature_likelihood} +% \end{subfigure} +% \hfill +% \begin{subfigure}[t]{0.49\textwidth} +% \centering +% \resizebox{\columnwidth}{!}{\input{figures/weakness_rec/failure-likelihood.pgf}} +% \caption{TODO.} +% \label{fig:failure_likelihood} +% \end{subfigure} +% \caption{Likelihoods} +% \label{fig:likelihoods} +% \end{figure} + + +\begin{figure*}[t] + \centering + \subfloat[Adversarial true positives.]{% + \resizebox{0.45\textwidth}{!}{ + \centerline{\includegraphics[width=0.6\textwidth]{figures/weakness_rec/MNIST-true-positives.png}} + } + \label{fig:true_positives} + } + \hspace{5mm} + \subfloat[Adversarial false negatives.]{% + \resizebox{0.45\textwidth}{!}{ + \centerline{\includegraphics[width=0.6\textwidth]{figures/weakness_rec/MNIST-false-negatives.png}} + } + \label{fig:true_positives} + } + \caption{MNIST failure predictions from the adversary.}\label{fig:predictions} +\end{figure*} + + +% % subfigure version. +% \begin{wrapfigure}{r}{0.3\textwidth} +% \vspace{-30pt} +% \centering +% \begin{subfigure}[t]{0.3\textwidth} +% \centering +% \centerline{\includegraphics[width=\textwidth]{figures/weakness_rec/MNIST-true-positives.png}} +% \caption{Adversarial true positives.} +% \label{fig:true_positives} +% \end{subfigure} +% \hfill +% \begin{subfigure}[t]{0.3\textwidth} +% \centering +% \centerline{\includegraphics[width=\textwidth]{figures/weakness_rec/MNIST-false-negatives.png}} +% \caption{Adversarial false negatives.} +% \label{fig:false_negatives} +% \end{subfigure} +% \caption{MNIST failure predictions from the adversary.}\label{fig:predictions} +% \end{wrapfigure} + + +\section{Conclusion and Future Work} +To avoid exhaustively searching an entire validation set for failures, we show that an iterative framework that uses an adversarial failure classifier trained on low-dimensional representations of the inputs can select failures about $3$ times more likely than randomly choosing candidates to evaluate. +To extend this framework, we could investigate different adversarial architectures, particularly around deep reinforcement learning. +We could also explore how to take the true failures found, automatically improve the system under test, and then in a continual learning approach we could rerun this validation loop to use prior knowledge of previous system failures to find new system failures. + +\section{Contributions} +Robert Moss consulted regularly with Bernard Lange, who is taking CS330 Meta Learning, regarding the project ideas. +Originally, Bernard and Robert were going to collaborate on this project but took different directions as the quarter progressed. +All of the work seen here (literature review, framework design, coding, training, analysis, plotting, and writing) was completed solely by Robert Moss. diff --git a/diagrams/arc-length.tex b/diagrams/arc-length.tex new file mode 100644 index 0000000..cfd6110 --- /dev/null +++ b/diagrams/arc-length.tex @@ -0,0 +1,61 @@ +\begin{tikzpicture} + [ + scale=16, every node/.style={scale=2}, + >=stealth, + point/.style = {draw, circle, fill = black, inner sep = 1pt}, + dot/.style = {draw, circle, fill = black, inner sep = .2pt}, + latlon/.style = {draw, rectangle, minimum width=0.0001mm, minimum height=4mm, fill=white, fill opacity=0.75, fill = black, inner sep = 0.1pt}, + latlonstart/.style = {draw, rectangle, minimum width=0.0001mm, minimum height=4mm, fill = black, inner sep = 0.3pt}, + wpt/.style = {diamond, fill=white, fill opacity=0.75}, + ] + + \tikzstyle{every node}=[font=\Large] + + + % the circle + \def\unit{0.5} + \def\rad{0.3} + \def\ang{45} + \def\failang{7} + \def\inner{0.3*\rad} + \def\failinner{0.6*\rad} + \def\failvalue{-28} % degrees + + \node (origin) at (0,0) [point, label = {below:$c$}]{}; + + \node (initial) at +(-\unit,\rad) [latlon] {}; + \node [rotate=-\failang] (failstart) at +(0, \rad) [latlonstart, red] {}; + \draw[red] (failstart) arc (90:\ang+\failvalue:\rad); + + \node (start) at +(0, \rad) [latlonstart, label = above:$s$] {}; + \node [rotate=-\ang] (end) at +(\ang:\rad) [latlon, label ={[label distance=-1mm]above:$e$}] {}; + \node (failend) at +(\ang+\failvalue:\rad) [rotate=-\ang, latlon,red] {}; + + \draw (start) arc (90:\ang:\rad); + + + \draw[-] (initial) -- node (ls) [label = {above:$\ell_1$}] {} (start); + + + \draw[dashed] + ($ (origin) ! 1 ! (start) $) + -- ($(start) ! 1 ! (origin)$ ) + node (center) [right,label={[pos=0.45]left:$r$}] {}; + + \draw[dashed] + ($ (origin) ! 1 ! (end) $) + -- ($(end) ! 1 ! (origin)$ ) + node [right] {}; + + \draw[->, rotate around={\ang:(end)}] (end) -- node (nextstraight) [very near end, label = {above:$\ell_2$},] {} (end |-, 0); + + % xshift=-4pt,yshift=0pt + \draw [,thick,decorate,decoration={brace,amplitude=30pt}] (start) -- (end) node [black,midway,above=33pt,pos=0.65] {$\alpha r$}; + \draw [red,,thick,decorate,decoration={brace,amplitude=20pt}] (failend) -- (failstart) node [red,midway,below=27pt,pos=0.63] {$\beta$}; + + \draw [dashed] (0, \inner) arc (90:\ang:\inner); + \node (innerangle) at +(90-\ang+\ang/1.4:\inner) [label = {[label distance=-2mm]45:$\alpha$}] {}; + + \node (mid) at +(90-\ang/2:\rad) [draw, wpt, inner sep=1pt, rotate=90-\ang/2] {}; + +\end{tikzpicture} \ No newline at end of file diff --git a/diagrams/ast-formulation.tex b/diagrams/ast-formulation.tex new file mode 100644 index 0000000..8d40719 --- /dev/null +++ b/diagrams/ast-formulation.tex @@ -0,0 +1,52 @@ +\begin{tikzpicture} + [ + node distance=1.5cm, + every node/.style={font=\large}, + align=center + ] + \tikzset{ + >={Latex[width=2mm,length=2mm]}, + base/.style = {rectangle, rounded corners, draw=black, + minimum width=1cm, minimum height=1cm, + text centered}, + block/.style = {base, minimum width=2.5cm, minimum height=1.5cm}, + envstyle/.style = {block, fill=red!15}, + sutstyle/.style = {block, fill=gray!50}, % fill=blue!10 + simstyle/.style = {base, thick, fill=gray!15, minimum width=4cm}, + metasimstyle/.style = {base, line width=0.07cm, fill=orange!80!gray!40, minimum width=4cm}, + learnerstyle/.style = {block, fill=red!15}, %blue!20 gray!15 + rewardstyle/.style = {block, fill=white}, %green!70!gray!20 %gray!15 + componentstyle/.style = {block, fill=white}, %red!15 %white + aircraftstyle/.style = {block, draw=none, fill=brown!50!red!30}, + casstyle/.style = {block, fill=orange!50}, + } + \pgfdeclarelayer{metasimlayer} + \pgfdeclarelayer{simlayer} + \pgfdeclarelayer{inputlayer} + \pgfdeclarelayer{blackboxlayer} + \pgfsetlayers{metasimlayer,simlayer,blackboxlayer,inputlayer,main} + + \node (wptdist) [componentstyle] {Waypoint Distribution\\$\vec{w} \overset{\bar{a}}{\sim} \mathcal{N}(\vec{\mu},\mat{\Sigma})$}; + \node (sut) [sutstyle, below right=1cm and -0.5cm of wptdist] {Trajectory Predictor\\ (Black-box SUT)}; + + \draw[->,dotted,line width=1pt] (wptdist) -| ($(sut.north)+(-5mm,0mm)$) node[pos=0.725,right,align=left]{{\sc Rollout$(s,d)$}\\then\\{\sc Evaluate$(\vec{w})$}}; + + \begin{pgfonlayer}{simlayer} + \path let \p1=(wptdist.north west), \p2=(sut.south east) in node (sim) [fit={($(\x1,\y1)+(-4cm,1.25cm)$) ($(\x2,\y2)+(1.3cm,-0.5cm)$)},simstyle,line width=0.08cm]{}; + \node at ($(sim.north west)+(2cm,-7mm)$) [font={\LARGE}] {Simulator $\mathcal{\bar{S}}$}; + \end{pgfonlayer} + + \draw[->,dashed,line width=0.5pt] (wptdist.south) |- ($(sim.west)+(0mm,-1cm)$) node[pos=0.5,xshift=-3cm,above]{transition probability $p$}; + \draw[->,dashed,line width=0.5pt] (sut) -- (sut -| sim.west) node[pos=0.5,below]{event $e$, miss distance $d$, terminal $\tau$}; + + \node (learner) [learnerstyle, above left=1.25cm and 4.5cm of sim.west,xshift=0cm] {Monte Carlo Tree Search\\with Progressive Widening}; + \node (reward) [rewardstyle, below=1.35cm of learner,xshift=0cm] {Reward Function\\[1mm]$R(p,e,d,\tau) = \begin{cases} + (\log(p) - d)R_E & \text{if } \tau \wedge e \\ + \log(p) - d & \text{if } \tau \wedge \neg e \\ + 0 & \text{otherwise} + \end{cases}$}; + + \draw[->] (learner) -- (sim.west |- learner) node[pos=0.5,above]{seed $\bar{a}$}; + \draw[->] (reward.north) -- (learner.south) node[pos=0.5,right]{reward $r$}; + \draw[<-] (reward) -- (reward -| sim.west) node[pos=0.5,above]{$\langle p,e,d,\tau \rangle$}; +\end{tikzpicture} \ No newline at end of file diff --git a/diagrams/course-direction.tex b/diagrams/course-direction.tex new file mode 100644 index 0000000..b5c026c --- /dev/null +++ b/diagrams/course-direction.tex @@ -0,0 +1,43 @@ +\begin{tikzpicture} + [ + scale=16, every node/.style={scale=2}, + >=stealth, + point/.style = {draw, circle, fill = black, inner sep = 1pt}, + dot/.style = {draw, circle, fill = black, inner sep = .2pt}, + latlon/.style = {draw, rectangle, minimum width=0.0001mm, minimum height=2mm, fill=white, fill opacity=0.75, fill = black, inner sep = 0.1pt}, + latlonstart/.style = {draw, rectangle, minimum width=0.0001mm, minimum height=2mm, fill = black, inner sep = 0.3pt}, + wpt/.style = {diamond, fill=white, fill opacity=0.75}, + ] + + \tikzstyle{every node}=[font=\Large] + + % the circle + \def\unit{0.5} + \def\rad{0.3} + \def\ang{45} + \def\failang{7} + \def\inner{0.1*\rad} + \def\failinner{0.6*\rad} + + \node (initial) at +(-\unit,\rad) [latlon, label = above:$p_1$] {}; + + \node (start) at +(0, \rad) [latlonstart, label = above:$s_1$] {}; + \node [rotate=-\ang] (end) at +(\ang:\rad) [latlon, label ={[label distance=-1mm]above:$e_1$}] {}; + \draw[->, dashed, rotate around={\ang:(end)}] (end) -- node (nextstraight) [pos=0.75, label={below right:$\theta_{\text{out}}$},] {} (end |-, \rad/4.25); + + \node (failinitial) at (0,\rad/2) [latlon, label = above:$p_2$] {}; + \node (failstart) at ($(failinitial) + (-0.25, 0)$) [latlonstart, label = above:$s_2$] {}; + + \draw (start) arc (90:\ang:\rad); + + \draw[-] (initial) -- node (ls) [label = {above:$\ell_1$}] {} (start); + + \draw[->,dashed] ($(failinitial) + (0.32, 0)$) -- node (dist) [label={right:$\theta_{\text{in}}$},pos=0.05] {} (failinitial); + \draw[-] (failinitial) -- node (fs) [label={above:$\ell_2$}] {} (failstart); + + \draw [red,thick,dashed,rotate=180] (-0.24, -\rad/2) arc (0:135:\inner); + \node (innerangle) at (0.225, \rad/3.6) [label = {[red,label distance=-3mm]above right:$\omega$}] {}; + + \node (mid) at +(90-\ang/2:\rad) [draw, wpt, inner sep=1pt, rotate=90-\ang/2] {}; + +\end{tikzpicture} \ No newline at end of file diff --git a/diagrams/disconnection.tex b/diagrams/disconnection.tex new file mode 100644 index 0000000..90a7b30 --- /dev/null +++ b/diagrams/disconnection.tex @@ -0,0 +1,39 @@ +\begin{tikzpicture} + [ + scale=16, every node/.style={scale=2}, + >=stealth, + point/.style = {draw, circle, fill = black, inner sep = 1pt}, + dot/.style = {draw, circle, fill = black, inner sep = .2pt}, + latlon/.style = {draw, rectangle, minimum width=0.0001mm, minimum height=2mm, fill=white, fill opacity=0.75, fill = black, inner sep = 0.1pt}, + latlonstart/.style = {draw, rectangle, minimum width=0.0001mm, minimum height=2mm, fill = black, inner sep = 0.3pt}, + wpt/.style = {diamond, fill=white, fill opacity=0.75}, + ] + + \tikzstyle{every node}=[font=\large] + + % the circle + \def\unit{0.5} + \def\rad{0.3} + \def\ang{45} + \def\failang{7} + \def\inner{0.3*\rad} + \def\failinner{0.6*\rad} + + \node (initial) at +(-\unit,\rad) [latlon, label = above:$p_1$] {}; + + \node (start) at +(0, \rad) [latlonstart, label = above:$s_1$] {}; + \node [rotate=-\ang] (end) at +(\ang:\rad) [latlon, label ={[label distance=-1mm]above:$e_1$}] {}; + + \node (failinitial) at (0,\rad/2) [latlon, label = above:$p_2$] {}; + \node (failstart) at ($(failinitial) + (-0.25, 0)$) [latlonstart, label = above:$s_2$] {}; + + \draw (start) arc (90:\ang:\rad); + + \draw[-] (initial) -- node (ls) [label = {above:$\ell_1$}] {} (start); + + \draw[dashed,red] (end) -- node (dist) [label={[label distance=-1mm]below:$\delta$},pos=0.45] {} (failinitial); + \draw[-] (failinitial) -- node (fs) [label={above:$\ell_2$}] {} (failstart); + + \node (mid) at +(90-\ang/2:\rad) [draw, wpt, inner sep=1pt, rotate=90-\ang/2] {}; + +\end{tikzpicture} \ No newline at end of file diff --git a/diagrams/lateral-packet.tex b/diagrams/lateral-packet.tex new file mode 100644 index 0000000..483d933 --- /dev/null +++ b/diagrams/lateral-packet.tex @@ -0,0 +1,98 @@ +\begin{tikzpicture} + [ + % scale=8, + % scale=16, every node/.style={scale=2}, + scale=16, every node/.style={scale=2}, + >=stealth, + point/.style = {draw, circle, fill = black, inner sep = 1pt}, + latlon/.style = {draw, rectangle, minimum width=0.0001mm, minimum height=2mm, fill = black, inner sep = 0.1pt}, + latlonstart/.style = {draw, rectangle, minimum width=0.0001mm, minimum height=2mm, fill = black, inner sep = 0.5pt}, + dot/.style = {draw, circle, fill = black, inner sep = .2pt}, + wpt/.style = {diamond, fill=white, fill opacity=0.75}, + ] + + \tikzstyle{every node}=[font=\normalsize] + + % the circle + \def\turnrad{0.05} + \def\ang{45} + + % Lateral packet #1 + \node (initial) at +(0,1/4+\turnrad) [latlon] {}; %, label = above:$i_1$] {}; + \node (center) at +(1/3,1/4) [point, inner sep=0.5pt] {}; %, label = {[label distance=-1mm]below:$c_1$}] {}; + \path (center) ++(90:\turnrad) node (start) [latlonstart, label = {[label distance=-1mm]above:$s_1$}] {}; + \path (center) ++(90-\ang:\turnrad) node (end) [] {}; % [, label = {[label distance=-2.5mm]above right:$e_1$}] {}; + + \draw (center) circle (\turnrad) [dotted,thick]; + + \def\startang{90} + \def\endang{90-\ang} + \draw (start) arc (\startang:\endang:\turnrad); + + \path (center) ++(90-\ang/2:\turnrad) node (mid) [draw, rotate=-\ang/2, wpt, inner sep=1pt] {}; % waypoint + + % straight segment line + \draw[-] (initial) -- node (ls) [label = {[label distance=-2mm]above left:$\ell_1$}] {} (start); + + % Lateral packet #2 + \node [rotate=-\ang] (initial2) at (end) [latlon] {}; %, label = right:$i_1$] {}; + \node (center2) at +(2/3+-\turnrad,2*\turnrad) [point, inner sep=0.5pt] {}; %, label = {[label distance=-1mm]above:$c_2$}] {}; + \path (center2) ++(180+\ang:\turnrad) node [rotate=-\ang] (start2) [latlonstart, label = {[label distance=-1.5mm]below:$s_2$}] {}; + \path (center2) ++(-\ang:\turnrad) node (end2) [] {}; % [, label = {[label/2 distance=-2.5mm]below right:$e_2$}] {}; + + \draw (center2) circle (\turnrad) [dotted,thick]; + + \def\startang{180+\ang} + \def\endang{180+3*\ang} + \draw (start2) arc (\startang:\endang:\turnrad); + + \path (center2) ++(270:\turnrad) node (mid2) [draw, wpt, inner sep=1pt] {}; % waypoint + + % straight segment line + \draw[-] (initial2) -- node (ls) [label = {[label distance=-3mm]above right:$\ell_2$}] {} (start2); + + + % Lateral packet #3 + \node [rotate=\ang] (initial3) at (end2) [latlon] {}; %, label = above:$i_3$] {}; + \node (center3) at +(3/3-2*\turnrad,1/4) [point, inner sep=0.5pt] {}; %, label = {[label distance=-1mm]below:$c_3$}] {}; + \path (center3) ++(90+\ang:\turnrad) node [rotate=\ang] (start3) [latlonstart, label = {[label distance=-1.5mm]above:$s_3$}] {}; + \path (center3) ++(90-\ang:\turnrad) node (end3) [] {}; % [, label = {[label distance=-3mm]above right:$e_3$}] {}; + + \draw (center3) circle (\turnrad) [dotted,thick]; + + \def\startang{90+\ang} + \def\endang{90-\ang} + \draw (start3) arc (\startang:\endang:\turnrad); + + \path (center3) ++(90:\turnrad) node (mid) [draw, wpt, inner sep=1pt] {}; % waypoint + + % straight segment line + \draw[-] (initial3) -- node (ls) [label = {[label distance=-3mm]above left:$\ell_3$}] {} (start3); + + + % Lateral packet #4 (no straight segment, arc only) + \node (initial4) at (end3) [] {}; %, label = above:$i_2$] {}; + \path (initial4) ++(\ang:\turnrad/2) node (center4) [point, inner sep=0.5pt] {}; %, label = {[label distance=-1mm]above:$c_4$}] {}; + \path (center4) ++(180+\ang:\turnrad/2) node [rotate=-\ang] (start4) [latlonstart, label = {[label distance=-2mm]below:$s_4$}] {}; + \path (center4) ++(-\ang:\turnrad/2) node [rotate=\ang] (end4) [latlon] {}; %, label = {[label distance=-1mm]right:$e_4$}] {}; + + \draw (center4) circle (\turnrad/2) [dotted,thick]; + + \def\startang{180+\ang} + \def\endang{180+3*\ang} + \draw (start4) arc (\startang:\endang:\turnrad/2); + + \path (center4) ++(270:\turnrad/2) node (mid) [draw, wpt, inner sep=1pt] {}; % waypoint + + + % Lateral packet #5 (straight segment only) + \path (end4) ++(\ang+\ang*\turnrad/2:2*\turnrad) node (start5) [] {}; %, label = {[label distance=-1mm]above left:$s_4$}] {}; + + % straight segment line + \draw[->] (end4) -- node (ls) [] {} (start5); + + % dashed box around tangency check "zoom" waypoint and arc + % \node [draw, rectangle, dashed, minimum height=33mm, minimum width=60mm, xshift=-15mm, yshift=-5mm] (outline) at (start) [] {}; + % \draw[->, dashed] (outline.north east) -- node (pointer) [] {} ($(outline.north east)+(0.5mm,0.5mm)$); + +\end{tikzpicture} \ No newline at end of file diff --git a/diagrams/mcts-diagram.tex b/diagrams/mcts-diagram.tex new file mode 100644 index 0000000..16198fc --- /dev/null +++ b/diagrams/mcts-diagram.tex @@ -0,0 +1,79 @@ +% Monte Carlo tree search (MCTS) 4-stage diagram: selection, expansion, rollout, and backpropagation. +\tikzset{ + nodes={draw, circle}, >=latex, -, level distance=0.5in, + every node/.style={draw=black, thin, minimum size=6mm}, + norm/.style={edge from parent/.style={black,thin,draw}}, + emph1/.style={edge from parent/.style={line width=0.8pt,draw}}, + emph2/.style={edge from parent/.style={line width=1.2pt,draw}}, + emph3/.style={edge from parent/.style={line width=1.4pt,draw}}, + emph4/.style={edge from parent/.style={line width=1.6pt,draw}}, + semiselected/.style={line width=0.8pt}, + selected/.style={line width=1pt}, + root/.style={label=\textsc{#1}}, + baseline=(selection-root.base), + state/.style={circle, norm,-}, + action/.style={rectangle, norm}, + rollout-end/.style={rectangle, draw=none, minimum height=0mm}, + rollout-edge/.style={->, decorate, decoration={snake, amplitude=1mm, post length=10pt, segment length=12pt}, dotted, line cap=round, dash pattern=on 0pt off 2\pgflinewidth}, +} +\begin{tikzpicture} + \node [root=Selection, state, selected] (selection-root) {} + child [emph1, ->] { node [action, selected] {} + child [state] { node {} } + child [state, emph2, ->] { node [selected] {} } + } + child [state] {node [action] {}} + child [state] {node [action] {} + child [state] { node {} } + child [state] { node {} } + }; +\end{tikzpicture} +\hspace{1cm} +\begin{tikzpicture} + \node [root=Expansion, state] {} + child { node [action] {} + child [state] { node {} } + child [state] { node [semiselected] {} + child [state, emph3] { node [action, selected] {} } + } + } + child [state] {node [action] {}} + child [state] {node [action] {} + child [state] { node {} } + child [state] { node {} } + }; +\end{tikzpicture} +\hspace{1cm} +\begin{tikzpicture} + \node [root=Rollout, state] {} + child { node [action] {} + child [state] { node {} } + child [state] { node {} + child [state] { node [action, selected] {} + child [state, emph4, level distance=0.74in] { node [rollout-end] {$Q$} + edge from parent [rollout-edge] + } + } + } + } + child [state] {node [action] {}} + child [state] {node [action] {} + child [state] { node {} } + child [state] { node {} } + }; +\end{tikzpicture} +\hspace{1cm} +\begin{tikzpicture} + \node [root=Backpropagation, state, selected] {} + child [<-,emph1] { node [action, selected] {} + child [state] { node {} } + child [state, emph2, <-] { node [selected] {} + child [state, emph3, <-] { node [action, selected] {$Q$} } + } + } + child [state] {node [action] {}} + child [state] {node [action] {} + child [state] { node {} } + child [state] { node {} } + }; +\end{tikzpicture} \ No newline at end of file diff --git a/diagrams/mcts-pw.tex b/diagrams/mcts-pw.tex new file mode 100644 index 0000000..7861c9c --- /dev/null +++ b/diagrams/mcts-pw.tex @@ -0,0 +1,37 @@ +\begin{tikzpicture}[ + nodes={draw, circle}, -, level distance=0.35in, % 0.4 worked well.. + every node/.style={circle, draw=black,thin, minimum size = 0.5cm}, + emph1/.style={edge from parent/.style={line width=0.8pt,draw}}, + emph2/.style={edge from parent/.style={line width=1.2pt,draw}}, + emph3/.style={edge from parent/.style={line width=1.4pt,draw}}, + emph4/.style={edge from parent/.style={line width=1.6pt,draw}}, + norm/.style={edge from parent/.style={black,thin,draw}}, + evaluate/.style={rectangle, draw=none, minimum height=1mm, edge from parent/.style={black,thin,draw,dotted}}, + action/.style={rectangle, minimum height=6mm, minimum width=6mm}, +% evaluate-edge/.style={>=latex, ->, decorate, decoration={snake, amplitude=1.0mm}, dotted, line cap=round, dash pattern=on 0pt off 2\pgflinewidth}, + evaluate-edge/.style={>=latex, ->, decorate, decoration={snake, amplitude=0.7mm, post length=10pt, segment length=12pt}, dotted, line cap=round, dash pattern=on 0pt off 2\pgflinewidth}, + level 2/.style={sibling distance=10mm}, +] +\node{$s_0$} + child [emph1] { node [norm, action] {$\bar{a}_1$} + % child [emph2] { node [label={[label distance=-1mm]right:{\scriptsize $\sim \mathcal{N}_{\bar{a}_1}(\mu,\sigma^2)$}}] {$s_1$} + child [emph2] { node [label={[label distance=-1mm]right:{\scriptsize $\sim G(s_0,\bar{a}_1)$}}] {$s_1$} + child [norm] { node [action] {$\bar{a}_3$} } + child [norm] { node [action] {$\bar{a}_4$} } + child [emph3] { node [action] {$\bar{a}_5$} + child [emph4, level distance=0.74in] { node [evaluate, label={[xshift=1.25cm, yshift=-0.55cm]above:{\scriptsize {\sc Rollout$(s_1,d)$}}}] {\scriptsize {\sc Evaluate$\left([s_0,s_1,\dots]\right)$}} + edge from parent [evaluate-edge] + } + } + } + } + child [norm, missing] + % child [norm, missing] + child [norm] {node [action] {$\bar{a}_2$} + % child [norm] { node [label={[label distance=-1mm]right:{\scriptsize $\sim \mathcal{N}_{\bar{a}_2}(\mu,\sigma^2)$}}] {$s_2$} + child [norm] { node [label={[label distance=-1mm]right:{\scriptsize $\sim G(s_0,\bar{a}_2)$}}] {$s_2$} + child [norm] { node [action] {$\bar{a}_6$} } + child [norm] { node [action] {$\bar{a}_7$} } + } + }; +\end{tikzpicture} \ No newline at end of file diff --git a/diagrams/standard-ast-formulation.tex b/diagrams/standard-ast-formulation.tex new file mode 100644 index 0000000..df99c02 --- /dev/null +++ b/diagrams/standard-ast-formulation.tex @@ -0,0 +1,45 @@ +\begin{tikzpicture} + [ + node distance=1.5cm, + every node/.style={font=\large}, + align=center + ] + \tikzset{ + >={Latex[width=2mm,length=2mm]}, + base/.style = {rectangle, rounded corners, draw=black, + minimum width=1cm, minimum height=1cm, + text centered}, + block/.style = {base, minimum width=2.5cm, minimum height=1.5cm}, + envstyle/.style = {block, fill=red!15}, + sutstyle/.style = {block, fill=gray!50}, % fill=blue!10 + simstyle/.style = {base, thick, fill=gray!15, minimum width=4cm}, + metasimstyle/.style = {base, line width=0.07cm, fill=orange!80!gray!40, minimum width=4cm}, + learnerstyle/.style = {block, fill=red!15}, %blue!20 gray!15 + rewardstyle/.style = {block, fill=white}, %green!70!gray!20 %gray!15 + componentstyle/.style = {block, fill=white}, %white + aircraftstyle/.style = {block, draw=none, fill=brown!50!red!30}, + casstyle/.style = {block, fill=orange!50}, + } + \pgfdeclarelayer{metasimlayer} + \pgfdeclarelayer{simlayer} + \pgfdeclarelayer{inputlayer} + \pgfdeclarelayer{blackboxlayer} + \pgfsetlayers{metasimlayer,simlayer,blackboxlayer,inputlayer,main} + + \node (wptdist) [componentstyle] {Environment}; + \node (sut) [sutstyle, right=0.5cm of wptdist] {System\\Under Test}; + + \begin{pgfonlayer}{simlayer} + \path let \p1=(wptdist.north west), \p2=(sut.south east) in node (sim) [fit={($(\x1,\y1)+(-0.5cm,1.25cm)$) ($(\x2,\y2)+(0.5cm,-0.5cm)$)},simstyle,line width=0.08cm]{}; + \node at ($(sim.north west)+(2cm,-7mm)$) [font={\LARGE}] {Simulator $\mathcal{\bar{S}}$}; + \end{pgfonlayer} + + \node (learner) [learnerstyle, above left=0.25cm and 7.25cm of sim.west,xshift=0cm] {Reinforcement\\Learner}; + \node (reward) [rewardstyle, below=1cm of learner,xshift=0cm] {Reward\\Function}; + + \draw[->] (learner) -- (sim.west |- learner) node[pos=0.5,above]{seed $\bar{a}$}; + \draw[->] (reward.north) -- (learner.south) node[pos=0.5,right]{reward $r$}; % DIFF: Changed from "right" to "left" + % \draw[<-] (reward) -| (reward -| sim.south) node[pos=0.5,above]{transition probability $p$,\\event $e$, miss distance $d$}; + % \draw[<-] (reward) -| (sim.south) node[pos=0.25,above]{transition probability $p$,\\event $e$, miss distance $d$}; + \draw[<-] (reward) -- (sim.west |- reward) node[pos=0.5,above]{terminal $\tau$,\\transition probability $p$,\\event $e$, miss distance $d$}; +\end{tikzpicture} \ No newline at end of file diff --git a/diagrams/tangent-angle.tex b/diagrams/tangent-angle.tex new file mode 100644 index 0000000..d705e78 --- /dev/null +++ b/diagrams/tangent-angle.tex @@ -0,0 +1,83 @@ +\begin{tikzpicture} + [ + scale=16, every node/.style={scale=2}, + >=stealth, + point/.style = {draw, circle, fill = black, inner sep = 1pt}, + dot/.style = {draw, circle, fill = black, inner sep = .2pt}, + latlon/.style = {draw, rectangle, minimum width=0.0001mm, minimum height=2mm, fill=white, fill opacity=0.75, fill = black, inner sep = 0.1pt}, + latlonstart/.style = {draw, rectangle, minimum width=0.0001mm, minimum height=2mm, fill = black, inner sep = 0.3pt}, + wpt/.style = {diamond, fill=white, fill opacity=0.75}, + ] + + \tikzstyle{every node}=[font=\Large] + + % the circle + \def\unit{0.5} + \def\rad{0.3} + \def\ang{45} + \def\failang{7} + \def\inner{0.3*\rad} + \def\failinner{0.6*\rad} + + \node (origin) at (0,0) [point, label = {below:$c$}]{}; + + \node (initial) at +(-\unit,\rad) [latlon, label = above:$p$] {}; + \node [rotate=-\failang] (failstart) at +(0, \rad) [latlonstart, red] {}; + \draw[red, rotate around={-\failang:(failstart)}] (failstart) arc (90:\ang:\rad); + + \node (start) at +(0, \rad) [latlonstart, label = above:$s$] {}; + \node [rotate=-\ang] (end) at +(\ang:\rad) [latlon, label ={[label distance=-1mm]above:$e$}] {}; + \node [rotate around={-\failang:(start)}] (failend) at +(\ang:\rad) [rotate=-\ang, latlon,red] {}; + + \node (failorigin) at (0,0) [point, red, rotate around={-\failang:(start)}]{}; + + \draw (start) arc (90:\ang:\rad); + + \draw[-] (initial) -- node (ls) [label = {above:$\ell_1$}] {} (start); + + \draw[dotted,thick,->] (start) -- node (tangent) [label={[label distance=-2.8mm,text=red, xshift=6.5mm, yshift=0.5mm]below right:\large$\theta$}] {} (1.25*\rad,\rad); + + + \draw[dashed] + ($ (origin) ! 1 ! (start) $) + -- ($(start) ! 1 ! (origin)$ ) + node (center) [right,label={[pos=0.35]right:$r$}] {}; + + \draw[dashed] + ($ (origin) ! 1 ! (end) $) + -- ($(end) ! 1 ! (origin)$ ) + node [right] {}; + + \draw[dotted,thick, red] + ($ (failorigin) ! 1 ! (start) $) + -- ($(start) ! 1 ! (failorigin)$ ) + node (center) [right] {}; + + \draw[dotted,thick, red] + ($ (failorigin) ! 1 ! (failend) $) + -- ($(failend) ! 1 ! (failorigin)$ ) + node [right] {}; + + \draw[->, rotate around={\ang:(end)}] (end) -- node (nextstraight) [very near end, label = {above:$\ell_2$},] {} (end |-, 0); + \draw[red, ->, rotate around={\ang-\failang:(failend)}] (failend) -- node (failnextstraight) [red] {} (failend |-, 0); + \draw [red] (1.25*\rad*5.06/7,\rad) arc (0:-\failang*5.06/7:1.25*\rad); % "fail" angle (i.e. kink) + \draw[dotted,thick,->,red, rotate around={-\failang:(start)}] (start) -- node (fail) [] {} (1.25*\rad,\rad); + + % Right angle symbols + \def\ralen{.2ex} % length of the short segment + \foreach \inter/\first/\last in {start/origin/tangent} % , end/origin/nextstraight + { + \draw let \p1 = ($(\inter)!\ralen!(\first)$), % point along first path + \p2 = ($(\inter)!\ralen!(\last)$), % point along second path + \p3 = ($(\p1)+(\p2)-(\inter)$) % corner point + in + (\p1) -- (\p3) -- (\p2) % path + ; + } + + \draw [dashed] (0, \inner) arc (90:\ang:\inner); + \node (innerangle) at +(90-\ang+\ang/1.4:\inner) [label = {[label distance=-3mm]above right:$\alpha$}] {}; + + \node (mid) at +(90-\ang/2:\rad) [draw, wpt, inner sep=1pt, rotate=90-\ang/2] {}; + +\end{tikzpicture} \ No newline at end of file diff --git a/figures/cem_variants/example1b-img0.png b/figures/cem_variants/example1b-img0.png new file mode 100644 index 0000000..c33ab0a Binary files /dev/null and b/figures/cem_variants/example1b-img0.png differ diff --git a/figures/cem_variants/example1b.pgf b/figures/cem_variants/example1b.pgf new file mode 100644 index 0000000..cce446e --- /dev/null +++ b/figures/cem_variants/example1b.pgf @@ -0,0 +1,1919 @@ +%% Creator: Matplotlib, PGF backend +%% +%% To include the figure in your LaTeX document, write +%% \input{.pgf} +%% +%% Make sure the required packages are loaded in your preamble +%% \usepackage{pgf} +%% +%% Figures using additional raster images can only be included by \input if +%% they are in the same directory as the main LaTeX file. For loading figures +%% from other directories you can use the `import` package +%% \usepackage{import} +%% and then include the figures with +%% \import{}{.pgf} +%% +%% Matplotlib used the following preamble +%% \usepackage{fontspec} +%% \setmainfont{DejaVuSans.ttf}[Path=C:/Users/mossr/.julia/conda/3/lib/site-packages/matplotlib/mpl-data/fonts/ttf/] +%% \setsansfont{DejaVuSans.ttf}[Path=C:/Users/mossr/.julia/conda/3/lib/site-packages/matplotlib/mpl-data/fonts/ttf/] +%% \setmonofont{DejaVuSansMono.ttf}[Path=C:/Users/mossr/.julia/conda/3/lib/site-packages/matplotlib/mpl-data/fonts/ttf/] +%% +\begingroup% +\makeatletter% +\begin{pgfpicture}% +% \pgfpathrectangle{\pgfpointorigin}{\pgfqpoint{6.400000in}{4.800000in}}% +\pgfpathrectangle{\pgfqpoint{1.0in}{0.0in}}{\pgfqpoint{4.0in}{4.8in}}% +\pgfusepath{use as bounding box, clip}% +\begin{pgfscope}% +\pgfsetbuttcap% +\pgfsetmiterjoin% +\definecolor{currentfill}{rgb}{1.000000,1.000000,1.000000}% +\pgfsetfillcolor{currentfill}% +\pgfsetlinewidth{0.000000pt}% +\definecolor{currentstroke}{rgb}{1.000000,1.000000,1.000000}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}% +\pgfpathlineto{\pgfqpoint{6.400000in}{0.000000in}}% +\pgfpathlineto{\pgfqpoint{6.400000in}{4.800000in}}% +\pgfpathlineto{\pgfqpoint{0.000000in}{4.800000in}}% +\pgfpathclose% +\pgfusepath{fill}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsetbuttcap% +\pgfsetmiterjoin% +\definecolor{currentfill}{rgb}{1.000000,1.000000,1.000000}% +\pgfsetfillcolor{currentfill}% +\pgfsetlinewidth{0.000000pt}% +\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetstrokeopacity{0.000000}% +\pgfsetdash{}{0pt}% +\pgfpathmoveto{\pgfqpoint{1.432000in}{0.528000in}}% +\pgfpathlineto{\pgfqpoint{5.128000in}{0.528000in}}% +\pgfpathlineto{\pgfqpoint{5.128000in}{4.224000in}}% +\pgfpathlineto{\pgfqpoint{1.432000in}{4.224000in}}% +\pgfpathclose% +\pgfusepath{fill}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfpathrectangle{\pgfqpoint{1.432000in}{0.528000in}}{\pgfqpoint{3.696000in}{3.696000in}}% +\pgfusepath{clip}% +\pgfsys@transformshift{1.432000in}{0.528000in}% +\pgftext[left,bottom]{\pgfimage[interpolate=true,width=3.700000in,height=3.700000in]{figures/cem_variants/example1b-img0.png}}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfpathrectangle{\pgfqpoint{1.432000in}{0.528000in}}{\pgfqpoint{3.696000in}{3.696000in}}% +\pgfusepath{clip}% +\pgfsetbuttcap% +\pgfsetroundjoin% +\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetfillcolor{currentfill}% +\pgfsetlinewidth{0.501875pt}% +\definecolor{currentstroke}{rgb}{1.000000,1.000000,1.000000}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfsys@defobject{currentmarker}{\pgfqpoint{-0.018373in}{-0.018373in}}{\pgfqpoint{0.018373in}{0.018373in}}{% +\pgfpathmoveto{\pgfqpoint{0.000000in}{-0.018373in}}% +\pgfpathcurveto{\pgfqpoint{0.004873in}{-0.018373in}}{\pgfqpoint{0.009546in}{-0.016437in}}{\pgfqpoint{0.012992in}{-0.012992in}}% +\pgfpathcurveto{\pgfqpoint{0.016437in}{-0.009546in}}{\pgfqpoint{0.018373in}{-0.004873in}}{\pgfqpoint{0.018373in}{0.000000in}}% +\pgfpathcurveto{\pgfqpoint{0.018373in}{0.004873in}}{\pgfqpoint{0.016437in}{0.009546in}}{\pgfqpoint{0.012992in}{0.012992in}}% +\pgfpathcurveto{\pgfqpoint{0.009546in}{0.016437in}}{\pgfqpoint{0.004873in}{0.018373in}}{\pgfqpoint{0.000000in}{0.018373in}}% +\pgfpathcurveto{\pgfqpoint{-0.004873in}{0.018373in}}{\pgfqpoint{-0.009546in}{0.016437in}}{\pgfqpoint{-0.012992in}{0.012992in}}% +\pgfpathcurveto{\pgfqpoint{-0.016437in}{0.009546in}}{\pgfqpoint{-0.018373in}{0.004873in}}{\pgfqpoint{-0.018373in}{0.000000in}}% +\pgfpathcurveto{\pgfqpoint{-0.018373in}{-0.004873in}}{\pgfqpoint{-0.016437in}{-0.009546in}}{\pgfqpoint{-0.012992in}{-0.012992in}}% +\pgfpathcurveto{\pgfqpoint{-0.009546in}{-0.016437in}}{\pgfqpoint{-0.004873in}{-0.018373in}}{\pgfqpoint{0.000000in}{-0.018373in}}% +\pgfpathclose% +\pgfusepath{stroke,fill}% +}% +\begin{pgfscope}% +\pgfsys@transformshift{3.466250in}{2.684576in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfpathrectangle{\pgfqpoint{1.432000in}{0.528000in}}{\pgfqpoint{3.696000in}{3.696000in}}% +\pgfusepath{clip}% +\pgfsetbuttcap% +\pgfsetroundjoin% +\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetfillcolor{currentfill}% +\pgfsetlinewidth{0.501875pt}% +\definecolor{currentstroke}{rgb}{1.000000,1.000000,1.000000}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfsys@defobject{currentmarker}{\pgfqpoint{-0.018373in}{-0.018373in}}{\pgfqpoint{0.018373in}{0.018373in}}{% +\pgfpathmoveto{\pgfqpoint{0.000000in}{-0.018373in}}% +\pgfpathcurveto{\pgfqpoint{0.004873in}{-0.018373in}}{\pgfqpoint{0.009546in}{-0.016437in}}{\pgfqpoint{0.012992in}{-0.012992in}}% +\pgfpathcurveto{\pgfqpoint{0.016437in}{-0.009546in}}{\pgfqpoint{0.018373in}{-0.004873in}}{\pgfqpoint{0.018373in}{0.000000in}}% +\pgfpathcurveto{\pgfqpoint{0.018373in}{0.004873in}}{\pgfqpoint{0.016437in}{0.009546in}}{\pgfqpoint{0.012992in}{0.012992in}}% +\pgfpathcurveto{\pgfqpoint{0.009546in}{0.016437in}}{\pgfqpoint{0.004873in}{0.018373in}}{\pgfqpoint{0.000000in}{0.018373in}}% +\pgfpathcurveto{\pgfqpoint{-0.004873in}{0.018373in}}{\pgfqpoint{-0.009546in}{0.016437in}}{\pgfqpoint{-0.012992in}{0.012992in}}% +\pgfpathcurveto{\pgfqpoint{-0.016437in}{0.009546in}}{\pgfqpoint{-0.018373in}{0.004873in}}{\pgfqpoint{-0.018373in}{0.000000in}}% +\pgfpathcurveto{\pgfqpoint{-0.018373in}{-0.004873in}}{\pgfqpoint{-0.016437in}{-0.009546in}}{\pgfqpoint{-0.012992in}{-0.012992in}}% +\pgfpathcurveto{\pgfqpoint{-0.009546in}{-0.016437in}}{\pgfqpoint{-0.004873in}{-0.018373in}}{\pgfqpoint{0.000000in}{-0.018373in}}% +\pgfpathclose% +\pgfusepath{stroke,fill}% +}% +\begin{pgfscope}% +\pgfsys@transformshift{2.179973in}{2.119944in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfpathrectangle{\pgfqpoint{1.432000in}{0.528000in}}{\pgfqpoint{3.696000in}{3.696000in}}% +\pgfusepath{clip}% +\pgfsetbuttcap% +\pgfsetroundjoin% +\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetfillcolor{currentfill}% +\pgfsetlinewidth{0.501875pt}% +\definecolor{currentstroke}{rgb}{1.000000,1.000000,1.000000}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfsys@defobject{currentmarker}{\pgfqpoint{-0.018373in}{-0.018373in}}{\pgfqpoint{0.018373in}{0.018373in}}{% +\pgfpathmoveto{\pgfqpoint{0.000000in}{-0.018373in}}% +\pgfpathcurveto{\pgfqpoint{0.004873in}{-0.018373in}}{\pgfqpoint{0.009546in}{-0.016437in}}{\pgfqpoint{0.012992in}{-0.012992in}}% +\pgfpathcurveto{\pgfqpoint{0.016437in}{-0.009546in}}{\pgfqpoint{0.018373in}{-0.004873in}}{\pgfqpoint{0.018373in}{0.000000in}}% +\pgfpathcurveto{\pgfqpoint{0.018373in}{0.004873in}}{\pgfqpoint{0.016437in}{0.009546in}}{\pgfqpoint{0.012992in}{0.012992in}}% +\pgfpathcurveto{\pgfqpoint{0.009546in}{0.016437in}}{\pgfqpoint{0.004873in}{0.018373in}}{\pgfqpoint{0.000000in}{0.018373in}}% +\pgfpathcurveto{\pgfqpoint{-0.004873in}{0.018373in}}{\pgfqpoint{-0.009546in}{0.016437in}}{\pgfqpoint{-0.012992in}{0.012992in}}% +\pgfpathcurveto{\pgfqpoint{-0.016437in}{0.009546in}}{\pgfqpoint{-0.018373in}{0.004873in}}{\pgfqpoint{-0.018373in}{0.000000in}}% +\pgfpathcurveto{\pgfqpoint{-0.018373in}{-0.004873in}}{\pgfqpoint{-0.016437in}{-0.009546in}}{\pgfqpoint{-0.012992in}{-0.012992in}}% +\pgfpathcurveto{\pgfqpoint{-0.009546in}{-0.016437in}}{\pgfqpoint{-0.004873in}{-0.018373in}}{\pgfqpoint{0.000000in}{-0.018373in}}% +\pgfpathclose% +\pgfusepath{stroke,fill}% +}% +\begin{pgfscope}% +\pgfsys@transformshift{1.833019in}{2.582119in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfpathrectangle{\pgfqpoint{1.432000in}{0.528000in}}{\pgfqpoint{3.696000in}{3.696000in}}% +\pgfusepath{clip}% +\pgfsetbuttcap% +\pgfsetroundjoin% +\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetfillcolor{currentfill}% +\pgfsetlinewidth{0.501875pt}% +\definecolor{currentstroke}{rgb}{1.000000,1.000000,1.000000}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfsys@defobject{currentmarker}{\pgfqpoint{-0.018373in}{-0.018373in}}{\pgfqpoint{0.018373in}{0.018373in}}{% +\pgfpathmoveto{\pgfqpoint{0.000000in}{-0.018373in}}% +\pgfpathcurveto{\pgfqpoint{0.004873in}{-0.018373in}}{\pgfqpoint{0.009546in}{-0.016437in}}{\pgfqpoint{0.012992in}{-0.012992in}}% +\pgfpathcurveto{\pgfqpoint{0.016437in}{-0.009546in}}{\pgfqpoint{0.018373in}{-0.004873in}}{\pgfqpoint{0.018373in}{0.000000in}}% +\pgfpathcurveto{\pgfqpoint{0.018373in}{0.004873in}}{\pgfqpoint{0.016437in}{0.009546in}}{\pgfqpoint{0.012992in}{0.012992in}}% +\pgfpathcurveto{\pgfqpoint{0.009546in}{0.016437in}}{\pgfqpoint{0.004873in}{0.018373in}}{\pgfqpoint{0.000000in}{0.018373in}}% +\pgfpathcurveto{\pgfqpoint{-0.004873in}{0.018373in}}{\pgfqpoint{-0.009546in}{0.016437in}}{\pgfqpoint{-0.012992in}{0.012992in}}% +\pgfpathcurveto{\pgfqpoint{-0.016437in}{0.009546in}}{\pgfqpoint{-0.018373in}{0.004873in}}{\pgfqpoint{-0.018373in}{0.000000in}}% +\pgfpathcurveto{\pgfqpoint{-0.018373in}{-0.004873in}}{\pgfqpoint{-0.016437in}{-0.009546in}}{\pgfqpoint{-0.012992in}{-0.012992in}}% +\pgfpathcurveto{\pgfqpoint{-0.009546in}{-0.016437in}}{\pgfqpoint{-0.004873in}{-0.018373in}}{\pgfqpoint{0.000000in}{-0.018373in}}% +\pgfpathclose% +\pgfusepath{stroke,fill}% +}% +\begin{pgfscope}% +\pgfsys@transformshift{6.337699in}{-1.123539in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfpathrectangle{\pgfqpoint{1.432000in}{0.528000in}}{\pgfqpoint{3.696000in}{3.696000in}}% +\pgfusepath{clip}% +\pgfsetbuttcap% +\pgfsetroundjoin% +\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetfillcolor{currentfill}% +\pgfsetlinewidth{0.501875pt}% +\definecolor{currentstroke}{rgb}{1.000000,1.000000,1.000000}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfsys@defobject{currentmarker}{\pgfqpoint{-0.018373in}{-0.018373in}}{\pgfqpoint{0.018373in}{0.018373in}}{% +\pgfpathmoveto{\pgfqpoint{0.000000in}{-0.018373in}}% 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+\pgfpathcurveto{\pgfqpoint{0.004873in}{-0.018373in}}{\pgfqpoint{0.009546in}{-0.016437in}}{\pgfqpoint{0.012992in}{-0.012992in}}% +\pgfpathcurveto{\pgfqpoint{0.016437in}{-0.009546in}}{\pgfqpoint{0.018373in}{-0.004873in}}{\pgfqpoint{0.018373in}{0.000000in}}% +\pgfpathcurveto{\pgfqpoint{0.018373in}{0.004873in}}{\pgfqpoint{0.016437in}{0.009546in}}{\pgfqpoint{0.012992in}{0.012992in}}% +\pgfpathcurveto{\pgfqpoint{0.009546in}{0.016437in}}{\pgfqpoint{0.004873in}{0.018373in}}{\pgfqpoint{0.000000in}{0.018373in}}% +\pgfpathcurveto{\pgfqpoint{-0.004873in}{0.018373in}}{\pgfqpoint{-0.009546in}{0.016437in}}{\pgfqpoint{-0.012992in}{0.012992in}}% +\pgfpathcurveto{\pgfqpoint{-0.016437in}{0.009546in}}{\pgfqpoint{-0.018373in}{0.004873in}}{\pgfqpoint{-0.018373in}{0.000000in}}% +\pgfpathcurveto{\pgfqpoint{-0.018373in}{-0.004873in}}{\pgfqpoint{-0.016437in}{-0.009546in}}{\pgfqpoint{-0.012992in}{-0.012992in}}% +\pgfpathcurveto{\pgfqpoint{-0.009546in}{-0.016437in}}{\pgfqpoint{-0.004873in}{-0.018373in}}{\pgfqpoint{0.000000in}{-0.018373in}}% +\pgfpathclose% +\pgfusepath{stroke,fill}% +}% +\begin{pgfscope}% +\pgfsys@transformshift{3.767108in}{3.388022in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{3.854908in}{3.232338in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{3.489383in}{3.552502in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{4.153498in}{3.221645in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{3.721939in}{3.052866in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{3.561904in}{3.105633in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{3.727049in}{3.004720in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{3.459884in}{3.094646in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{4.002040in}{2.926700in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{3.228311in}{3.985264in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{3.198559in}{3.058850in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{3.207265in}{3.035694in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{3.411530in}{2.795680in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{2.958975in}{3.226432in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{3.340771in}{4.324225in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{3.555160in}{2.594930in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{2.942991in}{3.892008in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{2.937226in}{3.931172in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{3.342402in}{2.602734in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{3.256282in}{2.645427in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{2.947868in}{4.056552in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{3.140240in}{2.626219in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{4.994570in}{3.185911in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{4.800802in}{4.275234in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{3.966170in}{4.874295in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{2.445224in}{3.575034in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{2.655100in}{4.289596in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{4.044445in}{5.023445in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{3.474291in}{1.988683in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{4.184926in}{1.888257in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{4.742332in}{4.968778in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{5.532920in}{4.003333in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{2.131186in}{3.031635in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{2.364746in}{2.447749in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{4.849666in}{1.897394in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{3.613073in}{1.636745in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{2.932568in}{1.844445in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{3.126227in}{1.745650in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{3.985167in}{1.489676in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{2.465834in}{2.019474in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{1.817167in}{3.758263in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{2.995454in}{1.615970in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{4.474361in}{1.422929in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{4.697693in}{1.437104in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{4.688725in}{1.409013in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{2.906429in}{1.467928in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{2.853665in}{1.487905in}% 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+\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfsys@defobject{currentmarker}{\pgfqpoint{0.000000in}{-0.048611in}}{\pgfqpoint{0.000000in}{0.000000in}}{% +\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}% +\pgfpathlineto{\pgfqpoint{0.000000in}{-0.048611in}}% +\pgfusepath{stroke,fill}% +}% +\begin{pgfscope}% +\pgfsys@transformshift{2.074783in}{0.528000in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\end{pgfscope}% +\begin{pgfscope}% +\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetstrokecolor{textcolor}% +\pgfsetfillcolor{textcolor}% +\pgftext[x=2.074783in,y=0.430778in,,top]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle -80\)}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsetbuttcap% +\pgfsetroundjoin% +\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetfillcolor{currentfill}% +\pgfsetlinewidth{0.803000pt}% 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+\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfsys@defobject{currentmarker}{\pgfqpoint{0.000000in}{-0.048611in}}{\pgfqpoint{0.000000in}{0.000000in}}{% +\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}% +\pgfpathlineto{\pgfqpoint{0.000000in}{-0.048611in}}% +\pgfusepath{stroke,fill}% +}% +\begin{pgfscope}% +\pgfsys@transformshift{3.360348in}{0.528000in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\end{pgfscope}% +\begin{pgfscope}% +\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetstrokecolor{textcolor}% +\pgfsetfillcolor{textcolor}% +\pgftext[x=3.360348in,y=0.430778in,,top]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle -40\)}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsetbuttcap% +\pgfsetroundjoin% +\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetfillcolor{currentfill}% +\pgfsetlinewidth{0.803000pt}% +\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfsys@defobject{currentmarker}{\pgfqpoint{0.000000in}{-0.048611in}}{\pgfqpoint{0.000000in}{0.000000in}}{% +\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}% +\pgfpathlineto{\pgfqpoint{0.000000in}{-0.048611in}}% +\pgfusepath{stroke,fill}% +}% +\begin{pgfscope}% +\pgfsys@transformshift{4.003130in}{0.528000in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\end{pgfscope}% +\begin{pgfscope}% +\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetstrokecolor{textcolor}% +\pgfsetfillcolor{textcolor}% +\pgftext[x=4.003130in,y=0.430778in,,top]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle -20\)}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsetbuttcap% +\pgfsetroundjoin% +\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetfillcolor{currentfill}% +\pgfsetlinewidth{0.803000pt}% +\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfsys@defobject{currentmarker}{\pgfqpoint{0.000000in}{-0.048611in}}{\pgfqpoint{0.000000in}{0.000000in}}{% +\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}% +\pgfpathlineto{\pgfqpoint{0.000000in}{-0.048611in}}% +\pgfusepath{stroke,fill}% +}% +\begin{pgfscope}% +\pgfsys@transformshift{4.645913in}{0.528000in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\end{pgfscope}% +\begin{pgfscope}% +\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetstrokecolor{textcolor}% +\pgfsetfillcolor{textcolor}% +\pgftext[x=4.645913in,y=0.430778in,,top]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle 0\)}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsetbuttcap% +\pgfsetroundjoin% +\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetfillcolor{currentfill}% +\pgfsetlinewidth{0.803000pt}% +\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfsys@defobject{currentmarker}{\pgfqpoint{-0.048611in}{0.000000in}}{\pgfqpoint{0.000000in}{0.000000in}}{% +\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}% +\pgfpathlineto{\pgfqpoint{-0.048611in}{0.000000in}}% +\pgfusepath{stroke,fill}% +}% +\begin{pgfscope}% +\pgfsys@transformshift{1.432000in}{0.528000in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\end{pgfscope}% +\begin{pgfscope}% +\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetstrokecolor{textcolor}% +\pgfsetfillcolor{textcolor}% +\pgftext[x=1.018419in,y=0.475238in,left,base]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle -100\)}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsetbuttcap% +\pgfsetroundjoin% +\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetfillcolor{currentfill}% +\pgfsetlinewidth{0.803000pt}% +\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfsys@defobject{currentmarker}{\pgfqpoint{-0.048611in}{0.000000in}}{\pgfqpoint{0.000000in}{0.000000in}}{% +\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}% +\pgfpathlineto{\pgfqpoint{-0.048611in}{0.000000in}}% +\pgfusepath{stroke,fill}% +}% +\begin{pgfscope}% +\pgfsys@transformshift{1.432000in}{1.170783in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\end{pgfscope}% +\begin{pgfscope}% +\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetstrokecolor{textcolor}% +\pgfsetfillcolor{textcolor}% +\pgftext[x=1.087863in,y=1.118021in,left,base]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle -80\)}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsetbuttcap% +\pgfsetroundjoin% +\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetfillcolor{currentfill}% +\pgfsetlinewidth{0.803000pt}% +\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfsys@defobject{currentmarker}{\pgfqpoint{-0.048611in}{0.000000in}}{\pgfqpoint{0.000000in}{0.000000in}}{% +\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}% +\pgfpathlineto{\pgfqpoint{-0.048611in}{0.000000in}}% +\pgfusepath{stroke,fill}% +}% +\begin{pgfscope}% +\pgfsys@transformshift{1.432000in}{1.813565in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\end{pgfscope}% +\begin{pgfscope}% +\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetstrokecolor{textcolor}% +\pgfsetfillcolor{textcolor}% +\pgftext[x=1.087863in,y=1.760804in,left,base]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle -60\)}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsetbuttcap% +\pgfsetroundjoin% +\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetfillcolor{currentfill}% +\pgfsetlinewidth{0.803000pt}% +\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfsys@defobject{currentmarker}{\pgfqpoint{-0.048611in}{0.000000in}}{\pgfqpoint{0.000000in}{0.000000in}}{% +\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}% +\pgfpathlineto{\pgfqpoint{-0.048611in}{0.000000in}}% +\pgfusepath{stroke,fill}% +}% +\begin{pgfscope}% +\pgfsys@transformshift{1.432000in}{2.456348in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\end{pgfscope}% +\begin{pgfscope}% +\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetstrokecolor{textcolor}% +\pgfsetfillcolor{textcolor}% +\pgftext[x=1.087863in,y=2.403586in,left,base]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle -40\)}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsetbuttcap% +\pgfsetroundjoin% +\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetfillcolor{currentfill}% +\pgfsetlinewidth{0.803000pt}% +\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfsys@defobject{currentmarker}{\pgfqpoint{-0.048611in}{0.000000in}}{\pgfqpoint{0.000000in}{0.000000in}}{% +\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}% +\pgfpathlineto{\pgfqpoint{-0.048611in}{0.000000in}}% +\pgfusepath{stroke,fill}% +}% +\begin{pgfscope}% +\pgfsys@transformshift{1.432000in}{3.099130in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\end{pgfscope}% +\begin{pgfscope}% +\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetstrokecolor{textcolor}% +\pgfsetfillcolor{textcolor}% +\pgftext[x=1.087863in,y=3.046369in,left,base]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle -20\)}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsetbuttcap% +\pgfsetroundjoin% +\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetfillcolor{currentfill}% +\pgfsetlinewidth{0.803000pt}% +\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfsys@defobject{currentmarker}{\pgfqpoint{-0.048611in}{0.000000in}}{\pgfqpoint{0.000000in}{0.000000in}}{% +\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}% +\pgfpathlineto{\pgfqpoint{-0.048611in}{0.000000in}}% +\pgfusepath{stroke,fill}% +}% +\begin{pgfscope}% +\pgfsys@transformshift{1.432000in}{3.741913in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\end{pgfscope}% +\begin{pgfscope}% +\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetstrokecolor{textcolor}% +\pgfsetfillcolor{textcolor}% +\pgftext[x=1.265333in,y=3.689152in,left,base]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle 0\)}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfpathrectangle{\pgfqpoint{1.432000in}{0.528000in}}{\pgfqpoint{3.696000in}{3.696000in}}% +\pgfusepath{clip}% +\pgfsetbuttcap% +\pgfsetroundjoin% +\pgfsetlinewidth{1.505625pt}% 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b/figures/cem_variants/k5_ce_mixture-img0.png differ diff --git a/figures/cem_variants/k5_ce_mixture.pgf b/figures/cem_variants/k5_ce_mixture.pgf new file mode 100644 index 0000000..d5fdb02 --- /dev/null +++ b/figures/cem_variants/k5_ce_mixture.pgf @@ -0,0 +1,1507 @@ +%% Creator: Matplotlib, PGF backend +%% +%% To include the figure in your LaTeX document, write +%% \input{.pgf} +%% +%% Make sure the required packages are loaded in your preamble +%% \usepackage{pgf} +%% +%% Figures using additional raster images can only be included by \input if +%% they are in the same directory as the main LaTeX file. For loading figures +%% from other directories you can use the `import` package +%% \usepackage{import} +%% and then include the figures with +%% \import{}{.pgf} +%% +%% Matplotlib used the following preamble +%% \usepackage{fontspec} +%% \setmainfont{DejaVuSans.ttf}[Path=C:/Users/mossr/.julia/conda/3/lib/site-packages/matplotlib/mpl-data/fonts/ttf/] +%% \setsansfont{DejaVuSans.ttf}[Path=C:/Users/mossr/.julia/conda/3/lib/site-packages/matplotlib/mpl-data/fonts/ttf/] +%% \setmonofont{DejaVuSansMono.ttf}[Path=C:/Users/mossr/.julia/conda/3/lib/site-packages/matplotlib/mpl-data/fonts/ttf/] +%% +\begingroup% +\makeatletter% +\begin{pgfpicture}% +% \pgfpathrectangle{\pgfpointorigin}{\pgfqpoint{5.400000in}{4.800000in}}% +% \pgfpathrectangle{\pgfqpoint{1.432000in}{0.0in}}{\pgfqpoint{3.696000in}{4.0in}}% +\pgfpathrectangle{\pgfqpoint{1.0in}{0.0in}}{\pgfqpoint{4.0in}{4.5in}}% +\pgfusepath{use as bounding box, clip}% +\begin{pgfscope}% +\pgfsetbuttcap% +\pgfsetmiterjoin% 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+\pgfpathcurveto{\pgfqpoint{0.004873in}{-0.018373in}}{\pgfqpoint{0.009546in}{-0.016437in}}{\pgfqpoint{0.012992in}{-0.012992in}}% +\pgfpathcurveto{\pgfqpoint{0.016437in}{-0.009546in}}{\pgfqpoint{0.018373in}{-0.004873in}}{\pgfqpoint{0.018373in}{0.000000in}}% +\pgfpathcurveto{\pgfqpoint{0.018373in}{0.004873in}}{\pgfqpoint{0.016437in}{0.009546in}}{\pgfqpoint{0.012992in}{0.012992in}}% +\pgfpathcurveto{\pgfqpoint{0.009546in}{0.016437in}}{\pgfqpoint{0.004873in}{0.018373in}}{\pgfqpoint{0.000000in}{0.018373in}}% +\pgfpathcurveto{\pgfqpoint{-0.004873in}{0.018373in}}{\pgfqpoint{-0.009546in}{0.016437in}}{\pgfqpoint{-0.012992in}{0.012992in}}% +\pgfpathcurveto{\pgfqpoint{-0.016437in}{0.009546in}}{\pgfqpoint{-0.018373in}{0.004873in}}{\pgfqpoint{-0.018373in}{0.000000in}}% +\pgfpathcurveto{\pgfqpoint{-0.018373in}{-0.004873in}}{\pgfqpoint{-0.016437in}{-0.009546in}}{\pgfqpoint{-0.012992in}{-0.012992in}}% +\pgfpathcurveto{\pgfqpoint{-0.009546in}{-0.016437in}}{\pgfqpoint{-0.004873in}{-0.018373in}}{\pgfqpoint{0.000000in}{-0.018373in}}% +\pgfpathclose% +\pgfusepath{stroke,fill}% +}% +\begin{pgfscope}% +\pgfsys@transformshift{3.098016in}{2.689295in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfpathrectangle{\pgfqpoint{1.432000in}{0.528000in}}{\pgfqpoint{3.696000in}{3.696000in}}% +\pgfusepath{clip}% +\pgfsetbuttcap% +\pgfsetroundjoin% +\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetfillcolor{currentfill}% +\pgfsetlinewidth{0.501875pt}% +\definecolor{currentstroke}{rgb}{1.000000,1.000000,1.000000}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfsys@defobject{currentmarker}{\pgfqpoint{-0.018373in}{-0.018373in}}{\pgfqpoint{0.018373in}{0.018373in}}{% +\pgfpathmoveto{\pgfqpoint{0.000000in}{-0.018373in}}% +\pgfpathcurveto{\pgfqpoint{0.004873in}{-0.018373in}}{\pgfqpoint{0.009546in}{-0.016437in}}{\pgfqpoint{0.012992in}{-0.012992in}}% +\pgfpathcurveto{\pgfqpoint{0.016437in}{-0.009546in}}{\pgfqpoint{0.018373in}{-0.004873in}}{\pgfqpoint{0.018373in}{0.000000in}}% +\pgfpathcurveto{\pgfqpoint{0.018373in}{0.004873in}}{\pgfqpoint{0.016437in}{0.009546in}}{\pgfqpoint{0.012992in}{0.012992in}}% +\pgfpathcurveto{\pgfqpoint{0.009546in}{0.016437in}}{\pgfqpoint{0.004873in}{0.018373in}}{\pgfqpoint{0.000000in}{0.018373in}}% +\pgfpathcurveto{\pgfqpoint{-0.004873in}{0.018373in}}{\pgfqpoint{-0.009546in}{0.016437in}}{\pgfqpoint{-0.012992in}{0.012992in}}% +\pgfpathcurveto{\pgfqpoint{-0.016437in}{0.009546in}}{\pgfqpoint{-0.018373in}{0.004873in}}{\pgfqpoint{-0.018373in}{0.000000in}}% +\pgfpathcurveto{\pgfqpoint{-0.018373in}{-0.004873in}}{\pgfqpoint{-0.016437in}{-0.009546in}}{\pgfqpoint{-0.012992in}{-0.012992in}}% +\pgfpathcurveto{\pgfqpoint{-0.009546in}{-0.016437in}}{\pgfqpoint{-0.004873in}{-0.018373in}}{\pgfqpoint{0.000000in}{-0.018373in}}% +\pgfpathclose% +\pgfusepath{stroke,fill}% +}% +\begin{pgfscope}% +\pgfsys@transformshift{3.366879in}{2.207284in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfpathrectangle{\pgfqpoint{1.432000in}{0.528000in}}{\pgfqpoint{3.696000in}{3.696000in}}% +\pgfusepath{clip}% +\pgfsetbuttcap% +\pgfsetroundjoin% +\definecolor{currentfill}{rgb}{1.000000,1.000000,1.000000}% +\pgfsetfillcolor{currentfill}% +\pgfsetlinewidth{0.501875pt}% +\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfsys@defobject{currentmarker}{\pgfqpoint{-0.018373in}{-0.018373in}}{\pgfqpoint{0.018373in}{0.018373in}}{% +\pgfpathmoveto{\pgfqpoint{0.000000in}{-0.018373in}}% +\pgfpathcurveto{\pgfqpoint{0.004873in}{-0.018373in}}{\pgfqpoint{0.009546in}{-0.016437in}}{\pgfqpoint{0.012992in}{-0.012992in}}% +\pgfpathcurveto{\pgfqpoint{0.016437in}{-0.009546in}}{\pgfqpoint{0.018373in}{-0.004873in}}{\pgfqpoint{0.018373in}{0.000000in}}% +\pgfpathcurveto{\pgfqpoint{0.018373in}{0.004873in}}{\pgfqpoint{0.016437in}{0.009546in}}{\pgfqpoint{0.012992in}{0.012992in}}% +\pgfpathcurveto{\pgfqpoint{0.009546in}{0.016437in}}{\pgfqpoint{0.004873in}{0.018373in}}{\pgfqpoint{0.000000in}{0.018373in}}% +\pgfpathcurveto{\pgfqpoint{-0.004873in}{0.018373in}}{\pgfqpoint{-0.009546in}{0.016437in}}{\pgfqpoint{-0.012992in}{0.012992in}}% +\pgfpathcurveto{\pgfqpoint{-0.016437in}{0.009546in}}{\pgfqpoint{-0.018373in}{0.004873in}}{\pgfqpoint{-0.018373in}{0.000000in}}% +\pgfpathcurveto{\pgfqpoint{-0.018373in}{-0.004873in}}{\pgfqpoint{-0.016437in}{-0.009546in}}{\pgfqpoint{-0.012992in}{-0.012992in}}% +\pgfpathcurveto{\pgfqpoint{-0.009546in}{-0.016437in}}{\pgfqpoint{-0.004873in}{-0.018373in}}{\pgfqpoint{0.000000in}{-0.018373in}}% +\pgfpathclose% +\pgfusepath{stroke,fill}% +}% +\begin{pgfscope}% +\pgfsys@transformshift{3.021506in}{2.604746in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{3.009619in}{2.610965in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{3.018887in}{2.642049in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{3.069656in}{2.587416in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{3.050345in}{2.668062in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{3.081278in}{2.634503in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{2.983145in}{2.595159in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{3.074851in}{2.663159in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{3.098658in}{2.597833in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{2.984381in}{2.675848in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{3.045474in}{2.693191in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{3.022118in}{2.699820in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{3.015609in}{2.702288in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{2.951934in}{2.600127in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{2.990125in}{2.545969in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{3.010441in}{2.710598in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{2.939820in}{2.612396in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{3.441894in}{2.170245in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{2.942339in}{2.679866in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{3.428978in}{2.136618in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{3.038084in}{2.730931in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{2.918428in}{2.631070in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{2.998621in}{2.732027in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{2.923882in}{2.582483in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{3.455832in}{2.210247in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{3.059775in}{2.741471in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{3.421590in}{2.182776in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{3.408426in}{2.143282in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{3.409622in}{2.102582in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{3.429322in}{2.203323in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{3.416081in}{2.184684in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{3.416886in}{2.192563in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{3.499057in}{2.254026in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{3.457462in}{2.236776in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{2.972485in}{2.749780in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{3.401035in}{2.174406in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{3.393417in}{2.164338in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{3.387745in}{2.132571in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{3.402907in}{2.193613in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{3.395123in}{2.179427in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{3.422308in}{2.225725in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{3.446402in}{2.250169in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{2.872313in}{2.599845in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{3.650728in}{2.769778in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{3.385703in}{2.182308in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{3.552798in}{2.280984in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{3.150187in}{2.724315in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{3.140142in}{2.739202in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{3.372249in}{2.121401in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{2.869300in}{2.703402in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfpathrectangle{\pgfqpoint{1.432000in}{0.528000in}}{\pgfqpoint{3.696000in}{3.696000in}}% +\pgfusepath{clip}% +\pgfsetbuttcap% +\pgfsetroundjoin% +\definecolor{currentfill}{rgb}{1.000000,0.000000,0.000000}% +\pgfsetfillcolor{currentfill}% +\pgfsetlinewidth{0.501875pt}% +\definecolor{currentstroke}{rgb}{1.000000,1.000000,1.000000}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfsys@defobject{currentmarker}{\pgfqpoint{-0.018373in}{-0.018373in}}{\pgfqpoint{0.018373in}{0.018373in}}{% +\pgfpathmoveto{\pgfqpoint{0.000000in}{-0.018373in}}% +\pgfpathcurveto{\pgfqpoint{0.004873in}{-0.018373in}}{\pgfqpoint{0.009546in}{-0.016437in}}{\pgfqpoint{0.012992in}{-0.012992in}}% +\pgfpathcurveto{\pgfqpoint{0.016437in}{-0.009546in}}{\pgfqpoint{0.018373in}{-0.004873in}}{\pgfqpoint{0.018373in}{0.000000in}}% +\pgfpathcurveto{\pgfqpoint{0.018373in}{0.004873in}}{\pgfqpoint{0.016437in}{0.009546in}}{\pgfqpoint{0.012992in}{0.012992in}}% +\pgfpathcurveto{\pgfqpoint{0.009546in}{0.016437in}}{\pgfqpoint{0.004873in}{0.018373in}}{\pgfqpoint{0.000000in}{0.018373in}}% +\pgfpathcurveto{\pgfqpoint{-0.004873in}{0.018373in}}{\pgfqpoint{-0.009546in}{0.016437in}}{\pgfqpoint{-0.012992in}{0.012992in}}% +\pgfpathcurveto{\pgfqpoint{-0.016437in}{0.009546in}}{\pgfqpoint{-0.018373in}{0.004873in}}{\pgfqpoint{-0.018373in}{0.000000in}}% +\pgfpathcurveto{\pgfqpoint{-0.018373in}{-0.004873in}}{\pgfqpoint{-0.016437in}{-0.009546in}}{\pgfqpoint{-0.012992in}{-0.012992in}}% +\pgfpathcurveto{\pgfqpoint{-0.009546in}{-0.016437in}}{\pgfqpoint{-0.004873in}{-0.018373in}}{\pgfqpoint{0.000000in}{-0.018373in}}% +\pgfpathclose% +\pgfusepath{stroke,fill}% +}% +\begin{pgfscope}% +\pgfsys@transformshift{3.050309in}{2.661601in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{3.098016in}{2.689295in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{3.413110in}{2.166836in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{3.128731in}{2.707201in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{3.573224in}{2.250984in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsetbuttcap% +\pgfsetroundjoin% +\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetfillcolor{currentfill}% +\pgfsetlinewidth{0.803000pt}% +\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfsys@defobject{currentmarker}{\pgfqpoint{0.000000in}{-0.048611in}}{\pgfqpoint{0.000000in}{0.000000in}}{% +\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}% +\pgfpathlineto{\pgfqpoint{0.000000in}{-0.048611in}}% +\pgfusepath{stroke,fill}% +}% +\begin{pgfscope}% +\pgfsys@transformshift{1.432000in}{0.528000in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\end{pgfscope}% +\begin{pgfscope}% +\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetstrokecolor{textcolor}% +\pgfsetfillcolor{textcolor}% +\pgftext[x=1.432000in,y=0.430778in,,top]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle -15\)}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsetbuttcap% +\pgfsetroundjoin% +\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetfillcolor{currentfill}% +\pgfsetlinewidth{0.803000pt}% +\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfsys@defobject{currentmarker}{\pgfqpoint{0.000000in}{-0.048611in}}{\pgfqpoint{0.000000in}{0.000000in}}{% +\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}% +\pgfpathlineto{\pgfqpoint{0.000000in}{-0.048611in}}% +\pgfusepath{stroke,fill}% +}% +\begin{pgfscope}% +\pgfsys@transformshift{2.048000in}{0.528000in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\end{pgfscope}% +\begin{pgfscope}% +\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetstrokecolor{textcolor}% +\pgfsetfillcolor{textcolor}% +\pgftext[x=2.048000in,y=0.430778in,,top]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle -10\)}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsetbuttcap% +\pgfsetroundjoin% +\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetfillcolor{currentfill}% +\pgfsetlinewidth{0.803000pt}% 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+\end{pgfpicture}% +\makeatother% +\endgroup% diff --git a/figures/cem_variants/k5_ce_surrogate-img0.png b/figures/cem_variants/k5_ce_surrogate-img0.png new file mode 100644 index 0000000..66eb88a Binary files /dev/null and b/figures/cem_variants/k5_ce_surrogate-img0.png differ diff --git a/figures/cem_variants/k5_ce_surrogate.pgf b/figures/cem_variants/k5_ce_surrogate.pgf new file mode 100644 index 0000000..2b6485b --- /dev/null +++ b/figures/cem_variants/k5_ce_surrogate.pgf @@ -0,0 +1,1635 @@ +%% Creator: Matplotlib, PGF backend +%% +%% To include the figure in your LaTeX document, write +%% \input{.pgf} +%% +%% Make sure the required packages are loaded in your preamble +%% \usepackage{pgf} +%% +%% Figures using additional raster images can only be included by \input if +%% they are in the same directory as the main LaTeX file. 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+\pgfpathcurveto{\pgfqpoint{0.004873in}{-0.018373in}}{\pgfqpoint{0.009546in}{-0.016437in}}{\pgfqpoint{0.012992in}{-0.012992in}}% +\pgfpathcurveto{\pgfqpoint{0.016437in}{-0.009546in}}{\pgfqpoint{0.018373in}{-0.004873in}}{\pgfqpoint{0.018373in}{0.000000in}}% +\pgfpathcurveto{\pgfqpoint{0.018373in}{0.004873in}}{\pgfqpoint{0.016437in}{0.009546in}}{\pgfqpoint{0.012992in}{0.012992in}}% +\pgfpathcurveto{\pgfqpoint{0.009546in}{0.016437in}}{\pgfqpoint{0.004873in}{0.018373in}}{\pgfqpoint{0.000000in}{0.018373in}}% +\pgfpathcurveto{\pgfqpoint{-0.004873in}{0.018373in}}{\pgfqpoint{-0.009546in}{0.016437in}}{\pgfqpoint{-0.012992in}{0.012992in}}% +\pgfpathcurveto{\pgfqpoint{-0.016437in}{0.009546in}}{\pgfqpoint{-0.018373in}{0.004873in}}{\pgfqpoint{-0.018373in}{0.000000in}}% +\pgfpathcurveto{\pgfqpoint{-0.018373in}{-0.004873in}}{\pgfqpoint{-0.016437in}{-0.009546in}}{\pgfqpoint{-0.012992in}{-0.012992in}}% +\pgfpathcurveto{\pgfqpoint{-0.009546in}{-0.016437in}}{\pgfqpoint{-0.004873in}{-0.018373in}}{\pgfqpoint{0.000000in}{-0.018373in}}% +\pgfpathclose% +\pgfusepath{stroke,fill}% +}% +\begin{pgfscope}% +\pgfsys@transformshift{3.283292in}{2.354501in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{3.273021in}{2.344113in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{3.319048in}{2.404178in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{3.233071in}{2.424603in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{3.039480in}{2.585090in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{3.054800in}{2.657985in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{3.276301in}{2.312427in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{3.035734in}{2.683244in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{2.948045in}{2.629035in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{2.950072in}{2.646289in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{2.999372in}{2.701313in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{3.103530in}{2.674313in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{3.425671in}{2.557898in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{2.966100in}{2.174734in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{3.399755in}{2.606349in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{3.459670in}{2.541984in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{3.075318in}{2.709145in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{3.433755in}{2.543333in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{2.983248in}{2.169458in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{3.504693in}{2.565738in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{3.228771in}{2.461407in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{3.519662in}{2.587057in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{3.419082in}{2.531620in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{3.190525in}{2.317681in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{3.576152in}{2.515948in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{3.634785in}{2.579710in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{3.557265in}{2.597375in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{3.585356in}{2.538750in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{3.633137in}{2.596459in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{3.585093in}{2.603143in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{3.022230in}{2.260224in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{2.933578in}{2.546695in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{2.958308in}{2.287580in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{3.396007in}{2.682468in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{3.355827in}{2.299261in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{3.182134in}{2.312724in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{2.939087in}{2.134911in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{3.159261in}{2.427724in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{3.821675in}{2.491402in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{3.786106in}{2.558550in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{3.856556in}{2.466622in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{3.243255in}{2.482748in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{3.371106in}{2.681308in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{3.344234in}{2.659058in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{3.492977in}{2.445895in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{3.272924in}{2.255793in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{3.943385in}{2.466196in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{3.404287in}{2.491013in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{3.389585in}{2.417220in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{3.002773in}{2.323183in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfpathrectangle{\pgfqpoint{1.432000in}{0.528000in}}{\pgfqpoint{3.696000in}{3.696000in}}% +\pgfusepath{clip}% +\pgfsetbuttcap% +\pgfsetroundjoin% +\definecolor{currentfill}{rgb}{1.000000,0.000000,0.000000}% +\pgfsetfillcolor{currentfill}% +\pgfsetlinewidth{0.501875pt}% +\definecolor{currentstroke}{rgb}{1.000000,1.000000,1.000000}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfsys@defobject{currentmarker}{\pgfqpoint{-0.018373in}{-0.018373in}}{\pgfqpoint{0.018373in}{0.018373in}}{% +\pgfpathmoveto{\pgfqpoint{0.000000in}{-0.018373in}}% +\pgfpathcurveto{\pgfqpoint{0.004873in}{-0.018373in}}{\pgfqpoint{0.009546in}{-0.016437in}}{\pgfqpoint{0.012992in}{-0.012992in}}% +\pgfpathcurveto{\pgfqpoint{0.016437in}{-0.009546in}}{\pgfqpoint{0.018373in}{-0.004873in}}{\pgfqpoint{0.018373in}{0.000000in}}% +\pgfpathcurveto{\pgfqpoint{0.018373in}{0.004873in}}{\pgfqpoint{0.016437in}{0.009546in}}{\pgfqpoint{0.012992in}{0.012992in}}% +\pgfpathcurveto{\pgfqpoint{0.009546in}{0.016437in}}{\pgfqpoint{0.004873in}{0.018373in}}{\pgfqpoint{0.000000in}{0.018373in}}% +\pgfpathcurveto{\pgfqpoint{-0.004873in}{0.018373in}}{\pgfqpoint{-0.009546in}{0.016437in}}{\pgfqpoint{-0.012992in}{0.012992in}}% +\pgfpathcurveto{\pgfqpoint{-0.016437in}{0.009546in}}{\pgfqpoint{-0.018373in}{0.004873in}}{\pgfqpoint{-0.018373in}{0.000000in}}% +\pgfpathcurveto{\pgfqpoint{-0.018373in}{-0.004873in}}{\pgfqpoint{-0.016437in}{-0.009546in}}{\pgfqpoint{-0.012992in}{-0.012992in}}% +\pgfpathcurveto{\pgfqpoint{-0.009546in}{-0.016437in}}{\pgfqpoint{-0.004873in}{-0.018373in}}{\pgfqpoint{0.000000in}{-0.018373in}}% +\pgfpathclose% +\pgfusepath{stroke,fill}% +}% +\begin{pgfscope}% +\pgfsys@transformshift{3.289556in}{2.412084in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{3.057383in}{2.621550in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{3.332165in}{2.424052in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{2.950585in}{2.694697in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{3.411789in}{2.556180in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsetbuttcap% +\pgfsetroundjoin% +\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetfillcolor{currentfill}% +\pgfsetlinewidth{0.803000pt}% +\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfsys@defobject{currentmarker}{\pgfqpoint{0.000000in}{-0.048611in}}{\pgfqpoint{0.000000in}{0.000000in}}{% +\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}% +\pgfpathlineto{\pgfqpoint{0.000000in}{-0.048611in}}% +\pgfusepath{stroke,fill}% +}% +\begin{pgfscope}% +\pgfsys@transformshift{1.432000in}{0.528000in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\end{pgfscope}% +\begin{pgfscope}% +\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetstrokecolor{textcolor}% +\pgfsetfillcolor{textcolor}% +\pgftext[x=1.432000in,y=0.430778in,,top]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle -15\)}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsetbuttcap% +\pgfsetroundjoin% +\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetfillcolor{currentfill}% +\pgfsetlinewidth{0.803000pt}% +\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfsys@defobject{currentmarker}{\pgfqpoint{0.000000in}{-0.048611in}}{\pgfqpoint{0.000000in}{0.000000in}}{% +\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}% +\pgfpathlineto{\pgfqpoint{0.000000in}{-0.048611in}}% +\pgfusepath{stroke,fill}% +}% +\begin{pgfscope}% +\pgfsys@transformshift{2.048000in}{0.528000in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\end{pgfscope}% +\begin{pgfscope}% +\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetstrokecolor{textcolor}% +\pgfsetfillcolor{textcolor}% +\pgftext[x=2.048000in,y=0.430778in,,top]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle -10\)}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsetbuttcap% +\pgfsetroundjoin% +\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetfillcolor{currentfill}% +\pgfsetlinewidth{0.803000pt}% +\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfsys@defobject{currentmarker}{\pgfqpoint{0.000000in}{-0.048611in}}{\pgfqpoint{0.000000in}{0.000000in}}{% +\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}% +\pgfpathlineto{\pgfqpoint{0.000000in}{-0.048611in}}% +\pgfusepath{stroke,fill}% +}% +\begin{pgfscope}% +\pgfsys@transformshift{2.664000in}{0.528000in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\end{pgfscope}% +\begin{pgfscope}% +\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetstrokecolor{textcolor}% +\pgfsetfillcolor{textcolor}% +\pgftext[x=2.664000in,y=0.430778in,,top]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle -5\)}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsetbuttcap% +\pgfsetroundjoin% +\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetfillcolor{currentfill}% +\pgfsetlinewidth{0.803000pt}% +\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfsys@defobject{currentmarker}{\pgfqpoint{0.000000in}{-0.048611in}}{\pgfqpoint{0.000000in}{0.000000in}}{% +\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}% +\pgfpathlineto{\pgfqpoint{0.000000in}{-0.048611in}}% +\pgfusepath{stroke,fill}% +}% +\begin{pgfscope}% +\pgfsys@transformshift{3.280000in}{0.528000in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\end{pgfscope}% +\begin{pgfscope}% +\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetstrokecolor{textcolor}% +\pgfsetfillcolor{textcolor}% +\pgftext[x=3.280000in,y=0.430778in,,top]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle 0\)}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsetbuttcap% +\pgfsetroundjoin% +\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetfillcolor{currentfill}% +\pgfsetlinewidth{0.803000pt}% +\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfsys@defobject{currentmarker}{\pgfqpoint{0.000000in}{-0.048611in}}{\pgfqpoint{0.000000in}{0.000000in}}{% +\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}% +\pgfpathlineto{\pgfqpoint{0.000000in}{-0.048611in}}% +\pgfusepath{stroke,fill}% +}% +\begin{pgfscope}% +\pgfsys@transformshift{3.896000in}{0.528000in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\end{pgfscope}% +\begin{pgfscope}% +\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetstrokecolor{textcolor}% +\pgfsetfillcolor{textcolor}% +\pgftext[x=3.896000in,y=0.430778in,,top]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle 5\)}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsetbuttcap% +\pgfsetroundjoin% +\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetfillcolor{currentfill}% +\pgfsetlinewidth{0.803000pt}% +\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfsys@defobject{currentmarker}{\pgfqpoint{0.000000in}{-0.048611in}}{\pgfqpoint{0.000000in}{0.000000in}}{% +\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}% +\pgfpathlineto{\pgfqpoint{0.000000in}{-0.048611in}}% +\pgfusepath{stroke,fill}% +}% +\begin{pgfscope}% +\pgfsys@transformshift{4.512000in}{0.528000in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\end{pgfscope}% +\begin{pgfscope}% +\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetstrokecolor{textcolor}% +\pgfsetfillcolor{textcolor}% +\pgftext[x=4.512000in,y=0.430778in,,top]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle 10\)}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsetbuttcap% +\pgfsetroundjoin% +\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetfillcolor{currentfill}% +\pgfsetlinewidth{0.803000pt}% +\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfsys@defobject{currentmarker}{\pgfqpoint{0.000000in}{-0.048611in}}{\pgfqpoint{0.000000in}{0.000000in}}{% +\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}% +\pgfpathlineto{\pgfqpoint{0.000000in}{-0.048611in}}% +\pgfusepath{stroke,fill}% +}% +\begin{pgfscope}% +\pgfsys@transformshift{5.128000in}{0.528000in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\end{pgfscope}% +\begin{pgfscope}% +\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetstrokecolor{textcolor}% +\pgfsetfillcolor{textcolor}% +\pgftext[x=5.128000in,y=0.430778in,,top]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle 15\)}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsetbuttcap% +\pgfsetroundjoin% +\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetfillcolor{currentfill}% +\pgfsetlinewidth{0.803000pt}% +\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfsys@defobject{currentmarker}{\pgfqpoint{-0.048611in}{0.000000in}}{\pgfqpoint{0.000000in}{0.000000in}}{% +\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}% +\pgfpathlineto{\pgfqpoint{-0.048611in}{0.000000in}}% +\pgfusepath{stroke,fill}% +}% +\begin{pgfscope}% +\pgfsys@transformshift{1.432000in}{0.528000in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\end{pgfscope}% +\begin{pgfscope}% +\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetstrokecolor{textcolor}% +\pgfsetfillcolor{textcolor}% +\pgftext[x=1.087863in,y=0.475238in,left,base]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle -15\)}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsetbuttcap% +\pgfsetroundjoin% +\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetfillcolor{currentfill}% +\pgfsetlinewidth{0.803000pt}% +\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfsys@defobject{currentmarker}{\pgfqpoint{-0.048611in}{0.000000in}}{\pgfqpoint{0.000000in}{0.000000in}}{% +\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}% +\pgfpathlineto{\pgfqpoint{-0.048611in}{0.000000in}}% +\pgfusepath{stroke,fill}% +}% +\begin{pgfscope}% +\pgfsys@transformshift{1.432000in}{1.144000in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\end{pgfscope}% +\begin{pgfscope}% +\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetstrokecolor{textcolor}% +\pgfsetfillcolor{textcolor}% +\pgftext[x=1.087863in,y=1.091238in,left,base]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle -10\)}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsetbuttcap% +\pgfsetroundjoin% +\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetfillcolor{currentfill}% +\pgfsetlinewidth{0.803000pt}% +\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfsys@defobject{currentmarker}{\pgfqpoint{-0.048611in}{0.000000in}}{\pgfqpoint{0.000000in}{0.000000in}}{% +\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}% +\pgfpathlineto{\pgfqpoint{-0.048611in}{0.000000in}}% +\pgfusepath{stroke,fill}% +}% +\begin{pgfscope}% +\pgfsys@transformshift{1.432000in}{1.760000in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\end{pgfscope}% +\begin{pgfscope}% +\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetstrokecolor{textcolor}% +\pgfsetfillcolor{textcolor}% +\pgftext[x=1.157308in,y=1.707238in,left,base]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle -5\)}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsetbuttcap% +\pgfsetroundjoin% +\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetfillcolor{currentfill}% +\pgfsetlinewidth{0.803000pt}% +\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfsys@defobject{currentmarker}{\pgfqpoint{-0.048611in}{0.000000in}}{\pgfqpoint{0.000000in}{0.000000in}}{% +\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}% +\pgfpathlineto{\pgfqpoint{-0.048611in}{0.000000in}}% +\pgfusepath{stroke,fill}% +}% +\begin{pgfscope}% +\pgfsys@transformshift{1.432000in}{2.376000in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\end{pgfscope}% +\begin{pgfscope}% +\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetstrokecolor{textcolor}% +\pgfsetfillcolor{textcolor}% +\pgftext[x=1.265333in,y=2.323238in,left,base]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle 0\)}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsetbuttcap% +\pgfsetroundjoin% +\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetfillcolor{currentfill}% +\pgfsetlinewidth{0.803000pt}% +\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfsys@defobject{currentmarker}{\pgfqpoint{-0.048611in}{0.000000in}}{\pgfqpoint{0.000000in}{0.000000in}}{% +\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}% +\pgfpathlineto{\pgfqpoint{-0.048611in}{0.000000in}}% +\pgfusepath{stroke,fill}% +}% +\begin{pgfscope}% +\pgfsys@transformshift{1.432000in}{2.992000in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\end{pgfscope}% +\begin{pgfscope}% +\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetstrokecolor{textcolor}% +\pgfsetfillcolor{textcolor}% +\pgftext[x=1.265333in,y=2.939238in,left,base]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle 5\)}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsetbuttcap% +\pgfsetroundjoin% +\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetfillcolor{currentfill}% +\pgfsetlinewidth{0.803000pt}% +\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfsys@defobject{currentmarker}{\pgfqpoint{-0.048611in}{0.000000in}}{\pgfqpoint{0.000000in}{0.000000in}}{% +\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}% +\pgfpathlineto{\pgfqpoint{-0.048611in}{0.000000in}}% +\pgfusepath{stroke,fill}% +}% +\begin{pgfscope}% +\pgfsys@transformshift{1.432000in}{3.608000in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\end{pgfscope}% +\begin{pgfscope}% +\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetstrokecolor{textcolor}% +\pgfsetfillcolor{textcolor}% +\pgftext[x=1.195888in,y=3.555238in,left,base]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle 10\)}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsetbuttcap% +\pgfsetroundjoin% +\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetfillcolor{currentfill}% +\pgfsetlinewidth{0.803000pt}% +\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfsys@defobject{currentmarker}{\pgfqpoint{-0.048611in}{0.000000in}}{\pgfqpoint{0.000000in}{0.000000in}}{% +\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}% +\pgfpathlineto{\pgfqpoint{-0.048611in}{0.000000in}}% +\pgfusepath{stroke,fill}% +}% +\begin{pgfscope}% +\pgfsys@transformshift{1.432000in}{4.224000in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\end{pgfscope}% +\begin{pgfscope}% +\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetstrokecolor{textcolor}% +\pgfsetfillcolor{textcolor}% +\pgftext[x=1.195888in,y=4.171238in,left,base]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle 15\)}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfpathrectangle{\pgfqpoint{1.432000in}{0.528000in}}{\pgfqpoint{3.696000in}{3.696000in}}% +\pgfusepath{clip}% +\pgfsetbuttcap% +\pgfsetroundjoin% +\pgfsetlinewidth{1.505625pt}% 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+\pgfpathlineto{\pgfqpoint{5.128000in}{4.224000in}}% +\pgfusepath{stroke}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsetrectcap% +\pgfsetmiterjoin% +\pgfsetlinewidth{0.803000pt}% +\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfpathmoveto{\pgfqpoint{1.432000in}{0.528000in}}% +\pgfpathlineto{\pgfqpoint{5.128000in}{0.528000in}}% +\pgfusepath{stroke}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsetrectcap% +\pgfsetmiterjoin% +\pgfsetlinewidth{0.803000pt}% +\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfpathmoveto{\pgfqpoint{1.432000in}{4.224000in}}% +\pgfpathlineto{\pgfqpoint{5.128000in}{4.224000in}}% +\pgfusepath{stroke}% +\end{pgfscope}% +\begin{pgfscope}% +\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetstrokecolor{textcolor}% +\pgfsetfillcolor{textcolor}% +\pgftext[x=3.280000in,y=4.307333in,,base]{\color{textcolor}\rmfamily\fontsize{12.000000}{14.400000}\selectfont Experiment 1A: CE-surrogate (\(\displaystyle k=5\))}% +\end{pgfscope}% +\end{pgfpicture}% +\makeatother% +\endgroup% diff --git a/figures/cem_variants/sierra_group.tex b/figures/cem_variants/sierra_group.tex new file mode 100644 index 0000000..47ccd88 --- /dev/null +++ b/figures/cem_variants/sierra_group.tex @@ -0,0 +1,18 @@ +\begin{tikzpicture}[, +scale=4] +\begin{groupplot}[group style={horizontal sep=1cm, y descriptions at=edge left, group size=3 by 2}] +\nextgroupplot [height = {8cm}, title = {$\eta=0.5$, decay=1}, xmajorticks=false, width = {8cm}, enlargelimits = false, axis on top]\addplot [point meta min=-0.00615171396062386, point meta max=-8.999491013175768e-6] graphics [xmin=-15, xmax=15, ymin=-15, ymax=15] {figures/cem_variants/tmp_10000000000056.png}; + +\nextgroupplot [height = {8cm}, title = {$\eta=2.0$, decay=1}, xmajorticks=false, width = {8cm}, enlargelimits = false, axis on top]\addplot [point meta min=-0.01017517566501975, point meta max=-3.188592122982145e-10] graphics [xmin=-15, xmax=15, ymin=-15, ymax=15] {figures/cem_variants/tmp_10000000000057.png}; + +\nextgroupplot [height = {8cm}, title = {$\eta=6.0$, decay=1}, xmajorticks=false, width = {8cm}, enlargelimits = false, axis on top, colormap={mycolormap}{ rgb(0cm)=(0.993248,0.906157,0.143936) rgb(1cm)=(0.983868,0.904867,0.136897) rgb(2cm)=(0.974417,0.90359,0.130215) rgb(3cm)=(0.964894,0.902323,0.123941) rgb(4cm)=(0.9553,0.901065,0.118128) rgb(5cm)=(0.945636,0.899815,0.112838) rgb(6cm)=(0.935904,0.89857,0.108131) rgb(7cm)=(0.926106,0.89733,0.104071) rgb(8cm)=(0.916242,0.896091,0.100717) rgb(9cm)=(0.906311,0.894855,0.098125) rgb(10cm)=(0.89632,0.893616,0.096335) rgb(11cm)=(0.886271,0.892374,0.095374) rgb(12cm)=(0.876168,0.891125,0.09525) rgb(13cm)=(0.866013,0.889868,0.095953) rgb(14cm)=(0.85581,0.888601,0.097452) rgb(15cm)=(0.845561,0.887322,0.099702) rgb(16cm)=(0.83527,0.886029,0.102646) rgb(17cm)=(0.82494,0.88472,0.106217) rgb(18cm)=(0.814576,0.883393,0.110347) rgb(19cm)=(0.804182,0.882046,0.114965) rgb(20cm)=(0.79376,0.880678,0.120005) rgb(21cm)=(0.783315,0.879285,0.125405) rgb(22cm)=(0.772852,0.877868,0.131109) rgb(23cm)=(0.762373,0.876424,0.137064) rgb(24cm)=(0.751884,0.874951,0.143228) rgb(25cm)=(0.741388,0.873449,0.149561) rgb(26cm)=(0.730889,0.871916,0.156029) rgb(27cm)=(0.720391,0.87035,0.162603) rgb(28cm)=(0.709898,0.868751,0.169257) rgb(29cm)=(0.699415,0.867117,0.175971) rgb(30cm)=(0.688944,0.865448,0.182725) rgb(31cm)=(0.678489,0.863742,0.189503) rgb(32cm)=(0.668054,0.861999,0.196293) rgb(33cm)=(0.657642,0.860219,0.203082) rgb(34cm)=(0.647257,0.8584,0.209861) rgb(35cm)=(0.636902,0.856542,0.21662) rgb(36cm)=(0.626579,0.854645,0.223353) rgb(37cm)=(0.616293,0.852709,0.230052) rgb(38cm)=(0.606045,0.850733,0.236712) rgb(39cm)=(0.595839,0.848717,0.243329) rgb(40cm)=(0.585678,0.846661,0.249897) rgb(41cm)=(0.575563,0.844566,0.256415) rgb(42cm)=(0.565498,0.84243,0.262877) rgb(43cm)=(0.555484,0.840254,0.269281) rgb(44cm)=(0.545524,0.838039,0.275626) rgb(45cm)=(0.535621,0.835785,0.281908) rgb(46cm)=(0.525776,0.833491,0.288127) rgb(47cm)=(0.515992,0.831158,0.294279) rgb(48cm)=(0.506271,0.828786,0.300362) rgb(49cm)=(0.496615,0.826376,0.306377) rgb(50cm)=(0.487026,0.823929,0.312321) rgb(51cm)=(0.477504,0.821444,0.318195) rgb(52cm)=(0.468053,0.818921,0.323998) rgb(53cm)=(0.458674,0.816363,0.329727) rgb(54cm)=(0.449368,0.813768,0.335384) rgb(55cm)=(0.440137,0.811138,0.340967) rgb(56cm)=(0.430983,0.808473,0.346476) rgb(57cm)=(0.421908,0.805774,0.35191) rgb(58cm)=(0.412913,0.803041,0.357269) rgb(59cm)=(0.404001,0.800275,0.362552) rgb(60cm)=(0.395174,0.797475,0.367757) rgb(61cm)=(0.386433,0.794644,0.372886) rgb(62cm)=(0.377779,0.791781,0.377939) rgb(63cm)=(0.369214,0.788888,0.382914) rgb(64cm)=(0.360741,0.785964,0.387814) rgb(65cm)=(0.35236,0.783011,0.392636) rgb(66cm)=(0.344074,0.780029,0.397381) rgb(67cm)=(0.335885,0.777018,0.402049) rgb(68cm)=(0.327796,0.77398,0.40664) rgb(69cm)=(0.319809,0.770914,0.411152) rgb(70cm)=(0.311925,0.767822,0.415586) rgb(71cm)=(0.304148,0.764704,0.419943) rgb(72cm)=(0.296479,0.761561,0.424223) rgb(73cm)=(0.288921,0.758394,0.428426) rgb(74cm)=(0.281477,0.755203,0.432552) rgb(75cm)=(0.274149,0.751988,0.436601) rgb(76cm)=(0.266941,0.748751,0.440573) rgb(77cm)=(0.259857,0.745492,0.444467) rgb(78cm)=(0.252899,0.742211,0.448284) rgb(79cm)=(0.24607,0.73891,0.452024) rgb(80cm)=(0.239374,0.735588,0.455688) rgb(81cm)=(0.232815,0.732247,0.459277) rgb(82cm)=(0.226397,0.728888,0.462789) rgb(83cm)=(0.220124,0.725509,0.466226) rgb(84cm)=(0.214,0.722114,0.469588) rgb(85cm)=(0.20803,0.718701,0.472873) rgb(86cm)=(0.202219,0.715272,0.476084) rgb(87cm)=(0.196571,0.711827,0.479221) rgb(88cm)=(0.19109,0.708366,0.482284) rgb(89cm)=(0.185783,0.704891,0.485273) rgb(90cm)=(0.180653,0.701402,0.488189) rgb(91cm)=(0.175707,0.6979,0.491033) rgb(92cm)=(0.170948,0.694384,0.493803) rgb(93cm)=(0.166383,0.690856,0.496502) rgb(94cm)=(0.162016,0.687316,0.499129) rgb(95cm)=(0.157851,0.683765,0.501686) rgb(96cm)=(0.153894,0.680203,0.504172) rgb(97cm)=(0.150148,0.676631,0.506589) rgb(98cm)=(0.146616,0.67305,0.508936) rgb(99cm)=(0.143303,0.669459,0.511215) rgb(100cm)=(0.14021,0.665859,0.513427) rgb(101cm)=(0.137339,0.662252,0.515571) rgb(102cm)=(0.134692,0.658636,0.517649) rgb(103cm)=(0.132268,0.655014,0.519661) rgb(104cm)=(0.130067,0.651384,0.521608) rgb(105cm)=(0.128087,0.647749,0.523491) rgb(106cm)=(0.126326,0.644107,0.525311) rgb(107cm)=(0.12478,0.640461,0.527068) rgb(108cm)=(0.123444,0.636809,0.528763) rgb(109cm)=(0.122312,0.633153,0.530398) rgb(110cm)=(0.12138,0.629492,0.531973) rgb(111cm)=(0.120638,0.625828,0.533488) rgb(112cm)=(0.120081,0.622161,0.534946) rgb(113cm)=(0.119699,0.61849,0.536347) rgb(114cm)=(0.119483,0.614817,0.537692) rgb(115cm)=(0.119423,0.611141,0.538982) rgb(116cm)=(0.119512,0.607464,0.540218) rgb(117cm)=(0.119738,0.603785,0.5414) rgb(118cm)=(0.120092,0.600104,0.54253) rgb(119cm)=(0.120565,0.596422,0.543611) rgb(120cm)=(0.121148,0.592739,0.544641) rgb(121cm)=(0.121831,0.589055,0.545623) rgb(122cm)=(0.122606,0.585371,0.546557) rgb(123cm)=(0.123463,0.581687,0.547445) rgb(124cm)=(0.124395,0.578002,0.548287) rgb(125cm)=(0.125394,0.574318,0.549086) rgb(126cm)=(0.126453,0.570633,0.549841) rgb(127cm)=(0.127568,0.566949,0.550556) rgb(128cm)=(0.128729,0.563265,0.551229) rgb(129cm)=(0.129933,0.559582,0.551864) rgb(130cm)=(0.131172,0.555899,0.552459) rgb(131cm)=(0.132444,0.552216,0.553018) rgb(132cm)=(0.133743,0.548535,0.553541) rgb(133cm)=(0.135066,0.544853,0.554029) rgb(134cm)=(0.136408,0.541173,0.554483) rgb(135cm)=(0.13777,0.537492,0.554906) rgb(136cm)=(0.139147,0.533812,0.555298) rgb(137cm)=(0.140536,0.530132,0.555659) rgb(138cm)=(0.141935,0.526453,0.555991) rgb(139cm)=(0.143343,0.522773,0.556295) rgb(140cm)=(0.144759,0.519093,0.556572) rgb(141cm)=(0.14618,0.515413,0.556823) rgb(142cm)=(0.147607,0.511733,0.557049) rgb(143cm)=(0.149039,0.508051,0.55725) rgb(144cm)=(0.150476,0.504369,0.55743) rgb(145cm)=(0.151918,0.500685,0.557587) rgb(146cm)=(0.153364,0.497,0.557724) rgb(147cm)=(0.154815,0.493313,0.55784) rgb(148cm)=(0.15627,0.489624,0.557936) rgb(149cm)=(0.157729,0.485932,0.558013) rgb(150cm)=(0.159194,0.482237,0.558073) rgb(151cm)=(0.160665,0.47854,0.558115) rgb(152cm)=(0.162142,0.474838,0.55814) rgb(153cm)=(0.163625,0.471133,0.558148) rgb(154cm)=(0.165117,0.467423,0.558141) rgb(155cm)=(0.166617,0.463708,0.558119) rgb(156cm)=(0.168126,0.459988,0.558082) rgb(157cm)=(0.169646,0.456262,0.55803) rgb(158cm)=(0.171176,0.45253,0.557965) rgb(159cm)=(0.172719,0.448791,0.557885) rgb(160cm)=(0.174274,0.445044,0.557792) rgb(161cm)=(0.175841,0.44129,0.557685) rgb(162cm)=(0.177423,0.437527,0.557565) rgb(163cm)=(0.179019,0.433756,0.55743) rgb(164cm)=(0.180629,0.429975,0.557282) rgb(165cm)=(0.182256,0.426184,0.55712) rgb(166cm)=(0.183898,0.422383,0.556944) rgb(167cm)=(0.185556,0.41857,0.556753) rgb(168cm)=(0.187231,0.414746,0.556547) rgb(169cm)=(0.188923,0.41091,0.556326) rgb(170cm)=(0.190631,0.407061,0.556089) rgb(171cm)=(0.192357,0.403199,0.555836) rgb(172cm)=(0.1941,0.399323,0.555565) rgb(173cm)=(0.19586,0.395433,0.555276) rgb(174cm)=(0.197636,0.391528,0.554969) rgb(175cm)=(0.19943,0.387607,0.554642) rgb(176cm)=(0.201239,0.38367,0.554294) rgb(177cm)=(0.203063,0.379716,0.553925) rgb(178cm)=(0.204903,0.375746,0.553533) rgb(179cm)=(0.206756,0.371758,0.553117) rgb(180cm)=(0.208623,0.367752,0.552675) rgb(181cm)=(0.210503,0.363727,0.552206) rgb(182cm)=(0.212395,0.359683,0.55171) rgb(183cm)=(0.214298,0.355619,0.551184) rgb(184cm)=(0.21621,0.351535,0.550627) rgb(185cm)=(0.21813,0.347432,0.550038) rgb(186cm)=(0.220057,0.343307,0.549413) rgb(187cm)=(0.221989,0.339161,0.548752) rgb(188cm)=(0.223925,0.334994,0.548053) rgb(189cm)=(0.225863,0.330805,0.547314) rgb(190cm)=(0.227802,0.326594,0.546532) rgb(191cm)=(0.229739,0.322361,0.545706) rgb(192cm)=(0.231674,0.318106,0.544834) rgb(193cm)=(0.233603,0.313828,0.543914) rgb(194cm)=(0.235526,0.309527,0.542944) rgb(195cm)=(0.237441,0.305202,0.541921) rgb(196cm)=(0.239346,0.300855,0.540844) rgb(197cm)=(0.241237,0.296485,0.539709) rgb(198cm)=(0.243113,0.292092,0.538516) rgb(199cm)=(0.244972,0.287675,0.53726) rgb(200cm)=(0.246811,0.283237,0.535941) rgb(201cm)=(0.248629,0.278775,0.534556) rgb(202cm)=(0.250425,0.27429,0.533103) rgb(203cm)=(0.252194,0.269783,0.531579) rgb(204cm)=(0.253935,0.265254,0.529983) rgb(205cm)=(0.255645,0.260703,0.528312) rgb(206cm)=(0.257322,0.25613,0.526563) rgb(207cm)=(0.258965,0.251537,0.524736) rgb(208cm)=(0.260571,0.246922,0.522828) rgb(209cm)=(0.262138,0.242286,0.520837) rgb(210cm)=(0.263663,0.237631,0.518762) rgb(211cm)=(0.265145,0.232956,0.516599) rgb(212cm)=(0.26658,0.228262,0.514349) rgb(213cm)=(0.267968,0.223549,0.512008) rgb(214cm)=(0.269308,0.218818,0.509577) rgb(215cm)=(0.270595,0.214069,0.507052) rgb(216cm)=(0.271828,0.209303,0.504434) rgb(217cm)=(0.273006,0.20452,0.501721) rgb(218cm)=(0.274128,0.199721,0.498911) rgb(219cm)=(0.275191,0.194905,0.496005) rgb(220cm)=(0.276194,0.190074,0.493001) rgb(221cm)=(0.277134,0.185228,0.489898) rgb(222cm)=(0.278012,0.180367,0.486697) rgb(223cm)=(0.278826,0.17549,0.483397) rgb(224cm)=(0.279574,0.170599,0.479997) rgb(225cm)=(0.280255,0.165693,0.476498) rgb(226cm)=(0.280868,0.160771,0.472899) rgb(227cm)=(0.281412,0.155834,0.469201) rgb(228cm)=(0.281887,0.150881,0.465405) rgb(229cm)=(0.28229,0.145912,0.46151) rgb(230cm)=(0.282623,0.140926,0.457517) rgb(231cm)=(0.282884,0.13592,0.453427) rgb(232cm)=(0.283072,0.130895,0.449241) rgb(233cm)=(0.283187,0.125848,0.44496) rgb(234cm)=(0.283229,0.120777,0.440584) rgb(235cm)=(0.283197,0.11568,0.436115) rgb(236cm)=(0.283091,0.110553,0.431554) rgb(237cm)=(0.28291,0.105393,0.426902) rgb(238cm)=(0.282656,0.100196,0.42216) rgb(239cm)=(0.282327,0.094955,0.417331) rgb(240cm)=(0.281924,0.089666,0.412415) rgb(241cm)=(0.281446,0.08432,0.407414) rgb(242cm)=(0.280894,0.078907,0.402329) rgb(243cm)=(0.280267,0.073417,0.397163) rgb(244cm)=(0.279566,0.067836,0.391917) rgb(245cm)=(0.278791,0.062145,0.386592) rgb(246cm)=(0.277941,0.056324,0.381191) rgb(247cm)=(0.277018,0.050344,0.375715) rgb(248cm)=(0.276022,0.044167,0.370164) rgb(249cm)=(0.274952,0.037752,0.364543) rgb(250cm)=(0.273809,0.031497,0.358853) rgb(251cm)=(0.272594,0.025563,0.353093) rgb(252cm)=(0.271305,0.019942,0.347269) rgb(253cm)=(0.269944,0.014625,0.341379) rgb(254cm)=(0.26851,0.009605,0.335427) rgb(255cm)=(0.267004,0.004874,0.329415) }, colorbar]\addplot [point meta min=-0.022002368421582257, point meta max=-1.7302938158670046e-22] graphics [xmin=-15, xmax=15, ymin=-15, ymax=15] {figures/cem_variants/tmp_10000000000058.png}; + +\nextgroupplot [height = {8cm}, title = {$\eta=0.5$, decay=0}, , width = {8cm}, enlargelimits = false, axis on top]\addplot [point meta min=-0.005899996159458542, point meta max=-1.4151795673351503e-11] graphics [xmin=-15, xmax=15, ymin=-15, ymax=15] {figures/cem_variants/tmp_10000000000059.png}; + +\nextgroupplot [height = {8cm}, title = {$\eta=2.0$, decay=0}, , width = {8cm}, enlargelimits = false, axis on top]\addplot [point meta min=-0.009946798929399269, point meta max=-1.196273392353628e-34] graphics [xmin=-15, xmax=15, ymin=-15, ymax=15] {figures/cem_variants/tmp_10000000000060.png}; + +\nextgroupplot [height = {8cm}, title = {$\eta=6.0$, decay=0}, , width = {8cm}, enlargelimits = false, axis on top, colormap={mycolormap}{ rgb(0cm)=(0.993248,0.906157,0.143936) rgb(1cm)=(0.983868,0.904867,0.136897) rgb(2cm)=(0.974417,0.90359,0.130215) rgb(3cm)=(0.964894,0.902323,0.123941) rgb(4cm)=(0.9553,0.901065,0.118128) rgb(5cm)=(0.945636,0.899815,0.112838) rgb(6cm)=(0.935904,0.89857,0.108131) rgb(7cm)=(0.926106,0.89733,0.104071) rgb(8cm)=(0.916242,0.896091,0.100717) rgb(9cm)=(0.906311,0.894855,0.098125) rgb(10cm)=(0.89632,0.893616,0.096335) rgb(11cm)=(0.886271,0.892374,0.095374) rgb(12cm)=(0.876168,0.891125,0.09525) rgb(13cm)=(0.866013,0.889868,0.095953) rgb(14cm)=(0.85581,0.888601,0.097452) rgb(15cm)=(0.845561,0.887322,0.099702) rgb(16cm)=(0.83527,0.886029,0.102646) rgb(17cm)=(0.82494,0.88472,0.106217) rgb(18cm)=(0.814576,0.883393,0.110347) rgb(19cm)=(0.804182,0.882046,0.114965) rgb(20cm)=(0.79376,0.880678,0.120005) rgb(21cm)=(0.783315,0.879285,0.125405) rgb(22cm)=(0.772852,0.877868,0.131109) rgb(23cm)=(0.762373,0.876424,0.137064) rgb(24cm)=(0.751884,0.874951,0.143228) rgb(25cm)=(0.741388,0.873449,0.149561) rgb(26cm)=(0.730889,0.871916,0.156029) rgb(27cm)=(0.720391,0.87035,0.162603) rgb(28cm)=(0.709898,0.868751,0.169257) rgb(29cm)=(0.699415,0.867117,0.175971) rgb(30cm)=(0.688944,0.865448,0.182725) rgb(31cm)=(0.678489,0.863742,0.189503) rgb(32cm)=(0.668054,0.861999,0.196293) rgb(33cm)=(0.657642,0.860219,0.203082) rgb(34cm)=(0.647257,0.8584,0.209861) rgb(35cm)=(0.636902,0.856542,0.21662) rgb(36cm)=(0.626579,0.854645,0.223353) rgb(37cm)=(0.616293,0.852709,0.230052) rgb(38cm)=(0.606045,0.850733,0.236712) rgb(39cm)=(0.595839,0.848717,0.243329) rgb(40cm)=(0.585678,0.846661,0.249897) rgb(41cm)=(0.575563,0.844566,0.256415) rgb(42cm)=(0.565498,0.84243,0.262877) rgb(43cm)=(0.555484,0.840254,0.269281) rgb(44cm)=(0.545524,0.838039,0.275626) rgb(45cm)=(0.535621,0.835785,0.281908) rgb(46cm)=(0.525776,0.833491,0.288127) rgb(47cm)=(0.515992,0.831158,0.294279) rgb(48cm)=(0.506271,0.828786,0.300362) rgb(49cm)=(0.496615,0.826376,0.306377) rgb(50cm)=(0.487026,0.823929,0.312321) rgb(51cm)=(0.477504,0.821444,0.318195) rgb(52cm)=(0.468053,0.818921,0.323998) rgb(53cm)=(0.458674,0.816363,0.329727) rgb(54cm)=(0.449368,0.813768,0.335384) rgb(55cm)=(0.440137,0.811138,0.340967) rgb(56cm)=(0.430983,0.808473,0.346476) rgb(57cm)=(0.421908,0.805774,0.35191) rgb(58cm)=(0.412913,0.803041,0.357269) rgb(59cm)=(0.404001,0.800275,0.362552) rgb(60cm)=(0.395174,0.797475,0.367757) rgb(61cm)=(0.386433,0.794644,0.372886) rgb(62cm)=(0.377779,0.791781,0.377939) rgb(63cm)=(0.369214,0.788888,0.382914) rgb(64cm)=(0.360741,0.785964,0.387814) rgb(65cm)=(0.35236,0.783011,0.392636) rgb(66cm)=(0.344074,0.780029,0.397381) rgb(67cm)=(0.335885,0.777018,0.402049) rgb(68cm)=(0.327796,0.77398,0.40664) rgb(69cm)=(0.319809,0.770914,0.411152) rgb(70cm)=(0.311925,0.767822,0.415586) rgb(71cm)=(0.304148,0.764704,0.419943) rgb(72cm)=(0.296479,0.761561,0.424223) rgb(73cm)=(0.288921,0.758394,0.428426) rgb(74cm)=(0.281477,0.755203,0.432552) rgb(75cm)=(0.274149,0.751988,0.436601) rgb(76cm)=(0.266941,0.748751,0.440573) rgb(77cm)=(0.259857,0.745492,0.444467) rgb(78cm)=(0.252899,0.742211,0.448284) rgb(79cm)=(0.24607,0.73891,0.452024) rgb(80cm)=(0.239374,0.735588,0.455688) rgb(81cm)=(0.232815,0.732247,0.459277) rgb(82cm)=(0.226397,0.728888,0.462789) rgb(83cm)=(0.220124,0.725509,0.466226) rgb(84cm)=(0.214,0.722114,0.469588) rgb(85cm)=(0.20803,0.718701,0.472873) rgb(86cm)=(0.202219,0.715272,0.476084) rgb(87cm)=(0.196571,0.711827,0.479221) rgb(88cm)=(0.19109,0.708366,0.482284) rgb(89cm)=(0.185783,0.704891,0.485273) rgb(90cm)=(0.180653,0.701402,0.488189) rgb(91cm)=(0.175707,0.6979,0.491033) rgb(92cm)=(0.170948,0.694384,0.493803) rgb(93cm)=(0.166383,0.690856,0.496502) rgb(94cm)=(0.162016,0.687316,0.499129) rgb(95cm)=(0.157851,0.683765,0.501686) rgb(96cm)=(0.153894,0.680203,0.504172) rgb(97cm)=(0.150148,0.676631,0.506589) rgb(98cm)=(0.146616,0.67305,0.508936) rgb(99cm)=(0.143303,0.669459,0.511215) rgb(100cm)=(0.14021,0.665859,0.513427) rgb(101cm)=(0.137339,0.662252,0.515571) rgb(102cm)=(0.134692,0.658636,0.517649) rgb(103cm)=(0.132268,0.655014,0.519661) rgb(104cm)=(0.130067,0.651384,0.521608) rgb(105cm)=(0.128087,0.647749,0.523491) rgb(106cm)=(0.126326,0.644107,0.525311) rgb(107cm)=(0.12478,0.640461,0.527068) rgb(108cm)=(0.123444,0.636809,0.528763) rgb(109cm)=(0.122312,0.633153,0.530398) rgb(110cm)=(0.12138,0.629492,0.531973) rgb(111cm)=(0.120638,0.625828,0.533488) rgb(112cm)=(0.120081,0.622161,0.534946) rgb(113cm)=(0.119699,0.61849,0.536347) rgb(114cm)=(0.119483,0.614817,0.537692) rgb(115cm)=(0.119423,0.611141,0.538982) rgb(116cm)=(0.119512,0.607464,0.540218) rgb(117cm)=(0.119738,0.603785,0.5414) rgb(118cm)=(0.120092,0.600104,0.54253) rgb(119cm)=(0.120565,0.596422,0.543611) rgb(120cm)=(0.121148,0.592739,0.544641) rgb(121cm)=(0.121831,0.589055,0.545623) rgb(122cm)=(0.122606,0.585371,0.546557) rgb(123cm)=(0.123463,0.581687,0.547445) rgb(124cm)=(0.124395,0.578002,0.548287) rgb(125cm)=(0.125394,0.574318,0.549086) rgb(126cm)=(0.126453,0.570633,0.549841) rgb(127cm)=(0.127568,0.566949,0.550556) rgb(128cm)=(0.128729,0.563265,0.551229) rgb(129cm)=(0.129933,0.559582,0.551864) rgb(130cm)=(0.131172,0.555899,0.552459) rgb(131cm)=(0.132444,0.552216,0.553018) rgb(132cm)=(0.133743,0.548535,0.553541) rgb(133cm)=(0.135066,0.544853,0.554029) rgb(134cm)=(0.136408,0.541173,0.554483) rgb(135cm)=(0.13777,0.537492,0.554906) rgb(136cm)=(0.139147,0.533812,0.555298) rgb(137cm)=(0.140536,0.530132,0.555659) rgb(138cm)=(0.141935,0.526453,0.555991) rgb(139cm)=(0.143343,0.522773,0.556295) rgb(140cm)=(0.144759,0.519093,0.556572) rgb(141cm)=(0.14618,0.515413,0.556823) rgb(142cm)=(0.147607,0.511733,0.557049) rgb(143cm)=(0.149039,0.508051,0.55725) rgb(144cm)=(0.150476,0.504369,0.55743) rgb(145cm)=(0.151918,0.500685,0.557587) rgb(146cm)=(0.153364,0.497,0.557724) rgb(147cm)=(0.154815,0.493313,0.55784) rgb(148cm)=(0.15627,0.489624,0.557936) rgb(149cm)=(0.157729,0.485932,0.558013) rgb(150cm)=(0.159194,0.482237,0.558073) rgb(151cm)=(0.160665,0.47854,0.558115) rgb(152cm)=(0.162142,0.474838,0.55814) rgb(153cm)=(0.163625,0.471133,0.558148) rgb(154cm)=(0.165117,0.467423,0.558141) rgb(155cm)=(0.166617,0.463708,0.558119) rgb(156cm)=(0.168126,0.459988,0.558082) rgb(157cm)=(0.169646,0.456262,0.55803) rgb(158cm)=(0.171176,0.45253,0.557965) rgb(159cm)=(0.172719,0.448791,0.557885) rgb(160cm)=(0.174274,0.445044,0.557792) rgb(161cm)=(0.175841,0.44129,0.557685) rgb(162cm)=(0.177423,0.437527,0.557565) rgb(163cm)=(0.179019,0.433756,0.55743) rgb(164cm)=(0.180629,0.429975,0.557282) rgb(165cm)=(0.182256,0.426184,0.55712) rgb(166cm)=(0.183898,0.422383,0.556944) rgb(167cm)=(0.185556,0.41857,0.556753) rgb(168cm)=(0.187231,0.414746,0.556547) rgb(169cm)=(0.188923,0.41091,0.556326) rgb(170cm)=(0.190631,0.407061,0.556089) rgb(171cm)=(0.192357,0.403199,0.555836) rgb(172cm)=(0.1941,0.399323,0.555565) rgb(173cm)=(0.19586,0.395433,0.555276) rgb(174cm)=(0.197636,0.391528,0.554969) rgb(175cm)=(0.19943,0.387607,0.554642) rgb(176cm)=(0.201239,0.38367,0.554294) rgb(177cm)=(0.203063,0.379716,0.553925) rgb(178cm)=(0.204903,0.375746,0.553533) rgb(179cm)=(0.206756,0.371758,0.553117) rgb(180cm)=(0.208623,0.367752,0.552675) rgb(181cm)=(0.210503,0.363727,0.552206) rgb(182cm)=(0.212395,0.359683,0.55171) rgb(183cm)=(0.214298,0.355619,0.551184) rgb(184cm)=(0.21621,0.351535,0.550627) rgb(185cm)=(0.21813,0.347432,0.550038) rgb(186cm)=(0.220057,0.343307,0.549413) rgb(187cm)=(0.221989,0.339161,0.548752) rgb(188cm)=(0.223925,0.334994,0.548053) rgb(189cm)=(0.225863,0.330805,0.547314) rgb(190cm)=(0.227802,0.326594,0.546532) rgb(191cm)=(0.229739,0.322361,0.545706) rgb(192cm)=(0.231674,0.318106,0.544834) rgb(193cm)=(0.233603,0.313828,0.543914) rgb(194cm)=(0.235526,0.309527,0.542944) rgb(195cm)=(0.237441,0.305202,0.541921) rgb(196cm)=(0.239346,0.300855,0.540844) rgb(197cm)=(0.241237,0.296485,0.539709) rgb(198cm)=(0.243113,0.292092,0.538516) rgb(199cm)=(0.244972,0.287675,0.53726) rgb(200cm)=(0.246811,0.283237,0.535941) rgb(201cm)=(0.248629,0.278775,0.534556) rgb(202cm)=(0.250425,0.27429,0.533103) rgb(203cm)=(0.252194,0.269783,0.531579) rgb(204cm)=(0.253935,0.265254,0.529983) rgb(205cm)=(0.255645,0.260703,0.528312) rgb(206cm)=(0.257322,0.25613,0.526563) rgb(207cm)=(0.258965,0.251537,0.524736) rgb(208cm)=(0.260571,0.246922,0.522828) rgb(209cm)=(0.262138,0.242286,0.520837) rgb(210cm)=(0.263663,0.237631,0.518762) rgb(211cm)=(0.265145,0.232956,0.516599) rgb(212cm)=(0.26658,0.228262,0.514349) rgb(213cm)=(0.267968,0.223549,0.512008) rgb(214cm)=(0.269308,0.218818,0.509577) rgb(215cm)=(0.270595,0.214069,0.507052) rgb(216cm)=(0.271828,0.209303,0.504434) rgb(217cm)=(0.273006,0.20452,0.501721) rgb(218cm)=(0.274128,0.199721,0.498911) rgb(219cm)=(0.275191,0.194905,0.496005) rgb(220cm)=(0.276194,0.190074,0.493001) rgb(221cm)=(0.277134,0.185228,0.489898) rgb(222cm)=(0.278012,0.180367,0.486697) rgb(223cm)=(0.278826,0.17549,0.483397) rgb(224cm)=(0.279574,0.170599,0.479997) rgb(225cm)=(0.280255,0.165693,0.476498) rgb(226cm)=(0.280868,0.160771,0.472899) rgb(227cm)=(0.281412,0.155834,0.469201) rgb(228cm)=(0.281887,0.150881,0.465405) rgb(229cm)=(0.28229,0.145912,0.46151) rgb(230cm)=(0.282623,0.140926,0.457517) rgb(231cm)=(0.282884,0.13592,0.453427) rgb(232cm)=(0.283072,0.130895,0.449241) rgb(233cm)=(0.283187,0.125848,0.44496) rgb(234cm)=(0.283229,0.120777,0.440584) rgb(235cm)=(0.283197,0.11568,0.436115) rgb(236cm)=(0.283091,0.110553,0.431554) rgb(237cm)=(0.28291,0.105393,0.426902) rgb(238cm)=(0.282656,0.100196,0.42216) rgb(239cm)=(0.282327,0.094955,0.417331) rgb(240cm)=(0.281924,0.089666,0.412415) rgb(241cm)=(0.281446,0.08432,0.407414) rgb(242cm)=(0.280894,0.078907,0.402329) rgb(243cm)=(0.280267,0.073417,0.397163) rgb(244cm)=(0.279566,0.067836,0.391917) rgb(245cm)=(0.278791,0.062145,0.386592) rgb(246cm)=(0.277941,0.056324,0.381191) rgb(247cm)=(0.277018,0.050344,0.375715) rgb(248cm)=(0.276022,0.044167,0.370164) rgb(249cm)=(0.274952,0.037752,0.364543) rgb(250cm)=(0.273809,0.031497,0.358853) rgb(251cm)=(0.272594,0.025563,0.353093) rgb(252cm)=(0.271305,0.019942,0.347269) rgb(253cm)=(0.269944,0.014625,0.341379) rgb(254cm)=(0.26851,0.009605,0.335427) rgb(255cm)=(0.267004,0.004874,0.329415) }, colorbar]\addplot [point meta min=-0.02126410264451447, point meta max=-2.738337589257707e-97] graphics [xmin=-15, xmax=15, ymin=-15, ymax=15] {figures/cem_variants/tmp_10000000000061.png}; + +\end{groupplot} + +\end{tikzpicture} diff --git a/figures/cem_variants/tmp_10000000000056.png b/figures/cem_variants/tmp_10000000000056.png new file mode 100644 index 0000000..bb7c909 Binary files /dev/null and b/figures/cem_variants/tmp_10000000000056.png differ diff --git a/figures/cem_variants/tmp_10000000000057.png b/figures/cem_variants/tmp_10000000000057.png new file mode 100644 index 0000000..ee6c101 Binary files /dev/null and b/figures/cem_variants/tmp_10000000000057.png differ diff --git a/figures/cem_variants/tmp_10000000000058.png b/figures/cem_variants/tmp_10000000000058.png new file mode 100644 index 0000000..6152cda Binary files /dev/null and b/figures/cem_variants/tmp_10000000000058.png differ diff --git a/figures/cem_variants/tmp_10000000000059.png b/figures/cem_variants/tmp_10000000000059.png new file mode 100644 index 0000000..736bcfc Binary files /dev/null and b/figures/cem_variants/tmp_10000000000059.png differ diff --git a/figures/cem_variants/tmp_10000000000060.png b/figures/cem_variants/tmp_10000000000060.png new file mode 100644 index 0000000..7b538a1 Binary files /dev/null and b/figures/cem_variants/tmp_10000000000060.png differ diff --git a/figures/cem_variants/tmp_10000000000061.png b/figures/cem_variants/tmp_10000000000061.png new file mode 100644 index 0000000..728bd87 Binary files /dev/null and b/figures/cem_variants/tmp_10000000000061.png differ diff --git a/figures/episodic_ast/dasc-failure-zoomed.pgf b/figures/episodic_ast/dasc-failure-zoomed.pgf new file mode 100644 index 0000000..535172a --- /dev/null +++ b/figures/episodic_ast/dasc-failure-zoomed.pgf @@ -0,0 +1,3774 @@ +%% Creator: Matplotlib, PGF backend +%% +%% To include the figure in your LaTeX document, write +%% \input{.pgf} +%% +%% Make sure the required packages are loaded in your preamble +%% \usepackage{pgf} +%% +%% Figures using additional raster images can only be included by \input if +%% they are in the same directory as the main LaTeX file. For loading figures +%% from other directories you can use the `import` package +%% \usepackage{import} +%% and then include the figures with +%% \import{}{.pgf} +%% +%% Matplotlib used the following preamble +%% \usepackage{fontspec} +%% \setmainfont{DejaVuSans.ttf}[Path=C:/Users/mossr/.julia/conda/3/lib/site-packages/matplotlib/mpl-data/fonts/ttf/] +%% \setsansfont{DejaVuSans.ttf}[Path=C:/Users/mossr/.julia/conda/3/lib/site-packages/matplotlib/mpl-data/fonts/ttf/] +%% \setmonofont{DejaVuSansMono.ttf}[Path=C:/Users/mossr/.julia/conda/3/lib/site-packages/matplotlib/mpl-data/fonts/ttf/] +%% +\begingroup% +\makeatletter% +\begin{pgfpicture}% +\pgfpathrectangle{\pgfpointorigin}{\pgfqpoint{6.400000in}{4.780000in}}% +\pgfusepath{use as bounding box, clip}% +\begin{pgfscope}% +\pgfsetbuttcap% +\pgfsetmiterjoin% +\definecolor{currentfill}{rgb}{1.000000,1.000000,1.000000}% +\pgfsetfillcolor{currentfill}% +\pgfsetlinewidth{0.000000pt}% +\definecolor{currentstroke}{rgb}{1.000000,1.000000,1.000000}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}% +\pgfpathlineto{\pgfqpoint{6.400000in}{0.000000in}}% +\pgfpathlineto{\pgfqpoint{6.400000in}{4.780000in}}% +\pgfpathlineto{\pgfqpoint{0.000000in}{4.780000in}}% +\pgfpathclose% +\pgfusepath{fill}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfpathrectangle{\pgfqpoint{1.063006in}{0.525800in}}{\pgfqpoint{4.433988in}{3.680600in}}% +\pgfusepath{clip}% +\pgfsetbuttcap% +\pgfsetmiterjoin% +\definecolor{currentfill}{rgb}{1.000000,1.000000,1.000000}% +\pgfsetfillcolor{currentfill}% +\pgfsetlinewidth{1.003750pt}% +\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfpathmoveto{\pgfqpoint{1.063006in}{0.525800in}}% +\pgfpathlineto{\pgfqpoint{5.496994in}{0.525800in}}% +\pgfpathlineto{\pgfqpoint{5.496994in}{4.206400in}}% 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+\pgfpathcurveto{\pgfqpoint{2.661939in}{3.399964in}}{\pgfqpoint{2.671615in}{3.403972in}}{\pgfqpoint{2.678747in}{3.411105in}}% +\pgfpathcurveto{\pgfqpoint{2.685880in}{3.418237in}}{\pgfqpoint{2.689888in}{3.427913in}}{\pgfqpoint{2.689888in}{3.438000in}}% +\pgfpathcurveto{\pgfqpoint{2.689888in}{3.448088in}}{\pgfqpoint{2.685880in}{3.457763in}}{\pgfqpoint{2.678747in}{3.464896in}}% +\pgfpathcurveto{\pgfqpoint{2.671615in}{3.472029in}}{\pgfqpoint{2.661939in}{3.476037in}}{\pgfqpoint{2.651852in}{3.476037in}}% +\pgfpathcurveto{\pgfqpoint{2.641764in}{3.476037in}}{\pgfqpoint{2.632089in}{3.472029in}}{\pgfqpoint{2.624956in}{3.464896in}}% +\pgfpathcurveto{\pgfqpoint{2.617823in}{3.457763in}}{\pgfqpoint{2.613815in}{3.448088in}}{\pgfqpoint{2.613815in}{3.438000in}}% +\pgfpathcurveto{\pgfqpoint{2.613815in}{3.427913in}}{\pgfqpoint{2.617823in}{3.418237in}}{\pgfqpoint{2.624956in}{3.411105in}}% 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+\pgfpathcurveto{\pgfqpoint{2.689888in}{3.448088in}}{\pgfqpoint{2.685880in}{3.457763in}}{\pgfqpoint{2.678747in}{3.464896in}}% +\pgfpathcurveto{\pgfqpoint{2.671615in}{3.472029in}}{\pgfqpoint{2.661939in}{3.476037in}}{\pgfqpoint{2.651852in}{3.476037in}}% +\pgfpathcurveto{\pgfqpoint{2.641764in}{3.476037in}}{\pgfqpoint{2.632089in}{3.472029in}}{\pgfqpoint{2.624956in}{3.464896in}}% +\pgfpathcurveto{\pgfqpoint{2.617823in}{3.457763in}}{\pgfqpoint{2.613815in}{3.448088in}}{\pgfqpoint{2.613815in}{3.438000in}}% +\pgfpathcurveto{\pgfqpoint{2.613815in}{3.427913in}}{\pgfqpoint{2.617823in}{3.418237in}}{\pgfqpoint{2.624956in}{3.411105in}}% +\pgfpathcurveto{\pgfqpoint{2.632089in}{3.403972in}}{\pgfqpoint{2.641764in}{3.399964in}}{\pgfqpoint{2.651852in}{3.399964in}}% +\pgfpathclose% +\pgfusepath{stroke,fill}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfpathrectangle{\pgfqpoint{1.063006in}{0.525800in}}{\pgfqpoint{4.433988in}{3.680600in}}% +\pgfusepath{clip}% +\pgfsetbuttcap% +\pgfsetroundjoin% 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included by \input if +%% they are in the same directory as the main LaTeX file. For loading figures +%% from other directories you can use the `import` package +%% \usepackage{import} +%% and then include the figures with +%% \import{}{.pgf} +%% +%% Matplotlib used the following preamble +%% \usepackage{fontspec} +%% \setmainfont{DejaVuSans.ttf}[Path=C:/Users/mossr/.julia/conda/3/lib/site-packages/matplotlib/mpl-data/fonts/ttf/] +%% \setsansfont{DejaVuSans.ttf}[Path=C:/Users/mossr/.julia/conda/3/lib/site-packages/matplotlib/mpl-data/fonts/ttf/] +%% \setmonofont{DejaVuSansMono.ttf}[Path=C:/Users/mossr/.julia/conda/3/lib/site-packages/matplotlib/mpl-data/fonts/ttf/] +%% +\begingroup% +\makeatletter% +\begin{pgfpicture}% +\pgfpathrectangle{\pgfpointorigin}{\pgfqpoint{6.400000in}{4.780000in}}% +\pgfusepath{use as bounding box, clip}% +\begin{pgfscope}% +\pgfsetbuttcap% +\pgfsetmiterjoin% +\definecolor{currentfill}{rgb}{1.000000,1.000000,1.000000}% +\pgfsetfillcolor{currentfill}% +\pgfsetlinewidth{0.000000pt}% 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/dev/null +++ b/figures/episodic_ast/distribution-figures.pgf @@ -0,0 +1,2866 @@ +%% Creator: Matplotlib, PGF backend +%% +%% To include the figure in your LaTeX document, write +%% \input{.pgf} +%% +%% Make sure the required packages are loaded in your preamble +%% \usepackage{pgf} +%% +%% Figures using additional raster images can only be included by \input if +%% they are in the same directory as the main LaTeX file. For loading figures +%% from other directories you can use the `import` package +%% \usepackage{import} +%% and then include the figures with +%% \import{}{.pgf} +%% +%% Matplotlib used the following preamble +%% \usepackage{fontspec} +%% \setmainfont{DejaVuSans.ttf}[Path=C:/Users/mossr/.julia/conda/3/lib/site-packages/matplotlib/mpl-data/fonts/ttf/] +%% \setsansfont{DejaVuSans.ttf}[Path=C:/Users/mossr/.julia/conda/3/lib/site-packages/matplotlib/mpl-data/fonts/ttf/] +%% \setmonofont{DejaVuSansMono.ttf}[Path=C:/Users/mossr/.julia/conda/3/lib/site-packages/matplotlib/mpl-data/fonts/ttf/] +%% +\begingroup% +\makeatletter% +\begin{pgfpicture}% +\pgfpathrectangle{\pgfpointorigin}{\pgfqpoint{6.000000in}{4.980000in}}% +\pgfusepath{use as bounding box, clip}% +\begin{pgfscope}% +\pgfsetbuttcap% +\pgfsetmiterjoin% +\definecolor{currentfill}{rgb}{1.000000,1.000000,1.000000}% +\pgfsetfillcolor{currentfill}% +\pgfsetlinewidth{0.000000pt}% 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b/figures/weakness_rec/MNIST-true-positives.png new file mode 100644 index 0000000..f5a4bf3 Binary files /dev/null and b/figures/weakness_rec/MNIST-true-positives.png differ diff --git a/figures/weakness_rec/autoencoder-nn.pdf b/figures/weakness_rec/autoencoder-nn.pdf new file mode 100644 index 0000000..ef01912 Binary files /dev/null and b/figures/weakness_rec/autoencoder-nn.pdf differ diff --git a/figures/weakness_rec/confusion_adversary-img0.png b/figures/weakness_rec/confusion_adversary-img0.png new file mode 100644 index 0000000..5315d8d Binary files /dev/null and b/figures/weakness_rec/confusion_adversary-img0.png differ diff --git a/figures/weakness_rec/confusion_adversary.pgf b/figures/weakness_rec/confusion_adversary.pgf new file mode 100644 index 0000000..2aead7d --- /dev/null +++ b/figures/weakness_rec/confusion_adversary.pgf @@ -0,0 +1,424 @@ +%% Creator: Matplotlib, PGF backend +%% +%% To include the figure in your LaTeX document, write +%% \input{.pgf} +%% +%% Make sure the required packages are loaded in your preamble +%% \usepackage{pgf} +%% +%% and, on pdftex +%% \usepackage[utf8]{inputenc}\DeclareUnicodeCharacter{2212}{-} +%% +%% or, on luatex and xetex +%% \usepackage{unicode-math} +%% +%% Figures using additional raster images can only be included by \input if +%% they are in the same directory as the main LaTeX file. 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+\begin{pgfscope}% +\definecolor{textcolor}{rgb}{0.150000,0.150000,0.150000}% +\pgfsetstrokecolor{textcolor}% +\pgfsetfillcolor{textcolor}% +\pgftext[x=1.119444in,y=2.233472in,,]{\color{textcolor}\rmfamily\fontsize{12.000000}{14.400000}\selectfont 8849}% +\end{pgfscope}% +\begin{pgfscope}% +\definecolor{textcolor}{rgb}{1.000000,1.000000,1.000000}% +\pgfsetstrokecolor{textcolor}% +\pgfsetfillcolor{textcolor}% +\pgftext[x=2.359444in,y=2.233472in,,]{\color{textcolor}\rmfamily\fontsize{12.000000}{14.400000}\selectfont 474}% +\end{pgfscope}% +\begin{pgfscope}% +\definecolor{textcolor}{rgb}{1.000000,1.000000,1.000000}% +\pgfsetstrokecolor{textcolor}% +\pgfsetfillcolor{textcolor}% +\pgftext[x=1.119444in,y=1.078472in,,]{\color{textcolor}\rmfamily\fontsize{12.000000}{14.400000}\selectfont 524}% +\end{pgfscope}% +\begin{pgfscope}% +\definecolor{textcolor}{rgb}{1.000000,1.000000,1.000000}% +\pgfsetstrokecolor{textcolor}% +\pgfsetfillcolor{textcolor}% 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+\pgfpathlineto{\pgfqpoint{3.134444in}{2.801949in}}% +\pgfpathlineto{\pgfqpoint{3.134444in}{2.810972in}}% +\pgfpathlineto{\pgfqpoint{3.249944in}{2.810972in}}% +\pgfpathlineto{\pgfqpoint{3.249944in}{2.801949in}}% +\pgfpathlineto{\pgfqpoint{3.249944in}{0.509995in}}% +\pgfpathlineto{\pgfqpoint{3.249944in}{0.500972in}}% +\pgfpathclose% +\pgfusepath{}% +\end{pgfscope}% +\end{pgfpicture}% +\makeatother% +\endgroup% diff --git a/figures/weakness_rec/confusion_sut-img0.png b/figures/weakness_rec/confusion_sut-img0.png new file mode 100644 index 0000000..322faed Binary files /dev/null and b/figures/weakness_rec/confusion_sut-img0.png differ diff --git a/figures/weakness_rec/confusion_sut.pgf b/figures/weakness_rec/confusion_sut.pgf new file mode 100644 index 0000000..7289d4c --- /dev/null +++ b/figures/weakness_rec/confusion_sut.pgf @@ -0,0 +1,3178 @@ +%% Creator: Matplotlib, PGF backend +%% +%% To include the figure in your LaTeX document, write +%% \input{.pgf} +%% +%% Make sure the required packages are loaded in your preamble +%% \usepackage{pgf} +%% +%% and, on pdftex +%% \usepackage[utf8]{inputenc}\DeclareUnicodeCharacter{2212}{-} +%% +%% or, on luatex and xetex +%% \usepackage{unicode-math} +%% +%% Figures using additional raster images can only be included by \input if +%% they are in the same directory as the main LaTeX file. For loading figures +%% from other directories you can use the `import` package +%% \usepackage{import} +%% +%% and then include the figures with +%% \import{}{.pgf} +%% +%% Matplotlib used the following preamble +%% \usepackage{fontspec} +%% +\begingroup% +\makeatletter% +\begin{pgfpicture}% +\pgfpathrectangle{\pgfpointorigin}{\pgfqpoint{3.724945in}{3.110111in}}% +\pgfusepath{use as bounding box, clip}% +\begin{pgfscope}% +\pgfsetbuttcap% +\pgfsetmiterjoin% +\definecolor{currentfill}{rgb}{1.000000,1.000000,1.000000}% +\pgfsetfillcolor{currentfill}% +\pgfsetlinewidth{0.000000pt}% +\definecolor{currentstroke}{rgb}{1.000000,1.000000,1.000000}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}% +\pgfpathlineto{\pgfqpoint{3.724945in}{0.000000in}}% +\pgfpathlineto{\pgfqpoint{3.724945in}{3.110111in}}% +\pgfpathlineto{\pgfqpoint{0.000000in}{3.110111in}}% +\pgfpathclose% +\pgfusepath{fill}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsetbuttcap% +\pgfsetmiterjoin% +\definecolor{currentfill}{rgb}{1.000000,1.000000,1.000000}% +\pgfsetfillcolor{currentfill}% +\pgfsetlinewidth{0.000000pt}% +\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetstrokeopacity{0.000000}% +\pgfsetdash{}{0pt}% +\pgfpathmoveto{\pgfqpoint{0.499444in}{0.499444in}}% +\pgfpathlineto{\pgfqpoint{2.979444in}{0.499444in}}% +\pgfpathlineto{\pgfqpoint{2.979444in}{2.809444in}}% +\pgfpathlineto{\pgfqpoint{0.499444in}{2.809444in}}% +\pgfpathclose% +\pgfusepath{fill}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfpathrectangle{\pgfqpoint{0.499444in}{0.499444in}}{\pgfqpoint{2.480000in}{2.310000in}}% +\pgfusepath{clip}% +\pgfsetbuttcap% +\pgfsetroundjoin% +\definecolor{currentfill}{rgb}{0.647257,0.858400,0.209861}% +\pgfsetfillcolor{currentfill}% +\pgfsetlinewidth{0.000000pt}% +\definecolor{currentstroke}{rgb}{1.000000,1.000000,1.000000}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% 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100644 index 0000000..adab217 --- /dev/null +++ b/figures/weakness_rec/failure-likelihood.pgf @@ -0,0 +1,14590 @@ +%% Creator: Matplotlib, PGF backend +%% +%% To include the figure in your LaTeX document, write +%% \input{.pgf} +%% +%% Make sure the required packages are loaded in your preamble +%% \usepackage{pgf} +%% +%% and, on pdftex +%% \usepackage[utf8]{inputenc}\DeclareUnicodeCharacter{2212}{-} +%% +%% or, on luatex and xetex +%% \usepackage{unicode-math} +%% +%% Figures using additional raster images can only be included by \input if +%% they are in the same directory as the main LaTeX file. For loading figures +%% from other directories you can use the `import` package +%% \usepackage{import} +%% +%% and then include the figures with +%% \import{}{.pgf} +%% +%% Matplotlib used the following preamble +%% \usepackage{fontspec} +%% +\begingroup% +\makeatletter% +\begin{pgfpicture}% +\pgfpathrectangle{\pgfpointorigin}{\pgfqpoint{3.640254in}{3.124000in}}% +\pgfusepath{use as bounding box, clip}% +\begin{pgfscope}% +\pgfsetbuttcap% +\pgfsetmiterjoin% +\definecolor{currentfill}{rgb}{1.000000,1.000000,1.000000}% +\pgfsetfillcolor{currentfill}% +\pgfsetlinewidth{0.000000pt}% +\definecolor{currentstroke}{rgb}{1.000000,1.000000,1.000000}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}% +\pgfpathlineto{\pgfqpoint{3.640254in}{0.000000in}}% +\pgfpathlineto{\pgfqpoint{3.640254in}{3.124000in}}% +\pgfpathlineto{\pgfqpoint{0.000000in}{3.124000in}}% +\pgfpathclose% +\pgfusepath{fill}% +\end{pgfscope}% +\begin{pgfscope}% 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+\pgfsetroundjoin% +\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetfillcolor{currentfill}% +\pgfsetlinewidth{0.803000pt}% +\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfsys@defobject{currentmarker}{\pgfqpoint{-0.048611in}{0.000000in}}{\pgfqpoint{0.000000in}{0.000000in}}{% +\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}% +\pgfpathlineto{\pgfqpoint{-0.048611in}{0.000000in}}% +\pgfusepath{stroke,fill}% +}% +\begin{pgfscope}% +\pgfsys@transformshift{0.515062in}{1.092500in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\end{pgfscope}% +\begin{pgfscope}% +\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetstrokecolor{textcolor}% +\pgfsetfillcolor{textcolor}% +\pgftext[x=0.278951in, y=1.044305in, left, base]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont 21}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsetbuttcap% +\pgfsetroundjoin% +\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetfillcolor{currentfill}% +\pgfsetlinewidth{0.803000pt}% +\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfsys@defobject{currentmarker}{\pgfqpoint{-0.048611in}{0.000000in}}{\pgfqpoint{0.000000in}{0.000000in}}{% +\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}% +\pgfpathlineto{\pgfqpoint{-0.048611in}{0.000000in}}% +\pgfusepath{stroke,fill}% +}% +\begin{pgfscope}% +\pgfsys@transformshift{0.515062in}{0.515000in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\end{pgfscope}% +\begin{pgfscope}% +\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetstrokecolor{textcolor}% +\pgfsetfillcolor{textcolor}% +\pgftext[x=0.278951in, y=0.466805in, left, base]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont 28}% +\end{pgfscope}% +\begin{pgfscope}% +\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetstrokecolor{textcolor}% +\pgfsetfillcolor{textcolor}% +\pgftext[x=0.223395in,y=1.670000in,,bottom,rotate=90.000000]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle y\)-label}% +\end{pgfscope}% +\begin{pgfscope}% +\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetstrokecolor{textcolor}% +\pgfsetfillcolor{textcolor}% +\pgftext[x=1.755062in,y=2.908333in,,base]{\color{textcolor}\rmfamily\fontsize{12.000000}{14.400000}\selectfont Failure likelihood per pixel}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfpathrectangle{\pgfqpoint{3.150062in}{0.515000in}}{\pgfqpoint{0.115500in}{2.310000in}}% +\pgfusepath{clip}% +\pgfsetbuttcap% +\pgfsetmiterjoin% +\definecolor{currentfill}{rgb}{1.000000,1.000000,1.000000}% +\pgfsetfillcolor{currentfill}% +\pgfsetlinewidth{0.010037pt}% +\definecolor{currentstroke}{rgb}{1.000000,1.000000,1.000000}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% 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+\pgfsetdash{}{0pt}% +\pgfsys@defobject{currentmarker}{\pgfqpoint{0.000000in}{0.000000in}}{\pgfqpoint{0.048611in}{0.000000in}}{% +\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}% +\pgfpathlineto{\pgfqpoint{0.048611in}{0.000000in}}% +\pgfusepath{stroke,fill}% +}% +\begin{pgfscope}% +\pgfsys@transformshift{3.265562in}{1.028934in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\end{pgfscope}% +\begin{pgfscope}% +\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetstrokecolor{textcolor}% +\pgfsetfillcolor{textcolor}% +\pgftext[x=3.362784in, y=0.980740in, left, base]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle {0.1}\)}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsetbuttcap% +\pgfsetroundjoin% +\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetfillcolor{currentfill}% +\pgfsetlinewidth{0.803000pt}% +\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetstrokecolor{currentstroke}% 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+\pgfsetdash{}{0pt}% +\pgfsys@defobject{currentmarker}{\pgfqpoint{0.000000in}{0.000000in}}{\pgfqpoint{0.048611in}{0.000000in}}{% +\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}% +\pgfpathlineto{\pgfqpoint{0.048611in}{0.000000in}}% +\pgfusepath{stroke,fill}% +}% +\begin{pgfscope}% +\pgfsys@transformshift{3.265562in}{2.137873in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\end{pgfscope}% +\begin{pgfscope}% +\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetstrokecolor{textcolor}% +\pgfsetfillcolor{textcolor}% +\pgftext[x=3.362784in, y=2.089679in, left, base]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle {0.3}\)}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsetbuttcap% +\pgfsetroundjoin% +\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetfillcolor{currentfill}% +\pgfsetlinewidth{0.803000pt}% +\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfsys@defobject{currentmarker}{\pgfqpoint{0.000000in}{0.000000in}}{\pgfqpoint{0.048611in}{0.000000in}}{% +\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}% +\pgfpathlineto{\pgfqpoint{0.048611in}{0.000000in}}% +\pgfusepath{stroke,fill}% +}% +\begin{pgfscope}% +\pgfsys@transformshift{3.265562in}{2.692343in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\end{pgfscope}% +\begin{pgfscope}% +\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetstrokecolor{textcolor}% +\pgfsetfillcolor{textcolor}% +\pgftext[x=3.362784in, y=2.644149in, left, base]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle {0.4}\)}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsetbuttcap% +\pgfsetmiterjoin% +\pgfsetlinewidth{0.000000pt}% +\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfpathmoveto{\pgfqpoint{3.150062in}{0.515000in}}% +\pgfpathlineto{\pgfqpoint{3.150062in}{0.524023in}}% +\pgfpathlineto{\pgfqpoint{3.150062in}{2.815976in}}% +\pgfpathlineto{\pgfqpoint{3.150062in}{2.825000in}}% +\pgfpathlineto{\pgfqpoint{3.265562in}{2.825000in}}% +\pgfpathlineto{\pgfqpoint{3.265562in}{2.815976in}}% +\pgfpathlineto{\pgfqpoint{3.265562in}{0.524023in}}% +\pgfpathlineto{\pgfqpoint{3.265562in}{0.515000in}}% +\pgfpathclose% +\pgfusepath{}% +\end{pgfscope}% +\end{pgfpicture}% +\makeatother% +\endgroup% diff --git a/figures/weakness_rec/feature-likelihood-img0.png b/figures/weakness_rec/feature-likelihood-img0.png new file mode 100644 index 0000000..3bb424e Binary files /dev/null and b/figures/weakness_rec/feature-likelihood-img0.png differ diff --git a/figures/weakness_rec/feature-likelihood.pgf b/figures/weakness_rec/feature-likelihood.pgf new file mode 100644 index 0000000..77d838a --- /dev/null +++ b/figures/weakness_rec/feature-likelihood.pgf @@ -0,0 +1,903846 @@ +%% Creator: Matplotlib, PGF backend +%% +%% To include the figure in your LaTeX document, write +%% \input{.pgf} +%% +%% Make sure the required packages are loaded in your preamble +%% \usepackage{pgf} +%% +%% and, on pdftex +%% \usepackage[utf8]{inputenc}\DeclareUnicodeCharacter{2212}{-} +%% +%% or, on luatex and xetex +%% \usepackage{unicode-math} +%% +%% Figures using additional raster images can only be included by \input if +%% they are in the same directory as the main LaTeX file. For loading figures +%% from other directories you can use the `import` package +%% \usepackage{import} +%% +%% and then include the figures with +%% \import{}{.pgf} +%% +%% Matplotlib used the following preamble +%% \usepackage{fontspec} +%% +\begingroup% +\makeatletter% +\begin{pgfpicture}% +\pgfpathrectangle{\pgfpointorigin}{\pgfqpoint{4.339032in}{3.826222in}}% +\pgfusepath{use as bounding box, clip}% +\begin{pgfscope}% +\pgfsetbuttcap% +\pgfsetmiterjoin% +\definecolor{currentfill}{rgb}{1.000000,1.000000,1.000000}% +\pgfsetfillcolor{currentfill}% +\pgfsetlinewidth{0.000000pt}% +\definecolor{currentstroke}{rgb}{1.000000,1.000000,1.000000}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}% +\pgfpathlineto{\pgfqpoint{4.339032in}{0.000000in}}% +\pgfpathlineto{\pgfqpoint{4.339032in}{3.826222in}}% +\pgfpathlineto{\pgfqpoint{0.000000in}{3.826222in}}% +\pgfpathclose% +\pgfusepath{fill}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsetbuttcap% +\pgfsetmiterjoin% +\definecolor{currentfill}{rgb}{1.000000,1.000000,1.000000}% +\pgfsetfillcolor{currentfill}% +\pgfsetlinewidth{0.000000pt}% +\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetstrokeopacity{0.000000}% +\pgfsetdash{}{0pt}% +\pgfpathmoveto{\pgfqpoint{0.447145in}{0.445555in}}% +\pgfpathlineto{\pgfqpoint{3.547145in}{0.445555in}}% +\pgfpathlineto{\pgfqpoint{3.547145in}{3.525555in}}% +\pgfpathlineto{\pgfqpoint{0.447145in}{3.525555in}}% +\pgfpathclose% +\pgfusepath{fill}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfpathrectangle{\pgfqpoint{0.447145in}{0.445555in}}{\pgfqpoint{3.100000in}{3.080000in}}% +\pgfusepath{clip}% +\pgfsetbuttcap% +\pgfsetroundjoin% +\definecolor{currentfill}{rgb}{0.267004,0.004874,0.329415}% +\pgfsetfillcolor{currentfill}% +\pgfsetlinewidth{0.000000pt}% +\definecolor{currentstroke}{rgb}{1.000000,1.000000,1.000000}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfpathmoveto{\pgfqpoint{0.447145in}{3.525555in}}% +\pgfpathlineto{\pgfqpoint{0.460984in}{3.525555in}}% +\pgfpathlineto{\pgfqpoint{0.460984in}{3.511805in}}% +\pgfpathlineto{\pgfqpoint{0.447145in}{3.511805in}}% +\pgfpathlineto{\pgfqpoint{0.447145in}{3.525555in}}% +\pgfusepath{fill}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfpathrectangle{\pgfqpoint{0.447145in}{0.445555in}}{\pgfqpoint{3.100000in}{3.080000in}}% +\pgfusepath{clip}% +\pgfsetbuttcap% +\pgfsetroundjoin% +\definecolor{currentfill}{rgb}{0.267004,0.004874,0.329415}% +\pgfsetfillcolor{currentfill}% +\pgfsetlinewidth{0.000000pt}% +\definecolor{currentstroke}{rgb}{1.000000,1.000000,1.000000}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfpathmoveto{\pgfqpoint{0.460984in}{3.525555in}}% +\pgfpathlineto{\pgfqpoint{0.474824in}{3.525555in}}% +\pgfpathlineto{\pgfqpoint{0.474824in}{3.511805in}}% +\pgfpathlineto{\pgfqpoint{0.460984in}{3.511805in}}% +\pgfpathlineto{\pgfqpoint{0.460984in}{3.525555in}}% +\pgfusepath{fill}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfpathrectangle{\pgfqpoint{0.447145in}{0.445555in}}{\pgfqpoint{3.100000in}{3.080000in}}% +\pgfusepath{clip}% +\pgfsetbuttcap% +\pgfsetroundjoin% +\definecolor{currentfill}{rgb}{0.267004,0.004874,0.329415}% +\pgfsetfillcolor{currentfill}% +\pgfsetlinewidth{0.000000pt}% +\definecolor{currentstroke}{rgb}{1.000000,1.000000,1.000000}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfpathmoveto{\pgfqpoint{0.474824in}{3.525555in}}% +\pgfpathlineto{\pgfqpoint{0.488663in}{3.525555in}}% +\pgfpathlineto{\pgfqpoint{0.488663in}{3.511805in}}% +\pgfpathlineto{\pgfqpoint{0.474824in}{3.511805in}}% +\pgfpathlineto{\pgfqpoint{0.474824in}{3.525555in}}% +\pgfusepath{fill}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfpathrectangle{\pgfqpoint{0.447145in}{0.445555in}}{\pgfqpoint{3.100000in}{3.080000in}}% +\pgfusepath{clip}% +\pgfsetbuttcap% +\pgfsetroundjoin% +\definecolor{currentfill}{rgb}{0.267004,0.004874,0.329415}% +\pgfsetfillcolor{currentfill}% 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+\end{pgfscope}% +\begin{pgfscope}% +\pgfpathrectangle{\pgfqpoint{0.447145in}{0.445555in}}{\pgfqpoint{3.100000in}{3.080000in}}% +\pgfusepath{clip}% +\pgfsetbuttcap% +\pgfsetroundjoin% +\definecolor{currentfill}{rgb}{0.267004,0.004874,0.329415}% +\pgfsetfillcolor{currentfill}% +\pgfsetlinewidth{0.000000pt}% +\definecolor{currentstroke}{rgb}{1.000000,1.000000,1.000000}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfpathmoveto{\pgfqpoint{3.505627in}{0.459305in}}% +\pgfpathlineto{\pgfqpoint{3.519466in}{0.459305in}}% +\pgfpathlineto{\pgfqpoint{3.519466in}{0.445555in}}% +\pgfpathlineto{\pgfqpoint{3.505627in}{0.445555in}}% +\pgfpathlineto{\pgfqpoint{3.505627in}{0.459305in}}% +\pgfusepath{fill}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfpathrectangle{\pgfqpoint{0.447145in}{0.445555in}}{\pgfqpoint{3.100000in}{3.080000in}}% +\pgfusepath{clip}% +\pgfsetbuttcap% +\pgfsetroundjoin% +\definecolor{currentfill}{rgb}{0.267004,0.004874,0.329415}% +\pgfsetfillcolor{currentfill}% +\pgfsetlinewidth{0.000000pt}% +\definecolor{currentstroke}{rgb}{1.000000,1.000000,1.000000}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfpathmoveto{\pgfqpoint{3.519466in}{0.459305in}}% +\pgfpathlineto{\pgfqpoint{3.533306in}{0.459305in}}% +\pgfpathlineto{\pgfqpoint{3.533306in}{0.445555in}}% +\pgfpathlineto{\pgfqpoint{3.519466in}{0.445555in}}% +\pgfpathlineto{\pgfqpoint{3.519466in}{0.459305in}}% +\pgfusepath{fill}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfpathrectangle{\pgfqpoint{0.447145in}{0.445555in}}{\pgfqpoint{3.100000in}{3.080000in}}% +\pgfusepath{clip}% +\pgfsetbuttcap% +\pgfsetroundjoin% +\definecolor{currentfill}{rgb}{0.267004,0.004874,0.329415}% +\pgfsetfillcolor{currentfill}% +\pgfsetlinewidth{0.000000pt}% +\definecolor{currentstroke}{rgb}{1.000000,1.000000,1.000000}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfpathmoveto{\pgfqpoint{3.533306in}{0.459305in}}% +\pgfpathlineto{\pgfqpoint{3.547145in}{0.459305in}}% +\pgfpathlineto{\pgfqpoint{3.547145in}{0.445555in}}% +\pgfpathlineto{\pgfqpoint{3.533306in}{0.445555in}}% +\pgfpathlineto{\pgfqpoint{3.533306in}{0.459305in}}% +\pgfusepath{fill}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsetbuttcap% +\pgfsetroundjoin% +\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetfillcolor{currentfill}% +\pgfsetlinewidth{0.803000pt}% +\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfsys@defobject{currentmarker}{\pgfqpoint{0.000000in}{-0.048611in}}{\pgfqpoint{0.000000in}{0.000000in}}{% +\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}% +\pgfpathlineto{\pgfqpoint{0.000000in}{-0.048611in}}% +\pgfusepath{stroke,fill}% +}% +\begin{pgfscope}% +\pgfsys@transformshift{0.640895in}{0.445555in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\end{pgfscope}% +\begin{pgfscope}% +\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetstrokecolor{textcolor}% +\pgfsetfillcolor{textcolor}% +\pgftext[x=0.675617in, y=0.278889in, left, base,rotate=90.000000]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont 1}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsetbuttcap% +\pgfsetroundjoin% +\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetfillcolor{currentfill}% +\pgfsetlinewidth{0.803000pt}% +\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfsys@defobject{currentmarker}{\pgfqpoint{0.000000in}{-0.048611in}}{\pgfqpoint{0.000000in}{0.000000in}}{% +\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}% +\pgfpathlineto{\pgfqpoint{0.000000in}{-0.048611in}}% +\pgfusepath{stroke,fill}% +}% +\begin{pgfscope}% +\pgfsys@transformshift{1.028395in}{0.445555in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\end{pgfscope}% +\begin{pgfscope}% +\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetstrokecolor{textcolor}% +\pgfsetfillcolor{textcolor}% +\pgftext[x=1.063117in, y=0.278889in, left, base,rotate=90.000000]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont 2}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsetbuttcap% +\pgfsetroundjoin% +\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetfillcolor{currentfill}% +\pgfsetlinewidth{0.803000pt}% +\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfsys@defobject{currentmarker}{\pgfqpoint{0.000000in}{-0.048611in}}{\pgfqpoint{0.000000in}{0.000000in}}{% +\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}% +\pgfpathlineto{\pgfqpoint{0.000000in}{-0.048611in}}% +\pgfusepath{stroke,fill}% +}% +\begin{pgfscope}% +\pgfsys@transformshift{1.415895in}{0.445555in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\end{pgfscope}% +\begin{pgfscope}% +\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetstrokecolor{textcolor}% +\pgfsetfillcolor{textcolor}% +\pgftext[x=1.450617in, y=0.278889in, left, base,rotate=90.000000]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont 3}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsetbuttcap% +\pgfsetroundjoin% +\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetfillcolor{currentfill}% +\pgfsetlinewidth{0.803000pt}% +\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfsys@defobject{currentmarker}{\pgfqpoint{0.000000in}{-0.048611in}}{\pgfqpoint{0.000000in}{0.000000in}}{% +\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}% +\pgfpathlineto{\pgfqpoint{0.000000in}{-0.048611in}}% +\pgfusepath{stroke,fill}% +}% +\begin{pgfscope}% +\pgfsys@transformshift{1.803395in}{0.445555in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\end{pgfscope}% +\begin{pgfscope}% +\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetstrokecolor{textcolor}% +\pgfsetfillcolor{textcolor}% +\pgftext[x=1.838117in, y=0.278889in, left, base,rotate=90.000000]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont 4}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsetbuttcap% +\pgfsetroundjoin% +\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetfillcolor{currentfill}% +\pgfsetlinewidth{0.803000pt}% +\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfsys@defobject{currentmarker}{\pgfqpoint{0.000000in}{-0.048611in}}{\pgfqpoint{0.000000in}{0.000000in}}{% +\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}% +\pgfpathlineto{\pgfqpoint{0.000000in}{-0.048611in}}% +\pgfusepath{stroke,fill}% +}% +\begin{pgfscope}% +\pgfsys@transformshift{2.190895in}{0.445555in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\end{pgfscope}% +\begin{pgfscope}% +\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetstrokecolor{textcolor}% +\pgfsetfillcolor{textcolor}% +\pgftext[x=2.225617in, y=0.278889in, left, base,rotate=90.000000]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont 5}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsetbuttcap% +\pgfsetroundjoin% +\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetfillcolor{currentfill}% +\pgfsetlinewidth{0.803000pt}% +\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfsys@defobject{currentmarker}{\pgfqpoint{0.000000in}{-0.048611in}}{\pgfqpoint{0.000000in}{0.000000in}}{% +\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}% +\pgfpathlineto{\pgfqpoint{0.000000in}{-0.048611in}}% +\pgfusepath{stroke,fill}% +}% +\begin{pgfscope}% +\pgfsys@transformshift{2.578395in}{0.445555in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\end{pgfscope}% +\begin{pgfscope}% +\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetstrokecolor{textcolor}% +\pgfsetfillcolor{textcolor}% +\pgftext[x=2.613117in, y=0.278889in, left, base,rotate=90.000000]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont 6}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsetbuttcap% +\pgfsetroundjoin% +\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetfillcolor{currentfill}% +\pgfsetlinewidth{0.803000pt}% +\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfsys@defobject{currentmarker}{\pgfqpoint{0.000000in}{-0.048611in}}{\pgfqpoint{0.000000in}{0.000000in}}{% +\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}% +\pgfpathlineto{\pgfqpoint{0.000000in}{-0.048611in}}% +\pgfusepath{stroke,fill}% +}% +\begin{pgfscope}% +\pgfsys@transformshift{2.965895in}{0.445555in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\end{pgfscope}% +\begin{pgfscope}% +\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetstrokecolor{textcolor}% +\pgfsetfillcolor{textcolor}% +\pgftext[x=3.000617in, y=0.278889in, left, base,rotate=90.000000]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont 7}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsetbuttcap% +\pgfsetroundjoin% +\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetfillcolor{currentfill}% +\pgfsetlinewidth{0.803000pt}% +\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfsys@defobject{currentmarker}{\pgfqpoint{0.000000in}{-0.048611in}}{\pgfqpoint{0.000000in}{0.000000in}}{% +\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}% +\pgfpathlineto{\pgfqpoint{0.000000in}{-0.048611in}}% +\pgfusepath{stroke,fill}% +}% +\begin{pgfscope}% +\pgfsys@transformshift{3.353395in}{0.445555in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\end{pgfscope}% +\begin{pgfscope}% +\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetstrokecolor{textcolor}% +\pgfsetfillcolor{textcolor}% +\pgftext[x=3.388117in, y=0.278889in, left, base,rotate=90.000000]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont 8}% +\end{pgfscope}% +\begin{pgfscope}% +\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetstrokecolor{textcolor}% +\pgfsetfillcolor{textcolor}% +\pgftext[x=1.997145in,y=0.223333in,,top]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont feature index \(\displaystyle i\)}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsetbuttcap% +\pgfsetroundjoin% +\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetfillcolor{currentfill}% +\pgfsetlinewidth{0.803000pt}% +\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfsys@defobject{currentmarker}{\pgfqpoint{-0.048611in}{0.000000in}}{\pgfqpoint{0.000000in}{0.000000in}}{% +\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}% +\pgfpathlineto{\pgfqpoint{-0.048611in}{0.000000in}}% +\pgfusepath{stroke,fill}% +}% +\begin{pgfscope}% +\pgfsys@transformshift{0.447145in}{3.333055in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\end{pgfscope}% +\begin{pgfscope}% +\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetstrokecolor{textcolor}% +\pgfsetfillcolor{textcolor}% +\pgftext[x=0.280478in, y=3.284861in, left, base]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont 1}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsetbuttcap% +\pgfsetroundjoin% +\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetfillcolor{currentfill}% +\pgfsetlinewidth{0.803000pt}% +\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfsys@defobject{currentmarker}{\pgfqpoint{-0.048611in}{0.000000in}}{\pgfqpoint{0.000000in}{0.000000in}}{% +\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}% +\pgfpathlineto{\pgfqpoint{-0.048611in}{0.000000in}}% +\pgfusepath{stroke,fill}% +}% +\begin{pgfscope}% +\pgfsys@transformshift{0.447145in}{2.948055in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\end{pgfscope}% +\begin{pgfscope}% +\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetstrokecolor{textcolor}% +\pgfsetfillcolor{textcolor}% +\pgftext[x=0.280478in, y=2.899861in, left, base]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont 2}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsetbuttcap% +\pgfsetroundjoin% +\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetfillcolor{currentfill}% +\pgfsetlinewidth{0.803000pt}% +\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfsys@defobject{currentmarker}{\pgfqpoint{-0.048611in}{0.000000in}}{\pgfqpoint{0.000000in}{0.000000in}}{% +\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}% +\pgfpathlineto{\pgfqpoint{-0.048611in}{0.000000in}}% +\pgfusepath{stroke,fill}% +}% +\begin{pgfscope}% +\pgfsys@transformshift{0.447145in}{2.563055in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\end{pgfscope}% +\begin{pgfscope}% +\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetstrokecolor{textcolor}% +\pgfsetfillcolor{textcolor}% +\pgftext[x=0.280478in, y=2.514861in, left, base]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont 3}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsetbuttcap% +\pgfsetroundjoin% +\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetfillcolor{currentfill}% +\pgfsetlinewidth{0.803000pt}% +\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfsys@defobject{currentmarker}{\pgfqpoint{-0.048611in}{0.000000in}}{\pgfqpoint{0.000000in}{0.000000in}}{% +\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}% +\pgfpathlineto{\pgfqpoint{-0.048611in}{0.000000in}}% +\pgfusepath{stroke,fill}% +}% +\begin{pgfscope}% +\pgfsys@transformshift{0.447145in}{2.178055in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\end{pgfscope}% +\begin{pgfscope}% +\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetstrokecolor{textcolor}% +\pgfsetfillcolor{textcolor}% +\pgftext[x=0.280478in, y=2.129861in, left, base]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont 4}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsetbuttcap% +\pgfsetroundjoin% +\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetfillcolor{currentfill}% +\pgfsetlinewidth{0.803000pt}% +\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfsys@defobject{currentmarker}{\pgfqpoint{-0.048611in}{0.000000in}}{\pgfqpoint{0.000000in}{0.000000in}}{% +\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}% +\pgfpathlineto{\pgfqpoint{-0.048611in}{0.000000in}}% +\pgfusepath{stroke,fill}% +}% +\begin{pgfscope}% +\pgfsys@transformshift{0.447145in}{1.793055in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\end{pgfscope}% +\begin{pgfscope}% +\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetstrokecolor{textcolor}% +\pgfsetfillcolor{textcolor}% +\pgftext[x=0.280478in, y=1.744861in, left, base]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont 5}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsetbuttcap% +\pgfsetroundjoin% +\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetfillcolor{currentfill}% +\pgfsetlinewidth{0.803000pt}% +\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfsys@defobject{currentmarker}{\pgfqpoint{-0.048611in}{0.000000in}}{\pgfqpoint{0.000000in}{0.000000in}}{% +\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}% +\pgfpathlineto{\pgfqpoint{-0.048611in}{0.000000in}}% +\pgfusepath{stroke,fill}% +}% +\begin{pgfscope}% +\pgfsys@transformshift{0.447145in}{1.408055in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\end{pgfscope}% +\begin{pgfscope}% +\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetstrokecolor{textcolor}% +\pgfsetfillcolor{textcolor}% +\pgftext[x=0.280478in, y=1.359861in, left, base]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont 6}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsetbuttcap% +\pgfsetroundjoin% +\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetfillcolor{currentfill}% +\pgfsetlinewidth{0.803000pt}% +\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfsys@defobject{currentmarker}{\pgfqpoint{-0.048611in}{0.000000in}}{\pgfqpoint{0.000000in}{0.000000in}}{% +\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}% +\pgfpathlineto{\pgfqpoint{-0.048611in}{0.000000in}}% +\pgfusepath{stroke,fill}% +}% +\begin{pgfscope}% +\pgfsys@transformshift{0.447145in}{1.023055in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\end{pgfscope}% +\begin{pgfscope}% +\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetstrokecolor{textcolor}% +\pgfsetfillcolor{textcolor}% +\pgftext[x=0.280478in, y=0.974861in, left, base]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont 7}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsetbuttcap% +\pgfsetroundjoin% +\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetfillcolor{currentfill}% +\pgfsetlinewidth{0.803000pt}% +\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfsys@defobject{currentmarker}{\pgfqpoint{-0.048611in}{0.000000in}}{\pgfqpoint{0.000000in}{0.000000in}}{% +\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}% +\pgfpathlineto{\pgfqpoint{-0.048611in}{0.000000in}}% +\pgfusepath{stroke,fill}% +}% +\begin{pgfscope}% +\pgfsys@transformshift{0.447145in}{0.638055in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\end{pgfscope}% +\begin{pgfscope}% +\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetstrokecolor{textcolor}% +\pgfsetfillcolor{textcolor}% +\pgftext[x=0.280478in, y=0.589861in, left, base]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont 8}% +\end{pgfscope}% +\begin{pgfscope}% +\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetstrokecolor{textcolor}% +\pgfsetfillcolor{textcolor}% +\pgftext[x=0.224923in,y=1.985555in,,bottom,rotate=90.000000]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont feature index \(\displaystyle j\)}% +\end{pgfscope}% +\begin{pgfscope}% +\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetstrokecolor{textcolor}% +\pgfsetfillcolor{textcolor}% +\pgftext[x=1.997145in,y=3.608889in,,base]{\color{textcolor}\rmfamily\fontsize{12.000000}{14.400000}\selectfont Likelihood sweep over low-dimensional features}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfpathrectangle{\pgfqpoint{3.740895in}{0.445555in}}{\pgfqpoint{0.154000in}{3.080000in}}% +\pgfusepath{clip}% +\pgfsetbuttcap% +\pgfsetmiterjoin% +\definecolor{currentfill}{rgb}{1.000000,1.000000,1.000000}% +\pgfsetfillcolor{currentfill}% +\pgfsetlinewidth{0.010037pt}% +\definecolor{currentstroke}{rgb}{1.000000,1.000000,1.000000}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfpathmoveto{\pgfqpoint{3.740895in}{0.445555in}}% +\pgfpathlineto{\pgfqpoint{3.740895in}{0.457587in}}% +\pgfpathlineto{\pgfqpoint{3.740895in}{3.513524in}}% +\pgfpathlineto{\pgfqpoint{3.740895in}{3.525555in}}% +\pgfpathlineto{\pgfqpoint{3.894895in}{3.525555in}}% +\pgfpathlineto{\pgfqpoint{3.894895in}{3.513524in}}% +\pgfpathlineto{\pgfqpoint{3.894895in}{0.457587in}}% +\pgfpathlineto{\pgfqpoint{3.894895in}{0.445555in}}% +\pgfpathclose% +\pgfusepath{stroke,fill}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{3.740000in}{0.456222in}% +\pgftext[left,bottom]{\includegraphics[interpolate=true,width=0.150000in,height=3.080000in]{figures/weakness_rec/feature-likelihood-img0.png}}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsetbuttcap% +\pgfsetroundjoin% +\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetfillcolor{currentfill}% +\pgfsetlinewidth{0.803000pt}% +\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfsys@defobject{currentmarker}{\pgfqpoint{0.000000in}{0.000000in}}{\pgfqpoint{0.048611in}{0.000000in}}{% +\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}% +\pgfpathlineto{\pgfqpoint{0.048611in}{0.000000in}}% +\pgfusepath{stroke,fill}% +}% +\begin{pgfscope}% +\pgfsys@transformshift{3.894895in}{0.445555in}% +\pgfsys@useobject{currentmarker}{}% 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+\end{pgfscope}% +\end{pgfpicture}% +\makeatother% +\endgroup% diff --git a/figures/weakness_rec/roc.pgf b/figures/weakness_rec/roc.pgf new file mode 100644 index 0000000..cc48ab6 --- /dev/null +++ b/figures/weakness_rec/roc.pgf @@ -0,0 +1,10418 @@ +%% Creator: Matplotlib, PGF backend +%% +%% To include the figure in your LaTeX document, write +%% \input{.pgf} +%% +%% Make sure the required packages are loaded in your preamble +%% \usepackage{pgf} +%% +%% and, on pdftex +%% \usepackage[utf8]{inputenc}\DeclareUnicodeCharacter{2212}{-} +%% +%% or, on luatex and xetex +%% \usepackage{unicode-math} +%% +%% Figures using additional raster images can only be included by \input if +%% they are in the same directory as the main LaTeX file. For loading figures +%% from other directories you can use the `import` package +%% \usepackage{import} +%% +%% and then include the figures with +%% \import{}{.pgf} +%% +%% Matplotlib used the following preamble +%% \usepackage{fontspec} +%% +\begingroup% +\makeatletter% +\begin{pgfpicture}% +\pgfpathrectangle{\pgfpointorigin}{\pgfqpoint{5.729392in}{3.119305in}}% +\pgfusepath{use as bounding box, clip}% +\begin{pgfscope}% +\pgfsetbuttcap% +\pgfsetmiterjoin% +\definecolor{currentfill}{rgb}{1.000000,1.000000,1.000000}% +\pgfsetfillcolor{currentfill}% +\pgfsetlinewidth{0.000000pt}% +\definecolor{currentstroke}{rgb}{1.000000,1.000000,1.000000}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}% +\pgfpathlineto{\pgfqpoint{5.729392in}{0.000000in}}% +\pgfpathlineto{\pgfqpoint{5.729392in}{3.119305in}}% +\pgfpathlineto{\pgfqpoint{0.000000in}{3.119305in}}% +\pgfpathclose% +\pgfusepath{fill}% +\end{pgfscope}% +\begin{pgfscope}% 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+\pgfsetstrokecolor{textcolor}% +\pgfsetfillcolor{textcolor}% +\pgftext[x=2.446641in,y=2.894305in,,base]{\color{textcolor}\rmfamily\fontsize{12.000000}{14.400000}\selectfont Receiver operating characteristic (ROC) curve per iteration \(\displaystyle t \in T\)}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsetbuttcap% +\pgfsetmiterjoin% +\definecolor{currentfill}{rgb}{1.000000,1.000000,1.000000}% +\pgfsetfillcolor{currentfill}% +\pgfsetfillopacity{0.800000}% +\pgfsetlinewidth{1.003750pt}% +\definecolor{currentstroke}{rgb}{0.800000,0.800000,0.800000}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetstrokeopacity{0.800000}% +\pgfsetdash{}{0pt}% +\pgfpathmoveto{\pgfqpoint{4.217863in}{0.667084in}}% +\pgfpathlineto{\pgfqpoint{5.601615in}{0.667084in}}% +\pgfpathquadraticcurveto{\pgfqpoint{5.629392in}{0.667084in}}{\pgfqpoint{5.629392in}{0.694862in}}% +\pgfpathlineto{\pgfqpoint{5.629392in}{2.617082in}}% +\pgfpathquadraticcurveto{\pgfqpoint{5.629392in}{2.644860in}}{\pgfqpoint{5.601615in}{2.644860in}}% +\pgfpathlineto{\pgfqpoint{4.217863in}{2.644860in}}% +\pgfpathquadraticcurveto{\pgfqpoint{4.190085in}{2.644860in}}{\pgfqpoint{4.190085in}{2.617082in}}% +\pgfpathlineto{\pgfqpoint{4.190085in}{0.694862in}}% +\pgfpathquadraticcurveto{\pgfqpoint{4.190085in}{0.667084in}}{\pgfqpoint{4.217863in}{0.667084in}}% +\pgfpathclose% +\pgfusepath{stroke,fill}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsetrectcap% +\pgfsetroundjoin% +\pgfsetlinewidth{1.505625pt}% +\definecolor{currentstroke}{rgb}{0.969000,0.984000,1.000000}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfpathmoveto{\pgfqpoint{4.245641in}{2.540693in}}% +\pgfpathlineto{\pgfqpoint{4.523419in}{2.540693in}}% +\pgfusepath{stroke}% +\end{pgfscope}% +\begin{pgfscope}% +\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetstrokecolor{textcolor}% +\pgfsetfillcolor{textcolor}% +\pgftext[x=4.634530in,y=2.492082in,left,base]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont AUC\(\displaystyle _{1}\) = \(\displaystyle 0.608\)}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsetrectcap% +\pgfsetroundjoin% +\pgfsetlinewidth{1.505625pt}% +\definecolor{currentstroke}{rgb}{0.871000,0.922000,0.969000}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfpathmoveto{\pgfqpoint{4.245641in}{2.347082in}}% +\pgfpathlineto{\pgfqpoint{4.523419in}{2.347082in}}% +\pgfusepath{stroke}% +\end{pgfscope}% +\begin{pgfscope}% +\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetstrokecolor{textcolor}% +\pgfsetfillcolor{textcolor}% +\pgftext[x=4.634530in,y=2.298471in,left,base]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont AUC\(\displaystyle _{2}\) = \(\displaystyle 0.641\)}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsetrectcap% +\pgfsetroundjoin% +\pgfsetlinewidth{1.505625pt}% +\definecolor{currentstroke}{rgb}{0.776000,0.859000,0.937000}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfpathmoveto{\pgfqpoint{4.245641in}{2.153472in}}% +\pgfpathlineto{\pgfqpoint{4.523419in}{2.153472in}}% +\pgfusepath{stroke}% +\end{pgfscope}% +\begin{pgfscope}% +\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetstrokecolor{textcolor}% +\pgfsetfillcolor{textcolor}% +\pgftext[x=4.634530in,y=2.104860in,left,base]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont AUC\(\displaystyle _{3}\) = \(\displaystyle 0.64\)}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsetrectcap% +\pgfsetroundjoin% +\pgfsetlinewidth{1.505625pt}% +\definecolor{currentstroke}{rgb}{0.620000,0.792000,0.882000}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfpathmoveto{\pgfqpoint{4.245641in}{1.959861in}}% +\pgfpathlineto{\pgfqpoint{4.523419in}{1.959861in}}% +\pgfusepath{stroke}% +\end{pgfscope}% +\begin{pgfscope}% +\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetstrokecolor{textcolor}% +\pgfsetfillcolor{textcolor}% +\pgftext[x=4.634530in,y=1.911249in,left,base]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont AUC\(\displaystyle _{4}\) = \(\displaystyle 0.668\)}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsetrectcap% +\pgfsetroundjoin% +\pgfsetlinewidth{1.505625pt}% +\definecolor{currentstroke}{rgb}{0.420000,0.682000,0.839000}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfpathmoveto{\pgfqpoint{4.245641in}{1.766250in}}% +\pgfpathlineto{\pgfqpoint{4.523419in}{1.766250in}}% +\pgfusepath{stroke}% +\end{pgfscope}% +\begin{pgfscope}% +\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetstrokecolor{textcolor}% +\pgfsetfillcolor{textcolor}% +\pgftext[x=4.634530in,y=1.717638in,left,base]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont AUC\(\displaystyle _{5}\) = \(\displaystyle 0.691\)}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsetrectcap% +\pgfsetroundjoin% +\pgfsetlinewidth{1.505625pt}% +\definecolor{currentstroke}{rgb}{0.259000,0.573000,0.776000}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfpathmoveto{\pgfqpoint{4.245641in}{1.572639in}}% +\pgfpathlineto{\pgfqpoint{4.523419in}{1.572639in}}% +\pgfusepath{stroke}% +\end{pgfscope}% +\begin{pgfscope}% +\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetstrokecolor{textcolor}% +\pgfsetfillcolor{textcolor}% +\pgftext[x=4.634530in,y=1.524027in,left,base]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont AUC\(\displaystyle _{6}\) = \(\displaystyle 0.664\)}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsetrectcap% +\pgfsetroundjoin% +\pgfsetlinewidth{1.505625pt}% +\definecolor{currentstroke}{rgb}{0.129000,0.443000,0.710000}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfpathmoveto{\pgfqpoint{4.245641in}{1.379028in}}% +\pgfpathlineto{\pgfqpoint{4.523419in}{1.379028in}}% +\pgfusepath{stroke}% +\end{pgfscope}% +\begin{pgfscope}% +\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetstrokecolor{textcolor}% +\pgfsetfillcolor{textcolor}% +\pgftext[x=4.634530in,y=1.330417in,left,base]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont AUC\(\displaystyle _{7}\) = \(\displaystyle 0.696\)}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsetrectcap% +\pgfsetroundjoin% +\pgfsetlinewidth{1.505625pt}% +\definecolor{currentstroke}{rgb}{0.031000,0.318000,0.612000}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfpathmoveto{\pgfqpoint{4.245641in}{1.185417in}}% +\pgfpathlineto{\pgfqpoint{4.523419in}{1.185417in}}% +\pgfusepath{stroke}% +\end{pgfscope}% +\begin{pgfscope}% +\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetstrokecolor{textcolor}% +\pgfsetfillcolor{textcolor}% +\pgftext[x=4.634530in,y=1.136806in,left,base]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont AUC\(\displaystyle _{8}\) = \(\displaystyle 0.684\)}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsetrectcap% +\pgfsetroundjoin% +\pgfsetlinewidth{1.505625pt}% +\definecolor{currentstroke}{rgb}{0.031000,0.188000,0.420000}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfpathmoveto{\pgfqpoint{4.245641in}{0.991806in}}% +\pgfpathlineto{\pgfqpoint{4.523419in}{0.991806in}}% +\pgfusepath{stroke}% +\end{pgfscope}% +\begin{pgfscope}% +\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetstrokecolor{textcolor}% +\pgfsetfillcolor{textcolor}% +\pgftext[x=4.634530in,y=0.943195in,left,base]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont AUC\(\displaystyle _{9}\) = \(\displaystyle 0.716\)}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsetrectcap% +\pgfsetroundjoin% +\pgfsetlinewidth{1.505625pt}% +\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfpathmoveto{\pgfqpoint{4.245641in}{0.798195in}}% +\pgfpathlineto{\pgfqpoint{4.523419in}{0.798195in}}% +\pgfusepath{stroke}% +\end{pgfscope}% +\begin{pgfscope}% +\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetstrokecolor{textcolor}% +\pgfsetfillcolor{textcolor}% +\pgftext[x=4.634530in,y=0.749584in,left,base]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont AUC\(\displaystyle _{10}\) = \(\displaystyle 0.705\)}% +\end{pgfscope}% +\end{pgfpicture}% +\makeatother% +\endgroup% diff --git a/figures/weakness_rec/sample-MNIST-autoencoder-5.png b/figures/weakness_rec/sample-MNIST-autoencoder-5.png new file mode 100644 index 0000000..3ecb96a Binary files /dev/null and b/figures/weakness_rec/sample-MNIST-autoencoder-5.png differ diff --git a/figures/weakness_rec/sample-MNIST-autoencoder.png b/figures/weakness_rec/sample-MNIST-autoencoder.png new file mode 100644 index 0000000..cb42c5c Binary files /dev/null and b/figures/weakness_rec/sample-MNIST-autoencoder.png differ diff --git a/figures/weakness_rec/threshold_sweep.pgf b/figures/weakness_rec/threshold_sweep.pgf new file mode 100644 index 0000000..001cf56 --- /dev/null +++ b/figures/weakness_rec/threshold_sweep.pgf @@ -0,0 +1,829 @@ +%% Creator: Matplotlib, PGF backend +%% +%% To include the figure in your LaTeX document, write +%% \input{.pgf} +%% +%% Make sure the required packages are loaded in your preamble +%% \usepackage{pgf} +%% +%% and, on pdftex +%% \usepackage[utf8]{inputenc}\DeclareUnicodeCharacter{2212}{-} +%% +%% or, on luatex and xetex +%% \usepackage{unicode-math} +%% +%% Figures using additional raster images can only be included by \input if +%% they are in the same directory as the main LaTeX file. For loading figures +%% from other directories you can use the `import` package +%% \usepackage{import} +%% +%% and then include the figures with +%% \import{}{.pgf} +%% +%% Matplotlib used the following preamble +%% \usepackage{fontspec} +%% +\begingroup% +\makeatletter% +\begin{pgfpicture}% +\pgfpathrectangle{\pgfpointorigin}{\pgfqpoint{3.912720in}{3.108568in}}% +\pgfusepath{use as bounding box, clip}% +\begin{pgfscope}% +\pgfsetbuttcap% +\pgfsetmiterjoin% +\definecolor{currentfill}{rgb}{1.000000,1.000000,1.000000}% +\pgfsetfillcolor{currentfill}% +\pgfsetlinewidth{0.000000pt}% +\definecolor{currentstroke}{rgb}{1.000000,1.000000,1.000000}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}% +\pgfpathlineto{\pgfqpoint{3.912720in}{0.000000in}}% +\pgfpathlineto{\pgfqpoint{3.912720in}{3.108568in}}% +\pgfpathlineto{\pgfqpoint{0.000000in}{3.108568in}}% +\pgfpathclose% +\pgfusepath{fill}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsetbuttcap% +\pgfsetmiterjoin% +\definecolor{currentfill}{rgb}{1.000000,1.000000,1.000000}% +\pgfsetfillcolor{currentfill}% +\pgfsetlinewidth{0.000000pt}% +\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetstrokeopacity{0.000000}% +\pgfsetdash{}{0pt}% +\pgfpathmoveto{\pgfqpoint{0.553581in}{0.499568in}}% +\pgfpathlineto{\pgfqpoint{3.653581in}{0.499568in}}% +\pgfpathlineto{\pgfqpoint{3.653581in}{2.809568in}}% +\pgfpathlineto{\pgfqpoint{0.553581in}{2.809568in}}% +\pgfpathclose% +\pgfusepath{fill}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsetbuttcap% +\pgfsetroundjoin% +\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetfillcolor{currentfill}% +\pgfsetlinewidth{0.803000pt}% +\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfsys@defobject{currentmarker}{\pgfqpoint{0.000000in}{-0.048611in}}{\pgfqpoint{0.000000in}{0.000000in}}{% +\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}% +\pgfpathlineto{\pgfqpoint{0.000000in}{-0.048611in}}% +\pgfusepath{stroke,fill}% +}% +\begin{pgfscope}% +\pgfsys@transformshift{0.694490in}{0.499568in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\end{pgfscope}% +\begin{pgfscope}% +\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetstrokecolor{textcolor}% +\pgfsetfillcolor{textcolor}% +\pgftext[x=0.694490in,y=0.402345in,,top]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle {0.0}\)}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsetbuttcap% +\pgfsetroundjoin% +\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetfillcolor{currentfill}% +\pgfsetlinewidth{0.803000pt}% +\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfsys@defobject{currentmarker}{\pgfqpoint{0.000000in}{-0.048611in}}{\pgfqpoint{0.000000in}{0.000000in}}{% +\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}% +\pgfpathlineto{\pgfqpoint{0.000000in}{-0.048611in}}% +\pgfusepath{stroke,fill}% +}% +\begin{pgfscope}% +\pgfsys@transformshift{1.258126in}{0.499568in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\end{pgfscope}% +\begin{pgfscope}% +\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetstrokecolor{textcolor}% +\pgfsetfillcolor{textcolor}% +\pgftext[x=1.258126in,y=0.402345in,,top]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle {0.2}\)}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsetbuttcap% +\pgfsetroundjoin% +\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetfillcolor{currentfill}% +\pgfsetlinewidth{0.803000pt}% +\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfsys@defobject{currentmarker}{\pgfqpoint{0.000000in}{-0.048611in}}{\pgfqpoint{0.000000in}{0.000000in}}{% +\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}% +\pgfpathlineto{\pgfqpoint{0.000000in}{-0.048611in}}% +\pgfusepath{stroke,fill}% +}% +\begin{pgfscope}% +\pgfsys@transformshift{1.821763in}{0.499568in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\end{pgfscope}% +\begin{pgfscope}% +\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetstrokecolor{textcolor}% +\pgfsetfillcolor{textcolor}% +\pgftext[x=1.821763in,y=0.402345in,,top]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle {0.4}\)}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsetbuttcap% +\pgfsetroundjoin% +\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetfillcolor{currentfill}% +\pgfsetlinewidth{0.803000pt}% +\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfsys@defobject{currentmarker}{\pgfqpoint{0.000000in}{-0.048611in}}{\pgfqpoint{0.000000in}{0.000000in}}{% +\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}% +\pgfpathlineto{\pgfqpoint{0.000000in}{-0.048611in}}% +\pgfusepath{stroke,fill}% +}% +\begin{pgfscope}% +\pgfsys@transformshift{2.385399in}{0.499568in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\end{pgfscope}% +\begin{pgfscope}% +\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetstrokecolor{textcolor}% +\pgfsetfillcolor{textcolor}% +\pgftext[x=2.385399in,y=0.402345in,,top]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle {0.6}\)}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsetbuttcap% +\pgfsetroundjoin% +\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetfillcolor{currentfill}% +\pgfsetlinewidth{0.803000pt}% +\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfsys@defobject{currentmarker}{\pgfqpoint{0.000000in}{-0.048611in}}{\pgfqpoint{0.000000in}{0.000000in}}{% +\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}% +\pgfpathlineto{\pgfqpoint{0.000000in}{-0.048611in}}% +\pgfusepath{stroke,fill}% +}% +\begin{pgfscope}% +\pgfsys@transformshift{2.949035in}{0.499568in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\end{pgfscope}% +\begin{pgfscope}% +\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetstrokecolor{textcolor}% +\pgfsetfillcolor{textcolor}% +\pgftext[x=2.949035in,y=0.402345in,,top]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle {0.8}\)}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsetbuttcap% +\pgfsetroundjoin% +\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetfillcolor{currentfill}% +\pgfsetlinewidth{0.803000pt}% +\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfsys@defobject{currentmarker}{\pgfqpoint{0.000000in}{-0.048611in}}{\pgfqpoint{0.000000in}{0.000000in}}{% +\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}% +\pgfpathlineto{\pgfqpoint{0.000000in}{-0.048611in}}% +\pgfusepath{stroke,fill}% +}% +\begin{pgfscope}% +\pgfsys@transformshift{3.512672in}{0.499568in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\end{pgfscope}% +\begin{pgfscope}% +\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetstrokecolor{textcolor}% +\pgfsetfillcolor{textcolor}% +\pgftext[x=3.512672in,y=0.402345in,,top]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle {1.0}\)}% +\end{pgfscope}% +\begin{pgfscope}% +\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetstrokecolor{textcolor}% +\pgfsetfillcolor{textcolor}% +\pgftext[x=2.103581in,y=0.223457in,,top]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont prediction threshold: \(\displaystyle \hat y \ge {\rm threshold}\)}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsetbuttcap% +\pgfsetroundjoin% +\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetfillcolor{currentfill}% +\pgfsetlinewidth{0.803000pt}% +\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfsys@defobject{currentmarker}{\pgfqpoint{-0.048611in}{0.000000in}}{\pgfqpoint{0.000000in}{0.000000in}}{% +\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}% +\pgfpathlineto{\pgfqpoint{-0.048611in}{0.000000in}}% +\pgfusepath{stroke,fill}% +}% +\begin{pgfscope}% +\pgfsys@transformshift{0.553581in}{0.521360in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\end{pgfscope}% +\begin{pgfscope}% +\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetstrokecolor{textcolor}% +\pgfsetfillcolor{textcolor}% +\pgftext[x=0.278889in, y=0.473166in, left, base]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle {0.0}\)}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsetbuttcap% +\pgfsetroundjoin% +\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetfillcolor{currentfill}% +\pgfsetlinewidth{0.803000pt}% +\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfsys@defobject{currentmarker}{\pgfqpoint{-0.048611in}{0.000000in}}{\pgfqpoint{0.000000in}{0.000000in}}{% +\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}% +\pgfpathlineto{\pgfqpoint{-0.048611in}{0.000000in}}% +\pgfusepath{stroke,fill}% +}% +\begin{pgfscope}% +\pgfsys@transformshift{0.553581in}{0.957209in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\end{pgfscope}% +\begin{pgfscope}% +\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetstrokecolor{textcolor}% +\pgfsetfillcolor{textcolor}% +\pgftext[x=0.278889in, y=0.909015in, left, base]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle {0.2}\)}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsetbuttcap% +\pgfsetroundjoin% +\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetfillcolor{currentfill}% +\pgfsetlinewidth{0.803000pt}% +\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfsys@defobject{currentmarker}{\pgfqpoint{-0.048611in}{0.000000in}}{\pgfqpoint{0.000000in}{0.000000in}}{% +\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}% +\pgfpathlineto{\pgfqpoint{-0.048611in}{0.000000in}}% +\pgfusepath{stroke,fill}% +}% +\begin{pgfscope}% +\pgfsys@transformshift{0.553581in}{1.393058in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\end{pgfscope}% +\begin{pgfscope}% +\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetstrokecolor{textcolor}% +\pgfsetfillcolor{textcolor}% +\pgftext[x=0.278889in, y=1.344864in, left, base]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle {0.4}\)}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsetbuttcap% +\pgfsetroundjoin% +\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetfillcolor{currentfill}% +\pgfsetlinewidth{0.803000pt}% +\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfsys@defobject{currentmarker}{\pgfqpoint{-0.048611in}{0.000000in}}{\pgfqpoint{0.000000in}{0.000000in}}{% +\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}% +\pgfpathlineto{\pgfqpoint{-0.048611in}{0.000000in}}% +\pgfusepath{stroke,fill}% +}% +\begin{pgfscope}% +\pgfsys@transformshift{0.553581in}{1.828907in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\end{pgfscope}% +\begin{pgfscope}% +\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetstrokecolor{textcolor}% +\pgfsetfillcolor{textcolor}% +\pgftext[x=0.278889in, y=1.780713in, left, base]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle {0.6}\)}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsetbuttcap% +\pgfsetroundjoin% +\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetfillcolor{currentfill}% +\pgfsetlinewidth{0.803000pt}% +\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfsys@defobject{currentmarker}{\pgfqpoint{-0.048611in}{0.000000in}}{\pgfqpoint{0.000000in}{0.000000in}}{% +\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}% +\pgfpathlineto{\pgfqpoint{-0.048611in}{0.000000in}}% +\pgfusepath{stroke,fill}% +}% +\begin{pgfscope}% +\pgfsys@transformshift{0.553581in}{2.264756in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\end{pgfscope}% +\begin{pgfscope}% +\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetstrokecolor{textcolor}% +\pgfsetfillcolor{textcolor}% +\pgftext[x=0.278889in, y=2.216562in, left, base]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle {0.8}\)}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsetbuttcap% +\pgfsetroundjoin% +\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetfillcolor{currentfill}% +\pgfsetlinewidth{0.803000pt}% +\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfsys@defobject{currentmarker}{\pgfqpoint{-0.048611in}{0.000000in}}{\pgfqpoint{0.000000in}{0.000000in}}{% +\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}% +\pgfpathlineto{\pgfqpoint{-0.048611in}{0.000000in}}% +\pgfusepath{stroke,fill}% +}% +\begin{pgfscope}% +\pgfsys@transformshift{0.553581in}{2.700605in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\end{pgfscope}% +\begin{pgfscope}% +\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetstrokecolor{textcolor}% +\pgfsetfillcolor{textcolor}% +\pgftext[x=0.278889in, y=2.652411in, left, base]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle {1.0}\)}% +\end{pgfscope}% +\begin{pgfscope}% +\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetstrokecolor{textcolor}% +\pgfsetfillcolor{textcolor}% +\pgftext[x=0.223333in,y=1.654568in,,bottom,rotate=90.000000]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont precision and recall}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfpathrectangle{\pgfqpoint{0.553581in}{0.499568in}}{\pgfqpoint{3.100000in}{2.310000in}}% +\pgfusepath{clip}% +\pgfsetrectcap% +\pgfsetroundjoin% +\pgfsetlinewidth{1.505625pt}% +\definecolor{currentstroke}{rgb}{0.000000,0.000000,1.000000}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfpathmoveto{\pgfqpoint{0.694490in}{0.668895in}}% +\pgfpathlineto{\pgfqpoint{0.835399in}{0.777811in}}% +\pgfpathlineto{\pgfqpoint{0.976308in}{0.825345in}}% +\pgfpathlineto{\pgfqpoint{1.117217in}{0.860803in}}% +\pgfpathlineto{\pgfqpoint{1.258126in}{0.893620in}}% +\pgfpathlineto{\pgfqpoint{1.399035in}{0.923129in}}% +\pgfpathlineto{\pgfqpoint{1.539944in}{0.943209in}}% +\pgfpathlineto{\pgfqpoint{1.680853in}{0.976464in}}% +\pgfpathlineto{\pgfqpoint{1.821763in}{1.002525in}}% +\pgfpathlineto{\pgfqpoint{1.962672in}{1.021757in}}% +\pgfpathlineto{\pgfqpoint{2.103581in}{1.053138in}}% +\pgfpathlineto{\pgfqpoint{2.244490in}{1.069215in}}% +\pgfpathlineto{\pgfqpoint{2.385399in}{1.088056in}}% +\pgfpathlineto{\pgfqpoint{2.526308in}{1.129779in}}% +\pgfpathlineto{\pgfqpoint{2.667217in}{1.159991in}}% +\pgfpathlineto{\pgfqpoint{2.808126in}{1.190641in}}% +\pgfpathlineto{\pgfqpoint{2.949035in}{1.254661in}}% +\pgfpathlineto{\pgfqpoint{3.089944in}{1.332612in}}% +\pgfpathlineto{\pgfqpoint{3.230853in}{1.500796in}}% +\pgfpathlineto{\pgfqpoint{3.371763in}{1.429379in}}% +\pgfusepath{stroke}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfpathrectangle{\pgfqpoint{0.553581in}{0.499568in}}{\pgfqpoint{3.100000in}{2.310000in}}% +\pgfusepath{clip}% +\pgfsetbuttcap% +\pgfsetroundjoin% +\definecolor{currentfill}{rgb}{0.000000,0.000000,1.000000}% +\pgfsetfillcolor{currentfill}% +\pgfsetlinewidth{1.003750pt}% +\definecolor{currentstroke}{rgb}{0.000000,0.000000,1.000000}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfsys@defobject{currentmarker}{\pgfqpoint{-0.020833in}{-0.020833in}}{\pgfqpoint{0.020833in}{0.020833in}}{% +\pgfpathmoveto{\pgfqpoint{0.000000in}{-0.020833in}}% +\pgfpathcurveto{\pgfqpoint{0.005525in}{-0.020833in}}{\pgfqpoint{0.010825in}{-0.018638in}}{\pgfqpoint{0.014731in}{-0.014731in}}% +\pgfpathcurveto{\pgfqpoint{0.018638in}{-0.010825in}}{\pgfqpoint{0.020833in}{-0.005525in}}{\pgfqpoint{0.020833in}{0.000000in}}% +\pgfpathcurveto{\pgfqpoint{0.020833in}{0.005525in}}{\pgfqpoint{0.018638in}{0.010825in}}{\pgfqpoint{0.014731in}{0.014731in}}% +\pgfpathcurveto{\pgfqpoint{0.010825in}{0.018638in}}{\pgfqpoint{0.005525in}{0.020833in}}{\pgfqpoint{0.000000in}{0.020833in}}% +\pgfpathcurveto{\pgfqpoint{-0.005525in}{0.020833in}}{\pgfqpoint{-0.010825in}{0.018638in}}{\pgfqpoint{-0.014731in}{0.014731in}}% +\pgfpathcurveto{\pgfqpoint{-0.018638in}{0.010825in}}{\pgfqpoint{-0.020833in}{0.005525in}}{\pgfqpoint{-0.020833in}{0.000000in}}% +\pgfpathcurveto{\pgfqpoint{-0.020833in}{-0.005525in}}{\pgfqpoint{-0.018638in}{-0.010825in}}{\pgfqpoint{-0.014731in}{-0.014731in}}% +\pgfpathcurveto{\pgfqpoint{-0.010825in}{-0.018638in}}{\pgfqpoint{-0.005525in}{-0.020833in}}{\pgfqpoint{0.000000in}{-0.020833in}}% +\pgfpathclose% +\pgfusepath{stroke,fill}% +}% +\begin{pgfscope}% +\pgfsys@transformshift{0.694490in}{0.668895in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{0.835399in}{0.777811in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{0.976308in}{0.825345in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{1.117217in}{0.860803in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{1.258126in}{0.893620in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{1.399035in}{0.923129in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{1.539944in}{0.943209in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{1.680853in}{0.976464in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{1.821763in}{1.002525in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{1.962672in}{1.021757in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{2.103581in}{1.053138in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{2.244490in}{1.069215in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{2.385399in}{1.088056in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{2.526308in}{1.129779in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{2.667217in}{1.159991in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{2.808126in}{1.190641in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{2.949035in}{1.254661in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{3.089944in}{1.332612in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{3.230853in}{1.500796in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{3.371763in}{1.429379in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfpathrectangle{\pgfqpoint{0.553581in}{0.499568in}}{\pgfqpoint{3.100000in}{2.310000in}}% +\pgfusepath{clip}% +\pgfsetrectcap% +\pgfsetroundjoin% +\pgfsetlinewidth{1.505625pt}% +\definecolor{currentstroke}{rgb}{1.000000,0.000000,0.000000}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfpathmoveto{\pgfqpoint{0.694490in}{2.700605in}}% +\pgfpathlineto{\pgfqpoint{0.835399in}{1.924833in}}% +\pgfpathlineto{\pgfqpoint{0.976308in}{1.702723in}}% +\pgfpathlineto{\pgfqpoint{1.117217in}{1.548213in}}% +\pgfpathlineto{\pgfqpoint{1.258126in}{1.425892in}}% +\pgfpathlineto{\pgfqpoint{1.399035in}{1.348636in}}% +\pgfpathlineto{\pgfqpoint{1.539944in}{1.258505in}}% +\pgfpathlineto{\pgfqpoint{1.680853in}{1.190907in}}% +\pgfpathlineto{\pgfqpoint{1.821763in}{1.129746in}}% +\pgfpathlineto{\pgfqpoint{1.962672in}{1.065367in}}% +\pgfpathlineto{\pgfqpoint{2.103581in}{1.013863in}}% +\pgfpathlineto{\pgfqpoint{2.244490in}{0.955922in}}% +\pgfpathlineto{\pgfqpoint{2.385399in}{0.917294in}}% +\pgfpathlineto{\pgfqpoint{2.526308in}{0.875447in}}% +\pgfpathlineto{\pgfqpoint{2.667217in}{0.833601in}}% +\pgfpathlineto{\pgfqpoint{2.808126in}{0.785316in}}% +\pgfpathlineto{\pgfqpoint{2.949035in}{0.749907in}}% +\pgfpathlineto{\pgfqpoint{3.089944in}{0.685528in}}% +\pgfpathlineto{\pgfqpoint{3.230853in}{0.650119in}}% +\pgfpathlineto{\pgfqpoint{3.371763in}{0.569645in}}% +\pgfpathlineto{\pgfqpoint{3.512672in}{0.521360in}}% +\pgfusepath{stroke}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfpathrectangle{\pgfqpoint{0.553581in}{0.499568in}}{\pgfqpoint{3.100000in}{2.310000in}}% +\pgfusepath{clip}% +\pgfsetbuttcap% +\pgfsetroundjoin% +\definecolor{currentfill}{rgb}{1.000000,0.000000,0.000000}% +\pgfsetfillcolor{currentfill}% +\pgfsetlinewidth{1.003750pt}% +\definecolor{currentstroke}{rgb}{1.000000,0.000000,0.000000}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfsys@defobject{currentmarker}{\pgfqpoint{-0.020833in}{-0.020833in}}{\pgfqpoint{0.020833in}{0.020833in}}{% +\pgfpathmoveto{\pgfqpoint{0.000000in}{-0.020833in}}% +\pgfpathcurveto{\pgfqpoint{0.005525in}{-0.020833in}}{\pgfqpoint{0.010825in}{-0.018638in}}{\pgfqpoint{0.014731in}{-0.014731in}}% +\pgfpathcurveto{\pgfqpoint{0.018638in}{-0.010825in}}{\pgfqpoint{0.020833in}{-0.005525in}}{\pgfqpoint{0.020833in}{0.000000in}}% +\pgfpathcurveto{\pgfqpoint{0.020833in}{0.005525in}}{\pgfqpoint{0.018638in}{0.010825in}}{\pgfqpoint{0.014731in}{0.014731in}}% +\pgfpathcurveto{\pgfqpoint{0.010825in}{0.018638in}}{\pgfqpoint{0.005525in}{0.020833in}}{\pgfqpoint{0.000000in}{0.020833in}}% +\pgfpathcurveto{\pgfqpoint{-0.005525in}{0.020833in}}{\pgfqpoint{-0.010825in}{0.018638in}}{\pgfqpoint{-0.014731in}{0.014731in}}% +\pgfpathcurveto{\pgfqpoint{-0.018638in}{0.010825in}}{\pgfqpoint{-0.020833in}{0.005525in}}{\pgfqpoint{-0.020833in}{0.000000in}}% +\pgfpathcurveto{\pgfqpoint{-0.020833in}{-0.005525in}}{\pgfqpoint{-0.018638in}{-0.010825in}}{\pgfqpoint{-0.014731in}{-0.014731in}}% +\pgfpathcurveto{\pgfqpoint{-0.010825in}{-0.018638in}}{\pgfqpoint{-0.005525in}{-0.020833in}}{\pgfqpoint{0.000000in}{-0.020833in}}% +\pgfpathclose% +\pgfusepath{stroke,fill}% +}% +\begin{pgfscope}% +\pgfsys@transformshift{0.694490in}{2.700605in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{0.835399in}{1.924833in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{0.976308in}{1.702723in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{1.117217in}{1.548213in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{1.258126in}{1.425892in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{1.399035in}{1.348636in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{1.539944in}{1.258505in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{1.680853in}{1.190907in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{1.821763in}{1.129746in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{1.962672in}{1.065367in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{2.103581in}{1.013863in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{2.244490in}{0.955922in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{2.385399in}{0.917294in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{2.526308in}{0.875447in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{2.667217in}{0.833601in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{2.808126in}{0.785316in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{2.949035in}{0.749907in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{3.089944in}{0.685528in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{3.230853in}{0.650119in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{3.371763in}{0.569645in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsys@transformshift{3.512672in}{0.521360in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfpathrectangle{\pgfqpoint{0.553581in}{0.499568in}}{\pgfqpoint{3.100000in}{2.310000in}}% +\pgfusepath{clip}% +\pgfsetbuttcap% +\pgfsetroundjoin% +\pgfsetlinewidth{1.505625pt}% +\definecolor{currentstroke}{rgb}{0.501961,0.501961,0.501961}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{{1.500000pt}{2.475000pt}}{0.000000pt}% +\pgfpathmoveto{\pgfqpoint{2.104990in}{0.499568in}}% +\pgfpathlineto{\pgfqpoint{2.104990in}{1.013863in}}% +\pgfusepath{stroke}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsetrectcap% +\pgfsetmiterjoin% +\pgfsetlinewidth{0.803000pt}% +\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfpathmoveto{\pgfqpoint{0.553581in}{0.499568in}}% +\pgfpathlineto{\pgfqpoint{0.553581in}{2.809568in}}% +\pgfusepath{stroke}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsetrectcap% +\pgfsetmiterjoin% +\pgfsetlinewidth{0.803000pt}% +\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfpathmoveto{\pgfqpoint{3.653581in}{0.499568in}}% +\pgfpathlineto{\pgfqpoint{3.653581in}{2.809568in}}% +\pgfusepath{stroke}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsetrectcap% +\pgfsetmiterjoin% +\pgfsetlinewidth{0.803000pt}% +\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfpathmoveto{\pgfqpoint{0.553581in}{0.499568in}}% +\pgfpathlineto{\pgfqpoint{3.653581in}{0.499568in}}% +\pgfusepath{stroke}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsetrectcap% +\pgfsetmiterjoin% +\pgfsetlinewidth{0.803000pt}% +\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfpathmoveto{\pgfqpoint{0.553581in}{2.809568in}}% +\pgfpathlineto{\pgfqpoint{3.653581in}{2.809568in}}% +\pgfusepath{stroke}% +\end{pgfscope}% +\begin{pgfscope}% +\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetstrokecolor{textcolor}% +\pgfsetfillcolor{textcolor}% +\pgftext[x=2.103581in,y=2.892901in,,base]{\color{textcolor}\rmfamily\fontsize{12.000000}{14.400000}\selectfont Prediction threshold sweep: precision and recall}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsetbuttcap% +\pgfsetmiterjoin% +\definecolor{currentfill}{rgb}{1.000000,1.000000,1.000000}% +\pgfsetfillcolor{currentfill}% +\pgfsetfillopacity{0.800000}% +\pgfsetlinewidth{1.003750pt}% +\definecolor{currentstroke}{rgb}{0.800000,0.800000,0.800000}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetstrokeopacity{0.800000}% +\pgfsetdash{}{0pt}% +\pgfpathmoveto{\pgfqpoint{2.560942in}{2.311235in}}% +\pgfpathlineto{\pgfqpoint{3.556358in}{2.311235in}}% +\pgfpathquadraticcurveto{\pgfqpoint{3.584136in}{2.311235in}}{\pgfqpoint{3.584136in}{2.339012in}}% +\pgfpathlineto{\pgfqpoint{3.584136in}{2.712345in}}% +\pgfpathquadraticcurveto{\pgfqpoint{3.584136in}{2.740123in}}{\pgfqpoint{3.556358in}{2.740123in}}% +\pgfpathlineto{\pgfqpoint{2.560942in}{2.740123in}}% +\pgfpathquadraticcurveto{\pgfqpoint{2.533164in}{2.740123in}}{\pgfqpoint{2.533164in}{2.712345in}}% +\pgfpathlineto{\pgfqpoint{2.533164in}{2.339012in}}% +\pgfpathquadraticcurveto{\pgfqpoint{2.533164in}{2.311235in}}{\pgfqpoint{2.560942in}{2.311235in}}% +\pgfpathclose% +\pgfusepath{stroke,fill}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsetrectcap% +\pgfsetroundjoin% +\pgfsetlinewidth{1.505625pt}% +\definecolor{currentstroke}{rgb}{0.000000,0.000000,1.000000}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfpathmoveto{\pgfqpoint{2.588720in}{2.635957in}}% +\pgfpathlineto{\pgfqpoint{2.866497in}{2.635957in}}% +\pgfusepath{stroke}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsetbuttcap% +\pgfsetroundjoin% +\definecolor{currentfill}{rgb}{0.000000,0.000000,1.000000}% +\pgfsetfillcolor{currentfill}% +\pgfsetlinewidth{1.003750pt}% +\definecolor{currentstroke}{rgb}{0.000000,0.000000,1.000000}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfsys@defobject{currentmarker}{\pgfqpoint{-0.020833in}{-0.020833in}}{\pgfqpoint{0.020833in}{0.020833in}}{% +\pgfpathmoveto{\pgfqpoint{0.000000in}{-0.020833in}}% +\pgfpathcurveto{\pgfqpoint{0.005525in}{-0.020833in}}{\pgfqpoint{0.010825in}{-0.018638in}}{\pgfqpoint{0.014731in}{-0.014731in}}% +\pgfpathcurveto{\pgfqpoint{0.018638in}{-0.010825in}}{\pgfqpoint{0.020833in}{-0.005525in}}{\pgfqpoint{0.020833in}{0.000000in}}% +\pgfpathcurveto{\pgfqpoint{0.020833in}{0.005525in}}{\pgfqpoint{0.018638in}{0.010825in}}{\pgfqpoint{0.014731in}{0.014731in}}% +\pgfpathcurveto{\pgfqpoint{0.010825in}{0.018638in}}{\pgfqpoint{0.005525in}{0.020833in}}{\pgfqpoint{0.000000in}{0.020833in}}% +\pgfpathcurveto{\pgfqpoint{-0.005525in}{0.020833in}}{\pgfqpoint{-0.010825in}{0.018638in}}{\pgfqpoint{-0.014731in}{0.014731in}}% +\pgfpathcurveto{\pgfqpoint{-0.018638in}{0.010825in}}{\pgfqpoint{-0.020833in}{0.005525in}}{\pgfqpoint{-0.020833in}{0.000000in}}% +\pgfpathcurveto{\pgfqpoint{-0.020833in}{-0.005525in}}{\pgfqpoint{-0.018638in}{-0.010825in}}{\pgfqpoint{-0.014731in}{-0.014731in}}% +\pgfpathcurveto{\pgfqpoint{-0.010825in}{-0.018638in}}{\pgfqpoint{-0.005525in}{-0.020833in}}{\pgfqpoint{0.000000in}{-0.020833in}}% +\pgfpathclose% +\pgfusepath{stroke,fill}% +}% +\begin{pgfscope}% +\pgfsys@transformshift{2.727608in}{2.635957in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\end{pgfscope}% +\begin{pgfscope}% +\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetstrokecolor{textcolor}% +\pgfsetfillcolor{textcolor}% +\pgftext[x=2.977608in,y=2.587345in,left,base]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont Precision}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsetrectcap% +\pgfsetroundjoin% +\pgfsetlinewidth{1.505625pt}% +\definecolor{currentstroke}{rgb}{1.000000,0.000000,0.000000}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfpathmoveto{\pgfqpoint{2.588720in}{2.442346in}}% +\pgfpathlineto{\pgfqpoint{2.866497in}{2.442346in}}% +\pgfusepath{stroke}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsetbuttcap% +\pgfsetroundjoin% +\definecolor{currentfill}{rgb}{1.000000,0.000000,0.000000}% +\pgfsetfillcolor{currentfill}% +\pgfsetlinewidth{1.003750pt}% +\definecolor{currentstroke}{rgb}{1.000000,0.000000,0.000000}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfsys@defobject{currentmarker}{\pgfqpoint{-0.020833in}{-0.020833in}}{\pgfqpoint{0.020833in}{0.020833in}}{% +\pgfpathmoveto{\pgfqpoint{0.000000in}{-0.020833in}}% +\pgfpathcurveto{\pgfqpoint{0.005525in}{-0.020833in}}{\pgfqpoint{0.010825in}{-0.018638in}}{\pgfqpoint{0.014731in}{-0.014731in}}% +\pgfpathcurveto{\pgfqpoint{0.018638in}{-0.010825in}}{\pgfqpoint{0.020833in}{-0.005525in}}{\pgfqpoint{0.020833in}{0.000000in}}% +\pgfpathcurveto{\pgfqpoint{0.020833in}{0.005525in}}{\pgfqpoint{0.018638in}{0.010825in}}{\pgfqpoint{0.014731in}{0.014731in}}% +\pgfpathcurveto{\pgfqpoint{0.010825in}{0.018638in}}{\pgfqpoint{0.005525in}{0.020833in}}{\pgfqpoint{0.000000in}{0.020833in}}% +\pgfpathcurveto{\pgfqpoint{-0.005525in}{0.020833in}}{\pgfqpoint{-0.010825in}{0.018638in}}{\pgfqpoint{-0.014731in}{0.014731in}}% +\pgfpathcurveto{\pgfqpoint{-0.018638in}{0.010825in}}{\pgfqpoint{-0.020833in}{0.005525in}}{\pgfqpoint{-0.020833in}{0.000000in}}% +\pgfpathcurveto{\pgfqpoint{-0.020833in}{-0.005525in}}{\pgfqpoint{-0.018638in}{-0.010825in}}{\pgfqpoint{-0.014731in}{-0.014731in}}% +\pgfpathcurveto{\pgfqpoint{-0.010825in}{-0.018638in}}{\pgfqpoint{-0.005525in}{-0.020833in}}{\pgfqpoint{0.000000in}{-0.020833in}}% +\pgfpathclose% +\pgfusepath{stroke,fill}% +}% +\begin{pgfscope}% +\pgfsys@transformshift{2.727608in}{2.442346in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\end{pgfscope}% +\begin{pgfscope}% +\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetstrokecolor{textcolor}% +\pgfsetfillcolor{textcolor}% +\pgftext[x=2.977608in,y=2.393734in,left,base]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont Recall}% +\end{pgfscope}% +\end{pgfpicture}% +\makeatother% +\endgroup% diff --git a/figures/weakness_rec/validation_diagram.pdf b/figures/weakness_rec/validation_diagram.pdf new file mode 100644 index 0000000..d688653 Binary files /dev/null and b/figures/weakness_rec/validation_diagram.pdf differ diff --git a/figures/weakness_rec/validation_diagram.tex b/figures/weakness_rec/validation_diagram.tex new file mode 100644 index 0000000..51acedf --- /dev/null +++ b/figures/weakness_rec/validation_diagram.tex @@ -0,0 +1,116 @@ +\tikzset{every picture/.style={line width=0.75pt}} %set default line width to 0.75pt + +\begin{tikzpicture}[x=0.75pt,y=0.75pt,yscale=-1,xscale=1] +%uncomment if require: \path (0,399); %set diagram left start at 0, and has height of 399 + +%Shape: Rectangle [id:dp3416440849450273] +\draw [dash pattern={on 4.5pt off 4.5pt}][line width=0.75] (91.17,38) -- (653.17,38) -- (653.17,329) -- (91.17,329) -- cycle ; +%Straight Lines [id:da6207923302069309] +\draw (39.17,144) -- (39.17,70) -- (95.5,70) ; +\draw [shift={(102.5,70)}, rotate = 180] [fill={rgb, 255:red, 0; green, 0; blue, 0 } ][line width=0.08] [draw opacity=0] (6.25,-3) -- (0,0) -- (6.25,3) -- cycle ; +%Straight Lines [id:da40087733759777344] +\draw (257.17,68) -- (540.57,68) -- (540.57,88) ; +\draw [shift={(540.57,91)}, rotate = 270] [fill={rgb, 255:red, 0; green, 0; blue, 0 } ][line width=0.08] [draw opacity=0] (6.25,-3) -- (0,0) -- (6.25,3) -- cycle ; +%Shape: Brace [id:dp16419611390886946] +\draw (638.17,107) .. controls (638.17,102.33) and (635.84,100) .. (631.17,100) -- (550.68,100) .. controls (544.01,100) and (540.68,97.67) .. (540.68,93) .. controls (540.68,97.67) and (537.35,100) .. (530.68,100)(533.68,100) -- (451,100) .. controls (446.33,100) and (444,102.33) .. (444,107) ; +%Straight Lines [id:da03991771123197685] +\draw (380.5,221) -- (235.5,221) ; +\draw [shift={(235.5,221)}, rotate = 360] [fill={rgb, 255:red, 0; green, 0; blue, 0 } ][line width=0.08] [draw opacity=0] (6.25,-3) -- (0,0) -- (6.25,3) -- cycle ; +%Straight Lines [id:da4068130382497208] +\draw (188.5,255) -- (188.5,344) ; +\draw [shift={(188.5,347)}, rotate = 270] [fill={rgb, 255:red, 0; green, 0; blue, 0 } ][line width=0.08] [draw opacity=0] (6.25,-3) -- (0,0) -- (6.25,3) -- cycle ; + +% Text Node +\draw [fill={rgb, 255:red, 189; green, 213; blue, 242 } ,fill opacity=1 ] (104.75,43.17) -- (269.75,43.17) -- (269.75,107.17) -- (104.75,107.17) -- cycle ; +\draw (187.25,75.17) node [align=left] {\begin{minipage}[lt]{109.32564pt}\setlength\topsep{0pt} +\begin{center} +Dataset Autoencoder $\displaystyle \mathcal{E}$ +\end{center} + +\end{minipage}}; +% Text Node +\draw [fill={rgb, 255:red, 155; green, 155; blue, 155 } ,fill opacity=1 ] (139.06,185) -- (236.06,185) -- (236.06,253) -- (139.06,253) -- cycle ; +\draw (187.56,219) node [align=left] {\begin{minipage}[lt]{63.197500000000005pt}\setlength\topsep{0pt} +\begin{center} +System\\Under Test\\$\displaystyle \mathcal{S}$ +\end{center} + +\end{minipage}}; +% Text Node +\draw (90,20.33) node [anchor=north west][inner sep=0.75pt] [font=\small] [align=left] {Sampled Validation Iteration: Loop $\displaystyle t \in T$}; +% Text Node +\draw [fill={rgb, 255:red, 255; green, 255; blue, 255 } ,fill opacity=1 ] (-4,143.33) -- (82,143.33) -- (82,190.33) -- (-4,190.33) -- cycle ; +\draw (2,154.33) node [anchor=north west][inner sep=0.75pt] [align=left] {\begin{minipage}[lt]{53.541216pt}\setlength\topsep{0pt} +\begin{center} +Dataset \\$\displaystyle (\mathbf{x}, \mathbf{y}) \in \mathcal{D}_\text{test}$ +\end{center} + +\end{minipage}}; +% Text Node +\draw (-10,45.33) node [anchor=north west][inner sep=0.75pt] [font=\small] [align=left] {\begin{minipage}[lt]{49.655912pt}\setlength\topsep{0pt} +\begin{center} +All samples\\$\displaystyle \mathbf{x}$ +\end{center} + +\end{minipage}}; +% Text Node +\draw (277,50.33) node [anchor=north west][inner sep=0.75pt] [font=\small] [align=left] {Sample $m$ encoded low-dimensional representations $\displaystyle \tilde{\mathbf{x}}_{t}^{(1:m)}$}; +% Text Node +\draw [fill={rgb, 255:red, 255; green, 255; blue, 255 } ,fill opacity=1 ] (442,108) -- (543,108) -- (543,130) -- (442,130) -- cycle ; +\draw (478,110) node [anchor=north west][inner sep=0.75pt] [align=left] {$\displaystyle \tilde{\mathcal{D}}_{\text{test}}$}; +% Text Node +\draw [fill={rgb, 255:red, 235; green, 235; blue, 235 } ,fill opacity=1 ] (362,151) -- (642,151) -- (642,302) -- (362,302) -- cycle ; +\draw (368,282) node [anchor=north west][inner sep=0.75pt] [align=left] {Candidate Failure Selector}; +% Text Node +\draw [fill={rgb, 255:red, 252; green, 134; blue, 148 } ,fill opacity=1 ] (514,191.33) -- (634,191.33) -- (634,259.33) -- (514,259.33) -- cycle ; +\draw (520,202.33) node [anchor=north west][inner sep=0.75pt] [align=left] {\begin{minipage}[lt]{78.6726pt}\setlength\topsep{0pt} +\begin{center} +Adversarial\\Failure Classifier\\$\displaystyle \mathcal{A}$ +\end{center} + +\end{minipage}}; +% Text Node +% \draw [fill={rgb, 255:red, 255; green, 255; blue, 255 } ,fill opacity=1 ] (419.5, 222) circle [x radius= 26.54, y radius= 26.54] ; +\draw [fill={rgb, 255:red, 255; green, 255; blue, 255 } ,fill opacity=1 ] (380,191.33) -- (500,191.33) -- (500,252) -- (380,252) -- cycle ; +\draw (385,198) node [anchor=north west][inner sep=0.75pt] [align=left] {\begin{minipage}[lt]{82.6726pt}\setlength\topsep{0pt} +\begin{center} +$\tilde{\mathbf{x}}_c = \mathcal{A}(\tilde{\mathcal{D}}_\text{test})_{\ge 0.5}$\\ +\phantom{}\\ +$\mathbf{x}_c \leftarrow \operatorname{mapping}(\tilde{\mathbf{x}}_c)$ +\end{center} +\end{minipage}}; + +% Text Node +\draw (245,190.33) node [anchor=north west][inner sep=0.75pt] [font=\small] [align=left] {\begin{minipage}[lt]{76.7176pt}\setlength\topsep{0pt} +\begin{center} +Candidate failures\\$\displaystyle \mathbf{x}_{c} \subseteq \mathbf{x}$ +\end{center} + +\end{minipage}}; +% Text Node +\draw (111,355.33) node [anchor=north west][inner sep=0.75pt] [font=\small] [align=left] {\begin{minipage}[lt]{118.05956pt}\setlength\topsep{0pt} +\begin{center} +Evaluated candidate failures\\$\displaystyle \mathbf{y}_{c} =\mathcal{S}(\mathbf{x}_{c})$ +\end{center} + +\end{minipage}}; +% Text Node +\draw [fill={rgb, 255:red, 255; green, 255; blue, 255 } ,fill opacity=1 ] (543,108) -- (639,108) -- (639,130) -- (543,130) -- cycle ; +\draw (574,110) node [anchor=north west][inner sep=0.75pt] [align=left] {$\displaystyle \tilde{\mathcal{D}}_{\text{train}} \ \ \ \ \ \ \ \ \ \ \ \ $}; + +%Straight Lines [id:D_train -> Adversary] +\draw [dash pattern={on 1.5pt off 1.5pt}][line width=0.75] (591,191.33) -- (591,130) ; +\draw [shift={(591,191.33)}, rotate = 270] [fill={rgb, 255:red, 0; green, 0; blue, 0 } ][line width=0.08] [draw opacity=0] (6.25,-3) -- (0,0) -- (6.25,3) -- cycle ; + +%Straight Lines [id:D_test -> Candidate selector] +\draw [dash pattern={on 1.5pt off 1.5pt}][line width=0.75] (492.5,191.33) -- (492.5,130) ; +\draw [shift={(492.5,191.33)}, rotate = 270] [fill={rgb, 255:red, 0; green, 0; blue, 0 } ][line width=0.08] [draw opacity=0] (6.25,-3) -- (0,0) -- (6.25,3) -- cycle ; + +%Straight Lines [id:Adversary -> Candidate selector] +\draw (574,259.33) -- (574,269.33) ; +\draw (574,269.33) -- (440,269.33) ; +\draw (440,269.33) -- (440,252) ; +\draw [shift={(440,252)}, rotate = 90] [fill={rgb, 255:red, 0; green, 0; blue, 0 } ][line width=0.08] [draw opacity=0] (6.25,-3) -- (0,0) -- (6.25,3) -- cycle ; + + +\end{tikzpicture} diff --git a/main.tex b/main.tex new file mode 100644 index 0000000..d648533 --- /dev/null +++ b/main.tex @@ -0,0 +1,93 @@ +% Stanford University PhD thesis style -- modifications to the report style +% This is unofficial so you should always double check against the +% Registrar's office rules +% See http://library.stanford.edu/research/bibliography-management/latex-and-bibtex +% +% Example of use below +% See the suthesis-ms-2e.sty file for documentation +% +\documentclass{report} +\usepackage{suthesis-ms-2e} +\dept{Computer Science} + +\input{preamble/preamble} + +% \usetikzlibrary{external} +% \tikzexternalize[prefix=figures/weakness_rec] + +% TODO: Combine into one `references.bib` +\addbibresource{references/cem_variants.bib} +\addbibresource{references/episodic_ast.bib} +\addbibresource{references/weakness_rec.bib} +\addbibresource{references/pomdpstresstesting.bib} + + +\begin{document} +\title{Algorithms for efficient validation of black-box systems} +\author{Robert John Moss} +\principaladviser{Mykel J. Kochenderfer} +\firstreader{Dorsa Sadigh} + +\beforepreface +\prefacesection{Preface} +This thesis tells you all you need to know about... +\prefacesection{Acknowledgments} +I would like to thank... +\afterpreface + +\chapter{Introduction} +\input{chapters/introduction} + +% Cross-Entropy Method Variants for Optimization +\chapter{Cross-Entropy Surrogate Method} % TODO: change +\input{chapters/cem_variants} + +\chapter{Episodic Adaptive Stress Testing} +\input{chapters/episodic_ast} + +\chapter{Adversarial Weakness Recognition} +\input{chapters/weakness_rec} + +% POMDPStressTesting.jl: Adaptive Stress Testing for Black-Box Systems +\chapter{POMDPStressTesting.jl} +\input{chapters/pomdpstresstesting} + +\chapter{Conclusions} +... + +\appendix +\input{appendices/episodic_ast_appendix} + +% \bibliographystyle{plain} +% \bibliography{cem_variants} +\printbibliography + + +\end{document} + +% TODO: +% [ ] combine references.bib +% [x] See Dorsa notes +% [ ] See Mykel notes +% [ ] Subsections for tooling: CrossEntropyVariants.jl and FailureRepresentation.jl +% [ ] Combine Acknowledgments +% [ ] Flow together chapters +% [x] "dissertation" wording in the signatures page +% [x] Remove "graduate studies" committee? + + +% Mykel notes: +% [x] Concatenate research papers from MS (if they're related work / extensions) +% [ ] Add introduction +% [ ] Flow together body chapters +% [ ] Remove redundancies between them +% [ ] Change conclusions/future work into discussion +% - Two big things: +% [ ] 1) intro chapter +% - shortest intro chapter possible (concise) +% - "freshman undergrad could understand contributions" +% [ ] 2) final chapter +% [ ] one section "Summary" high level, no jargon, no non-sense +% [ ] second section "Contributions", summarize how you've supported your claims (back references, specialized terminology) +% [ ] third: future work +% https://www2.eecs.berkeley.edu/Pubs/Theses/ \ No newline at end of file diff --git a/preamble/preamble.tex b/preamble/preamble.tex new file mode 100644 index 0000000..a4aab99 --- /dev/null +++ b/preamble/preamble.tex @@ -0,0 +1,337 @@ +\usepackage{amsmath} % JIC. +\usepackage{algorithmicx} +\usepackage{algorithm} +\usepackage{algpseudocode} +\usepackage{amsmath} +\usepackage{amsfonts} +\usepackage{siunitx} +\usepackage{commath} + +\usepackage{preamble/vector} % local vector.sty for bold Greek math letters + +%%% Mathematical operators (from mathematics.tex) +\DeclareMathOperator{\Var}{Var} +\DeclareMathOperator{\SD}{SD} +\DeclareMathOperator{\Ber}{Ber} +\DeclareMathOperator{\Bin}{Bin} +\DeclareMathOperator{\Poi}{Poi} +\DeclareMathOperator{\Geo}{Geo} +\DeclareMathOperator{\NegBin}{NegBin} +\DeclareMathOperator{\Uni}{Uni} +\DeclareMathOperator{\Exp}{Exp} +\DeclareMathOperator{\Dir}{Dir} +\newcommand*\Eval[1]{\left.#1\right\rvert} % derivative/integration evaluation bar | +\DeclareMathOperator{\Cov}{Cov} +\DeclareMathOperator{\BetaDistribution}{Beta} +\DeclareMathOperator{\Beta}{Beta} +\DeclareMathOperator{\GammaDist}{Gamma} +\DeclareMathOperator{\Gumbel}{Gumbel} +\DeclareMathOperator{\Std}{Std} +% \DeclareMathOperator{\Dirichlet}{Dir} +\DeclareMathOperator{\Train}{\mathcal{D}_{\text{train}}} +\DeclareMathOperator{\Dtrain}{\mathcal{D}_{\text{train}}} +% \newcommand{\Dtrain}{\mathcal{D}_\text{train}} +\DeclareMathOperator{\TrainLoss}{TrainLoss} +\DeclareMathOperator{\Loss}{Loss} +\DeclareMathOperator{\ZeroOneLoss}{Loss_{0\text{-}1}} +\DeclareMathOperator{\SquaredLoss}{Loss_{\text{squared}}} +\DeclareMathOperator{\AbsDevLoss}{Loss_{\text{absdev}}} +\DeclareMathOperator{\HingeLoss}{Loss_{\text{hinge}}} +\DeclareMathOperator{\LogisticLoss}{Loss_{\text{logistic}}} +\newcommand{\bfw}{\mathbf{w}} +\newcommand{\bbI}{\mathbb{I}} +\newcommand{\E}{\mathbb{E}} +\DeclareMathOperator{\Miss}{Miss} +\DeclareMathOperator{\sgn}{sgn} +\newcommand{\1}{\mathbb{1}} +% \newcommand{\R}{\mathbb{R}} +\renewcommand{\v}{\mathbf{v}} +\newcommand{\V}{\mathbf{V}} +\newcommand{\w}{\mathbf{w}} +\newcommand{\h}{\mathbf{h}} +\newcommand{\M}{\mathbf{M}} +\newcommand{\m}{\mathbf{m}} +\newcommand{\B}{\mathbf{B}} +\newcommand{\e}{\mathbf{e}} +\newcommand{\bfE}{\mathbf{E}} +\newcommand{\surrogate}{\hat{S}} % Surrogate model (\mathcal{S}) +\newcommand{\Sierra}{\mathbf{M}_\mathcal{S}} + +\newcommand{\opt}{*} +\DeclareMathOperator{\States}{States} +\DeclareMathOperator{\StartState}{s_{\text{state}}} +\DeclareMathOperator{\Actions}{Actions} +\DeclareMathOperator{\Reward}{Reward} +\DeclareMathOperator{\IsEnd}{IsEnd} +\DeclareMathOperator{\Cost}{Cost} +\DeclareMathOperator{\FutureCost}{FutureCost} +\DeclareMathOperator{\Succ}{Succ} + +% From tufte_algorithms_book.tex +\usepackage{mathtools} +\DeclarePairedDelimiter{\paren}{\lparen}{\rparen} +\DeclarePairedDelimiter{\brock}{\lbrack}{\rbrack} +\DeclarePairedDelimiter{\curly}{\{}{\}} +% \DeclarePairedDelimiter{\norm}{\lVert}{\rVert} +% \DeclarePairedDelimiter{\abs}{\lvert}{\rvert} +\DeclarePairedDelimiter{\anglebrackets}{\langle}{\rangle} +\DeclarePairedDelimiter{\ceil}{\lceil}{\rceil} +\DeclarePairedDelimiter{\floor}{\lfloor}{\rfloor} +\DeclarePairedDelimiter{\card}{|}{|} + +\newcommand{\minimize}{\operatornamewithlimits{minimize}} +\newcommand{\maximize}{\operatornamewithlimits{maximize}} +\newcommand{\supremum}{\operatornamewithlimits{supremum}} +\newcommand{\argmin}{\operatornamewithlimits{arg\,min}} +\newcommand{\argmax}{\operatornamewithlimits{arg\,max}} +\newcommand{\subjectto}{\operatorname{subject~to}} +\newcommand{\for}{\text{for} \;} +\newcommand{\dimension}[1]{\text{dim}\paren*{#1}} +\newcommand{\gaussian}[2]{\mathcal{N}(#1, #2)} +\newcommand{\Gaussian}[2]{\mathcal{N}\paren*{#1, #2}} +\newcommand{\R}{\mathbb{R}} +\newcommand{\Z}{\mathbb{Z}} +\newcommand{\N}{\mathbb{N}} +\DeclareMathOperator{\sign}{sign} +\DeclareMathOperator{\Real}{\text{Re}} +\DeclareMathOperator{\Imag}{\text{Im}} +\DeclareMathOperator{\nil}{\textsc{nil}} +\DeclareMathOperator{\Expectation}{\mathbb{E}} +\DeclareMathOperator{\Variance}{\mathrm{Var}} +\DeclareMathOperator{\Normal}{\mathcal{N}} +\DeclareMathOperator{\Uniform}{\mathcal{U}} +\DeclareMathOperator{\Dirichlet}{Dir} +\DeclareMathOperator{\atantwo}{atan2} +\DeclareMathOperator{\modOne}{mod_1} +\DeclareMathOperator{\trace}{Tr} +\newcommand{\minprob}[3]{ +\begin{aligned} + \minimize_{#1} & & #2\\ + \subjectto & & #3 \\ +\end{aligned} +} +\newcommand{\mat}[1]{\vect{#1}} +\renewcommand{\vec}[1]{\vect{#1}} + + +% Math operatrs +\DeclareMathOperator{\ReLU}{ReLU} +\DeclareMathOperator{\LeakyReLU}{LeakyReLU} +\DeclareMathOperator{\softmax}{softmax} + + + +%%% Algorithm settings +\algtext*{EndLoop}% Remove "end _X_" text +\algtext*{EndFor} +\algtext*{EndIf} +\algtext*{EndFunction} + +% Rounding notation +\DeclarePairedDelimiter{\round}\lfloor\rceil + +%%% FROM CEM VARIANTS +\usepackage{tikz} +\usepackage{algorithmicx} +\usepackage{algorithm} +\usepackage{algpseudocode} +\usepackage{amsmath} +\usepackage{amsfonts} +\usepackage{siunitx} +\usepackage{commath} +% \usepackage[backend=biber,style=ieee,natbib=true]{biblatex} % TODO. +\usepackage[backend=biber,natbib=true]{biblatex} % TODO. +% \renewcommand{\bibfont}{\footnotesize} % for IEEE bibfont size TODO. +\usepackage{multirow} +\usepackage{bbm} +\usepackage{hyperref} +\usepackage{cleveref} +% \usepackage[keeplastbox]{flushend} % TODO. + + +\usepackage{longtable,tabularx,booktabs} +\usepackage[flushleft]{threeparttable} + +% Separation after algorithm environment +% \setlength{\textfloatsep}{\baselineskip} % TODO. + +% \addbibresource{cem_variants.bib} % TODO + +% Flipped vector arrow +\makeatletter +\DeclareRobustCommand{\cev}[1]{% + {\mathpalette\do@cev{#1}}% +} +\newcommand{\do@cev}[2]{% + \vbox{\offinterlineskip + \sbox\z@{$\m@th#1 x$}% + \ialign{##\cr + \hidewidth\reflectbox{$\m@th#1\vec{}\mkern4mu$}\hidewidth\cr + \noalign{\kern-\ht\z@} + $\m@th#1#2$\cr + }% + } +}%late +\makeatother + +\usepackage{multirow} + +\usetikzlibrary{calc} +\usetikzlibrary{shapes.geometric} +\usetikzlibrary{external} +\usetikzlibrary{patterns} +\usetikzlibrary{shapes,arrows,fit} +\usetikzlibrary{positioning} +\usetikzlibrary{arrows.meta, calc, shapes} +\usetikzlibrary{graphs} +\usetikzlibrary{decorations.pathmorphing} +\usetikzlibrary{decorations.pathreplacing} + +\usepackage[caption=false]{subfig} % TODO? + +\usepackage{pgfplots} +\pgfplotsset{compat=newest} +\pgfplotsset{every axis legend/.append style={% +cells={anchor=west}} +} +\usetikzlibrary{arrows} +\tikzset{>=stealth'} + +\usepgfplotslibrary{fillbetween} +\usepgfplotslibrary{groupplots} + +\newcommand{\smallcaps}[1]{\textsc{#1}} + + + +%%%%%% Episodic AST +% \usepackage[utf8]{inputenc} +\usepackage{fancyhdr,graphicx} +\usepackage[margin=1in]{geometry} +\usepackage[nolist]{acronym} +\usepackage{booktabs} +% \usepackage[table]{xcolor} +% \usepackage{amsmath} +% \usepackage{pgfplots} +% \usepackage{silence} +% \usepackage{tikz} +% \usepackage{algorithmicx} +% \usepackage{algorithm} +% \usepackage{algpseudocode} +% \usepackage{bm} +% \usepackage{amsfonts} +% \usepackage{siunitx} +% \usepackage{commath} +% \usepackage[hidelinks,bookmarks=false]{hyperref} +% \usepackage{cleveref} +% \usepackage{multirow} +% \usepackage{wrapfig} +% \usepackage{subfig} +% \usepackage[font=small]{caption} + +\usepackage{longtable,tabularx,booktabs} +\usepackage[flushleft]{threeparttable} +\usepackage[keeplastbox]{flushend} + +% \addbibresource{references.bib} + +% Algorithm style. +\algtext*{EndLoop} % Remove "end _X_" text +\algtext*{EndIf} +\algtext*{EndFunction} +\renewcommand\algorithmicthen{} +\renewcommand\algorithmicdo{} + +% PGFPlots and TikZ settings +\pgfplotsset{compat=newest} +\usetikzlibrary{shapes.geometric} +\usetikzlibrary{external} +\usetikzlibrary{patterns} +\usetikzlibrary{shapes,arrows,fit} +\usetikzlibrary{positioning} +\usetikzlibrary{arrows.meta, calc} +\usetikzlibrary{graphs} +\usetikzlibrary{decorations.pathmorphing} +\usetikzlibrary{decorations.pathreplacing} + + +% Custom colors +\definecolor{pastelMagenta}{HTML}{FF48CF} +\definecolor{pastelPurple}{HTML}{8770FE} +\definecolor{pastelBlue}{HTML}{1BA1EA} +\definecolor{pastelSeaGreen}{HTML}{14B57F} +\definecolor{pastelGreen}{HTML}{3EAA0D} +\definecolor{pastelOrange}{HTML}{C38D09} +\definecolor{pastelRed}{HTML}{F5615C} +% \input{preamble/pastelcolormap} % TODO +% \input{preamble/pastelcolorlist} % TODO + +% Custom commands +\newcommand{\todo}[1]{\textbf{[[TODO: #1]]}} +\crefrangelabelformat{section}{#3#1#4--#5\crefstripprefix{#1}{#2}#6} % Reference range of sections with a dash +% \newcommand{\citefull}[1]{\citeauthor{#1}~\cite{#1}} + +%%% full author citation +% {\newrobustcmd*{\citefirstlastauthor}{\AtNextCite{\DeclareNameAlias{labelname}{given-family}}\citeauthor} + + + + +%% Weakness recognition +\usepackage{graphbox} % for [align=c] in \includegraphics +\usepackage{wrapfig} +% \usepackage{subfigure} +\usepackage{caption} +% \usepackage{subcaption} +\usepackage{graphicx} + + + + + + +%%% POMDPStressTesting.jl +\usepackage{listings} + +\lstdefinelanguage{Julia}{ + keywords=[3]{initialize!, transition!, evaluate!, distance, isevent, isterminal, environment}, + keywords=[2]{Nothing, Tuple, Real, Bool, Simulation, BlackBox, GrayBox, Sampleable, Environment}, + keywords=[1]{function, abstract, type, end}, + sensitive=true, + morecomment=[l]{\#}, + morecomment=[n]{\#=}{=\#}, + morestring=[s]{"}{"}, + morestring=[m]{'}{'}, + alsoletter=!?, + literate={,}{{\color[HTML]{0F6FA3},}}1 + {\{}{{\color[HTML]{0F6FA3}\{}}1 + {\}}{{\color[HTML]{0F6FA3}\}}}1 +} + +\lstset{ + language = Julia, + backgroundcolor = \color[HTML]{F2F2F2}, + basicstyle = \small\ttfamily\color[HTML]{19177C}, + numberstyle = \ttfamily\scriptsize\color[HTML]{7F7F7F}, + keywordstyle = [1]{\bfseries\color[HTML]{1BA1EA}}, + keywordstyle = [2]{\color[HTML]{0F6FA3}}, + keywordstyle = [3]{\color[HTML]{0000FF}}, + stringstyle = \color[HTML]{F5615C}, + commentstyle = \color[HTML]{AAAAAA}, + rulecolor = \color[HTML]{000000}, + frame=lines, + xleftmargin=10pt, + framexleftmargin=10pt, + framextopmargin=4pt, + framexbottommargin=4pt, + tabsize=4, + captionpos=b, + breaklines=true, + breakatwhitespace=false, + showstringspaces=false, + showspaces=false, + showtabs=false, + columns=fullflexible, + keepspaces=true, + numbers=none, +} \ No newline at end of file diff --git a/preamble/vector.sty b/preamble/vector.sty new file mode 100644 index 0000000..2a5a96a --- /dev/null +++ b/preamble/vector.sty @@ -0,0 +1,70 @@ +\ProvidesPackage{vector} +% based on: http://tex.stackexchange.com/questions/167172/consistent-macro-for-bold-upright-vectors-in-both-latin-and-greek + +\RequirePackage{xparse} +\RequirePackage{bm,upgreek} + +\ExplSyntaxOn +\NewDocumentCommand\vect{m} +{ + \commexo_vector:n { #1 } +} + +\cs_new_protected:Npn \commexo_vector:n #1 +{ + \tl_map_inline:nn { #1 } + { + \commexo_vector_inner:n { ##1 } + } +} + +\cs_new_protected:Npn \commexo_vector_inner:n #1 +{ + \tl_if_in:VnTF \g_commexo_latin_tl { #1 } + {% we check whether the argument is a Latin letter + \mathbf { #1 } % a Latin letter + } + {% if not a Latin letter, we check if it's an uppercase Greek letter + \tl_if_in:VnTF \g_commexo_ucgreek_tl { #1 } + { + \bm { #1 } % a Greek uppercase letter + } + {% if not, we check if it's a lowercase Greek letter + \tl_if_in:VnTF \g_commexo_lcgreek_tl { #1 } + { + \commexo_makeboldupright:n { #1 } + } + {% none of the above, just issue #1 + #1 % fall back + } + } + } +} + +\cs_new_protected:Npn \commexo_makeboldupright:n #1 +{ + \bm { \use:c { up \cs_to_str:N #1 } } +} + +\tl_new:N \g_commexo_latin_tl +\tl_new:N \g_commexo_ucgreek_tl +\tl_new:N \g_commexo_lcgreek_tl +\tl_gset:Nn \g_commexo_latin_tl +{ + ABCDEFGHIJKLMNOPQRSTUVWXYZ + abcdefghijklmnopqrstuvwxyz + 0123456789 +} +\tl_gset:Nn \g_commexo_ucgreek_tl +{ + \Gamma\Delta\Theta\Lambda\Pi\Sigma\Upsilon\Phi\Chi\Psi\Omega +} +\tl_gset:Nn \g_commexo_lcgreek_tl +{ + \alpha\beta\gamma\delta\epsilon\zeta\eta\theta\iota\kappa + \lambda\mu\nu\xi\pi\rho\sigma\tau\upsilon\phi\chi\psi\omega + \varepsilon\vartheta\varpi\varphi\varsigma\varrho +} + +\ExplSyntaxOff +\endinput diff --git a/references/cem_variants.bib b/references/cem_variants.bib new file mode 100644 index 0000000..7b852b2 --- /dev/null +++ b/references/cem_variants.bib @@ -0,0 +1,386 @@ + +@ARTICLE{monte_carlo, + author = {{Bird}, G.~A.}, + title = "{Monte-Carlo simulation in an engineering context}", + journal = {Progress in Astronautics and Aeronautics}, + keywords = {Computational Fluid Dynamics, Computerized Simulation, Fluid Flow, Kinetic Theory, Mechanical Engineering, Monte Carlo Method, Computer Programs, Mathematical Models, Minicomputers, Molecular Collisions, Thermodynamics and Statistical Physics}, + year = 1981, + month = jan, + volume = {74}, + pages = {239-255}, + adsurl = {https://ui.adsabs.harvard.edu/abs/1981PrAA...74..239B}, + adsnote = {Provided by the SAO/NASA Astrophysics Data System} +} + + +@INPROCEEDINGS{ast_acasx, +author={R. {Lee} and M. J. {Kochenderfer} and O. J. {Mengshoel} and G. P. {Brat} and M. P. {Owen}}, +booktitle={2015 IEEE/AIAA 34th Digital Avionics Systems Conference (DASC)}, +title={Adaptive stress testing of airborne collision avoidance systems}, +year={2015}, +volume={}, +number={}, +pages={6C2-1-6C2-13}, +keywords={aircraft;collision avoidance;Monte Carlo methods;tree searching;adaptive stress testing;airborne collision avoidance systems;reinforcement learning formulation;Monte Carlo tree search;MCTS;aircraft collision avoidance system;mid-air collisions;Lead;Atmospheric modeling;Quality of service}, +doi={10.1109/DASC.2015.7311450}, +ISSN={2155-7209}, +month={Sep.},} + + +@INPROCEEDINGS{ast_av, +author={M. {Koren} and S. {Alsaif} and R. {Lee} and M. J. {Kochenderfer}}, +booktitle={2018 IEEE Intelligent Vehicles Symposium (IV)}, +title={Adaptive Stress Testing for Autonomous Vehicles}, +year={2018}, +volume={}, +number={}, +pages={1-7}, +keywords={decision making;learning (artificial intelligence);Markov processes;Monte Carlo methods;stochastic processes;tree searching;vehicles;autonomous vehicles;collision scenarios;Markov decision process;failure scenarios;Monte Carlo Tree Search;MCTS;Deep Reinforcement Learning solutions;DRL;Monte Carlo sampling;reinforcement learning algorithms;adaptive stress testing;stochastic element perturbation;Autonomous vehicles;Sensors;Testing;Markov processes;Roads;Stress;Monte Carlo methods}, +doi={10.1109/IVS.2018.8500400}, +ISSN={1931-0587}, +month={June},} + + +@inbook{dast_acasx, +author = {Ritchie Lee and Ole Mengshoel and Anshu Saksena and Ryan Gardner and Daniel Genin and Jeffrey Brush and Mykel J. Kochenderfer}, +title = {Differential Adaptive Stress Testing of Airborne Collision Avoidance Systems}, +booktitle = {2018 AIAA Modeling and Simulation Technologies Conference}, +chapter = {}, +pages = {}, +doi = {10.2514/6.2018-1923} +} + + +@incollection{ast_safety, + title={Adaptive Stress Testing of Safety-Critical Systems}, + author={Lee, Ritchie and Mengshoel, Ole J and Kochenderfer, Mykel J}, + booktitle={Safe, Autonomous and Intelligent Vehicles}, + pages={77--95}, + year={2019}, + publisher={Springer} +} + +@inproceedings{ast_traj_plan, + title={Adaptive Stress Testing of Trajectory Planning Systems}, + author={Lee, Ritchie and Puig-Navarro, Javier and Agogino, Adrian K and Giannakoupoulou, Dimitra and Mengshoel, Ole J and Kochenderfer, Mykel J and Allen, B Danette}, + booktitle={AIAA Scitech 2019 Forum}, + pages={1454}, + year={2019} +} + +@phdthesis{lee_thesis, + title={AdaStress: Adaptive Stress Testing and Interpretable Categorization for Safety-Critical Systems}, + author={Lee, Ritchie}, + year={2019}, + school={Carnegie Mellon University} +} + +@article{trustworthy_ai, + title={Efficient Black-box Assessment of Autonomous Vehicle Safety}, + author={Norden, Justin and O'Kelly, Matthew and Sinha, Aman}, + journal={arXiv preprint arXiv:1912.03618}, + year={2019} +} + +@INPROCEEDINGS{fms, +author={S. {Liden}}, +booktitle={AIAA/IEEE Digital Avionics Systems Conference. 13th DASC}, +title={The evolution of Flight Management Systems}, +year={1994}, +volume={}, +number={}, +pages={157-169}, +keywords={aircraft computers;decision support systems;aircraft displays;computerised navigation;flight management;commercial aircraft;avionic equipment;757/767 systems;747-400;MD-80;MD-90;A310/A300-A600;A320-A321;ARINC 739;A330/A340;Aircraft;Aerospace electronics;Crisis management;Computer displays;Cost function;Fuels;Software design;Navigation;Computer interfaces;Aerospace industry}, +doi={10.1109/DASC.1994.369487}, +ISSN={null}, +month={Oct},} + +@incollection{fms_workload, + title={Flight deck automation and pilot workload}, + author={Roscoe, Alan H}, + booktitle={Vigilance and performance in automatized systems/vigilance et performance de l’Homme dans les syst{\`e}mes automatis{\'e}s}, + pages={111--122}, + year={1989}, + publisher={Springer} +} + +@inproceedings{mcts_ucb, + title={Continuous upper confidence trees}, + author={Cou{\"e}toux, Adrien and Hoock, Jean-Baptiste and Sokolovska, Nataliya and Teytaud, Olivier and Bonnard, Nicolas}, + booktitle={International Conference on Learning and Intelligent Optimization}, + pages={433--445}, + year={2011}, + organization={Springer} +} + +@misc{mcts_wildfire, + title={A Comparison of Monte Carlo Tree Search and Mathematical Optimization for Large Scale Dynamic Resource Allocation}, + author={Dimitris Bertsimas and J. Daniel Griffith and Vishal Gupta and Mykel J. Kochenderfer and Velibor V. Mišić and Robert Moss}, + year={2014}, + eprint={1405.5498}, + archivePrefix={arXiv}, +} + +@article{julia, + title={Julia: A fresh approach to numerical computing}, + author={Bezanson, Jeff and Edelman, Alan and Karpinski, Stefan and Shah, Viral B}, + journal={SIAM review}, + volume={59}, + number={1}, + pages={65--98}, + year={2017}, + publisher={SIAM} +} + +@article{arch_comp, + title={ARCH-COMP 2019 category report: falsification}, + author={Ernst, Gidon and Arcaini, Paolo and Donze, Alexandre and Fainekos, Georgios and Mathesen, Logan and Pedrielli, Giulia and Yaghoubi, Shakiba and Yamagata, Yoriyuki and Zhang, Zhenya}, + journal={EPiC Series in Computing}, + volume={61}, + pages={129--140}, + year={2019}, + publisher={EasyChair} +} + + +@article{pomdps_jl, + author = {Maxim Egorov and Zachary N. Sunberg and Edward Balaban and Tim A. Wheeler and Jayesh K. Gupta and Mykel J. Kochenderfer}, + title = {{POMDP}s.jl: A Framework for Sequential Decision Making under Uncertainty}, + journal = {Journal of Machine Learning Research}, + year = {2017}, + volume = {18}, + number = {26}, + pages = {1-5} +} + +@article{vincenty, + title={Direct and inverse solutions of geodesics on the ellipsoid with application of nested equations}, + author={Vincenty, Thaddeus}, + journal={Survey review}, + volume={23}, + number={176}, + pages={88--93}, + year={1975}, + publisher={Taylor \& Francis} +} + +@inproceedings{bayes_opt, + title={Generating adversarial driving scenarios in high-fidelity simulators}, + author={Abeysirigoonawardena, Yasasa and Shkurti, Florian and Dudek, Gregory}, + booktitle={2019 International Conference on Robotics and Automation (ICRA)}, + pages={8271--8277}, + year={2019}, + organization={IEEE} +} + +@inproceedings{hill_climbing, + title={Multi-armed Bandits for Boolean Connectives in Hybrid System Falsification}, + author={Zhang, Zhenya and Hasuo, Ichiro and Arcaini, Paolo}, + booktitle={International Conference on Computer Aided Verification}, + pages={401--420}, + year={2019}, + organization={Springer} +} + +@article{rrts, + title={Rapidly-exploring random trees-based test generation for autonomous vehicles}, + author={Tuncali, Cumhur Erkan and Fainekos, Georgios}, + journal={arXiv preprint arXiv:1903.10629}, + year={2019} +} + +@inproceedings{bootstrap, + title={Analyzing neighborhoods of falsifying traces in cyber-physical systems}, + author={Diwakaran, Ram Das and Sankaranarayanan, Sriram and Trivedi, Ashutosh}, + booktitle={Proceedings of the 8th International Conference on Cyber-Physical Systems}, + pages={109--119}, + year={2017} +} + +@article{mc_limitations, + title={Improvements to and limitations of Latin hypercube sampling}, + author={Huntington, DE and Lyrintzis, CS}, + journal={Probabilistic engineering mechanics}, + volume={13}, + number={4}, + pages={245--253}, + year={1998}, + publisher={Elsevier} +} + +@book{rubinstein2004cross, + title={The Cross-Entropy Method: A Unified Approach to Combinatorial Optimization, {Monte-Carlo} Simulation and Machine Learning}, + author={Rubinstein, RY and Kroese, DP}, + year={2004}, + publisher={Springer} +} + +@article{de2005tutorial, + title={A Tutorial on the Cross-Entropy Method}, + author={De Boer, Pieter-Tjerk and Kroese, Dirk P and Mannor, Shie and Rubinstein, Reuven Y}, + journal={{Annals of Operations Research}}, + volume={134}, + number={1}, + pages={19--67}, + year={2005}, + publisher={Springer} +} + +@Book{Kochenderfer2019, + Title = {Algorithms for Optimization}, + Author = {Kochenderfer, Mykel J and Wheeler, Tim A}, + Publisher = {MIT Press}, + Year = {2019} +} + + +@book{kochenderfer2015decision, + title={{Decision Making Under Uncertainty: Theory and Application}}, + author={Kochenderfer, Mykel J.}, + year={2015}, + publisher={MIT Press} +} + +@article{dempster1977maximum, + title={{Maximum likelihood from incomplete data via the EM algorithm}}, + author={Dempster, Arthur P and Laird, Nan M and Rubin, Donald B}, + journal={Journal of the Royal Statistical Society: Series B (Methodological)}, + volume={39}, + number={1}, + pages={1--22}, + year={1977}, + publisher={Wiley Online Library} +} + +@article{aitkin1980mixture, + title={{Mixture models, outliers, and the EM algorithm}}, + author={Aitkin, Murray and Wilson, Granville Tunnicliffe}, + journal={Technometrics}, + volume={22}, + number={3}, + pages={325--331}, + year={1980}, + publisher={Taylor \& Francis Group} +} + + + + +# Related work to CE-surrogate. + +@inproceedings{bardenet2010surrogating, + title={Surrogating the Surrogate: Accelerating Gaussian-Process-Based Global Optimization with a Mixture Cross-Entropy Algorithm}, + author={Bardenet, R{\'e}mi and K{\'e}gl, Bal{\'a}zs}, + booktitle={International Conference on Machine Learning (ICML)}, + pages={55--62}, + year={2010} +} + +@article{li2010evaluation, + title={Evaluation of failure probability via surrogate models}, + author={Li, Jing and Xiu, Dongbin}, + journal={Journal of Computational Physics}, + volume={229}, + number={23}, + pages={8966--8980}, + year={2010}, + publisher={Elsevier} +} + +@article{li2011efficient, + title={An efficient surrogate-based method for computing rare failure probability}, + author={Li, Jing and Li, Jinglai and Xiu, Dongbin}, + journal={Journal of Computational Physics}, + volume={230}, + number={24}, + pages={8683--8697}, + year={2011}, + publisher={Elsevier} +} + +@INPROCEEDINGS{tan2018gaussian, + author={Y. T. {Tan} and A. {Kunapareddy} and M. {Kobilarov}}, + booktitle={International Conference on Robotics and Automation (ICRA)}, + title={Gaussian Process Adaptive Sampling Using the Cross-Entropy Method for Environmental Sensing and Monitoring}, + year={2018}, + volume={}, + number={}, + pages={6220-6227}, +} + + + +@incollection{NIPS2015_5672, + title = {Model-Based Relative Entropy Stochastic Search}, + author = {Abdolmaleki, Abbas and Lioutikov, Rudolf and Peters, Jan R and Lau, Nuno and Pualo Reis, Luis and Neumann, Gerhard}, + booktitle = {Advances in Neural Information Processing Systems (NIPS)}, + pages = {3537--3545}, + year = {2015}, +} + +@article{kroese2006cross, + title={The cross-entropy method for continuous multi-extremal optimization}, + author={Kroese, Dirk P and Porotsky, Sergey and Rubinstein, Reuven Y}, + journal={Methodology and Computing in Applied Probability}, + volume={8}, + number={3}, + pages={383--407}, + year={2006}, + publisher={Springer} +} + +@book{mclachlan2004finite, + title={Finite mixture models}, + author={McLachlan, Geoffrey J and Peel, David}, + year={2004}, + publisher={John Wiley \& Sons} +} + + + +@article{botev2007generalized, +author = {Z.I. Botev and D.P. Kroese and T. Taimre}, +title ={Generalized Cross-entropy Methods with Applications to Rare-event Simulation and Optimization}, +journal = {SIMULATION}, +volume = {83}, +number = {11}, +pages = {785-806}, +year = {2007}, +doi = {10.1177/0037549707087067}, +abstract = { The cross-entropy and minimum cross-entropy methods are well-known Monte Carlo simulation techniques for rare-event probability estimation and optimization. In this paper, we investigate how these methods can be eXtended to provide a general non-parametric cross-entropy framework based on φ-divergence distance measures. We show how the χ2 distance, in particular, yields a viable alternative to the Kullback—Leibler distance. The theory is illustrated with various eXamples from density estimation, rare-event simulation and continuous multi-eXtremal optimization. } +} + + + + +@article{kurtz2013cross, + title={Cross-entropy-based adaptive importance sampling using Gaussian mixture}, + author={Kurtz, Nolan and Song, Junho}, + journal={Structural Safety}, + volume={42}, + pages={35--44}, + year={2013}, + publisher={Elsevier} +} + +@article{wang2016cross, + title={Cross-entropy-based adaptive importance sampling using von {Mises-Fisher} mixture for high dimensional reliability analysis}, + author={Wang, Ziqi and Song, Junho}, + journal={Structural Safety}, + volume={59}, + pages={42--52}, + year={2016}, + publisher={Elsevier} +} + + +@article{rubinstein1999cross, + title={The Cross-Entropy Method for Combinatorial and Continuous Optimization}, + author={Rubinstein, Reuven}, + journal={Methodology and Computing in Applied Probability}, + volume={1}, + number={2}, + pages={127--190}, + year={1999}, + publisher={Springer} +} \ No newline at end of file diff --git a/references/episodic_ast.bib b/references/episodic_ast.bib new file mode 100644 index 0000000..f4f17b3 --- /dev/null +++ b/references/episodic_ast.bib @@ -0,0 +1,510 @@ +% Encoding: UTF-8 + +@String { aaai = {AAAI Conference on Artificial Intelligence (AAAI)} } +@String { aamas = {International Conference on Autonomous Agents and Multiagent Systems (AAMAS)} } +@String { acc = {American Control Conference (ACC)} } +@String { aiaa_info = {AIAA Infotech@Aerospace Conference} } +@String { aiaa_jacic = {Journal of Aerospace Computing, Information, and Communication} } +@String { allerton = {Allerton Conference on Communication, Control, and Compution} } +@String { atio = {AIAA Aviation Technology, Integration, and Operations Conference (ATIO)} } +@String { cacm = {Communications of the ACM} } +@String { cdc = {IEEE Conference on Decision and Control (CDC)} } +@String { cvpr = {IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR)} } +@String { dasc = {Digital Avionics Systems Conference (DASC)} } +@String { ecml = {European Conference on Machine Learning (ECML)} } +@String { gnc = {AIAA Guidance, Navigation, and Control Conference (GNC)} } +@String { icaart = {International Conference on Agents and Artificial Intelligence (ICAART)} } +@String { icassp = {International Conference on Acoustics, Speech, and Signal Processing (ICASSP)} } +@String { icml = {International Conference on Machine Learning (ICML)} } +@String { icmla = {International Conference on Machine Learning and Applications (ICMLA)} } +@String { icra = {IEEE International Conference on Robotics and Automation (ICRA)} } +@String { icslp = {International Conference on Spoken Language Processing (ICSLP)} } +@String { ieee_csm = {IEEE Control Systems Magazine} } +@String { ieee_j_ac = {IEEE Transactions on Automatic Control} } +@String { ieeeaero = {IEEE Aerospace Conference} } +@String { ieeeciaig = {IEEE Transactions on Computational Intelligence and AI in Games} } +@String { ieeecst = {IEEE Transactions on Control Systems Technology} } +@String { ieeetac = {IEEE Transactions on Automatic Control} } +@String { ieeetsp = {IEEE Transactions on Signal Processing} } +@String { ijcai = {International Joint Conference on Artificial Intelligence (IJCAI)} } +@String { interspeech = {Annual Conference of the International Speech Communication Association (INTERSPEECH)} } +@String { iros = {IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS)} } +@String { itsc = {IEEE International Conference on Intelligent Transportation Systems (ITSC)} } +@String { jair = {Journal of Artificial Intelligence Research} } +@String { jgcd = {AIAA Journal on Guidance, Control, and Dynamics} } +@String { jmlr = {Journal of Machine Learning} } +@String { jota = {Journal of Optimization Theory and Applications} } +@String { jstor = {Journal of the American Statistical Association} } +@String { lion = {Learning and Intelligent Optimization (LION)} } +@String { mit = {Massachusetts Institute of Technology} } +@String { mitaa = {Massachusetts Institute of Technology, Department of Aeronautics and Astronautics} } +@String { mitee = {Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science} } +@String { mitme = {Massachusetts Institute of Technology, Department of Mechanical Engineering} } +@String { mitpress = {MIT Press}} +@String { mor = {Mathematics of Operations Research} } +@String { nips = {Advances in Neural Information Processing Systems (NIPS)} } +@String { or = {Operations Research} } +@String { rss = {Robotics: Science and Systems} } +@String { sigcomm = {ACM Special Interest Group on Data Communication (SIGCOMM)} } +@String { springer = {Springer}} +@String { suaa = {Stanford University, Department of Aeronautics and Astronautics} } +@String { suee = {Stanford University, Department of Electrical Engineering} } +@String { sume = {Stanford University, Department of Mechanical Engineering} } +@String { tac = {IEEE Transactions on Automatic Control} } +@String { tacas = {International Conference on Tools and Algorithms for the Construction and Analysis of Systems (TACAS)} } +@String { taes = {IEEE Transactions on Aerospace and Electronic Systems} } +@String { toms = {ACM Transactions on Mathematical Software} } +@String { uai = {Conference on Uncertainty in Artificial Intelligence (UAI)} } +@String { wiley = {Wiley}} + +@Book{kochenderfer2019algorithms, + Title = {Algorithms for Optimization}, + Author = {Kochenderfer, Mykel J. and Wheeler, Tim A.}, + Publisher = mitpress, + Year = {2019}, + ISBN = {9780262039420} +} + +@Article{Acikmese2013, + Title = {Lossless Convexification of Nonconvex Control Bound and Pointing Constraints of the Soft Landing Optimal Control Problem}, + Author = {A\c{c}ikme\c{s}e, Beh\c{c}et and Carson, John M. III and Blackmore, Lars}, + Journal = ieeecst, + Year = {2013}, + Number = {6}, + Pages = {2104--2113}, + Volume = {21} +} + +@Conference{Bethke2008, + Title = {Group health management of {UAV} teams with applications to persistent surveillance}, + Author = {Bethke, B. and How, J. P. and Vian, J.}, + Booktitle = acc, + Year = {2008}, + + Address = {Seattle, WA}, + Month = {11-13 June}, + Pages = {3145-3150}, + + Bdsk-url-1 = {http://acl.mit.edu/papers/acc-fuel-2008-bbethke.pdf}, + Bdsk-url-online-1 = {10.1109/ACC.2008.4586976}, + Date-added = {2011-04-02 08:44:34 -0400}, + Date-modified = {2011-04-02 08:44:34 -0400}, + ISBN = {0743-1619}, + Keywords = {aircraft control; mobile robots; multi-robot systems; remotely operated vehicles; autonomous mission system; border patrol; group health management; military surveillance; mission system design; persistent surveillance; search and rescue; unmanned aerial vehicles; decision making}, + Owner = {MY20473}, + Timestamp = {2012.05.25}, + Ty = {CONF}, + Url = {http://acl.mit.edu/papers/acc-fuel-2008-bbethke.pdf}, + Url-online = {10.1109/ACC.2008.4586976} +} + +@MastersThesis{Krige1951, + Title = {A statistical approach to some mine valuation and allied problems on the {Witwatersrand}}, + Author = {Krige, D G}, + School = {University of Witwatersrand}, + Year = {1951} +} + +@PhdThesis{Kochenderfer2006, + Title = {Adaptive Modelling and Planning for Learning Intelligent Behaviour}, + Author = {Mykel J. Kochenderfer}, + School = {University of Edinburgh}, + Year = {2006}, + + Owner = {MY20473}, + Quality = {1}, + Timestamp = {2012.12.29} +} + +@InCollection{Bader2004, + Title = {Parallel Algorithm Design for Branch and Bound}, + author = {Bader, David A and Hart, William E and Phillips, Cynthia A}, + booktitle = {Tutorials on Emerging Methodologies and Applications in Operations Research}, + Editor = {Greenberg, H J}, + Publisher = {Kluwer Academic Press}, + Year = {2004} +} + +@InProceedings{Bethke2009, + Title = {Multi-{UAV} Persistent Surveillance with Communication Constraints and Health Management}, + Author = {Bethke, B. and How, J. P. and Vian, J.}, + Booktitle = gnc, + Year = {2009}, + Month = aug, + + Date-added = {2011-04-18 10:04:12 -0400}, + Date-modified = {2011-08-06 07:41:29 -0400}, + Keywords = {decision making}, + Owner = {MY20473}, + Timestamp = {2013.09.12} +} + +@TechReport{Andrews1981, + Title = {An Improved Technique for Altitude Tracking of Aircraft}, + Author = {John W. Andrews}, + Institution = {Massachusetts Institute of Technology, Lincoln Laboratory}, + Year = {1981}, + Month = mar, + Number = {ATC-105}, + Type = {Project Report}, + + Owner = {MY20473}, + Timestamp = {2012.03.01} +} + +@Comment{jabref-meta: databaseType:biblatex;} + + +%%% CS 109: Probability for Computer Scientists +@book{ross2006first, + title={A first course in probability}, + author={Ross, Sheldon M and others}, + volume={7}, + year={2006} +} + +% K. Rosen, Discrete Mathematics and its Applications, 6th Ed., New York: McGraw-Hill, 2007. +@book{rosen2007discrete, + title={Discrete Mathematics and its Applications}, + author={K. Rosen}, + volume={6}, + year={2007} +} + + + +%%% AST + + +@ARTICLE{monte_carlo, + author = {{Bird}, G.~A.}, + title = {{Monte-Carlo simulation in an engineering context}}, + journal = {Progress in Astronautics and Aeronautics}, + keywords = {Computational Fluid Dynamics, Computerized Simulation, Fluid Flow, Kinetic Theory, Mechanical Engineering, Monte Carlo Method, Computer Programs, Mathematical Models, Minicomputers, Molecular Collisions, Thermodynamics and Statistical Physics}, + year = {1981}, + month = {1}, + volume = {74}, + pages = {239-255}, + adsurl = {https://ui.adsabs.harvard.edu/abs/1981PrAA...74..239B}, + adsnote = {Provided by the SAO/NASA Astrophysics Data System} +} + + +@INPROCEEDINGS{ast_acasx, +author={R. {Lee} and M. J. {Kochenderfer} and O. J. {Mengshoel} and G. P. {Brat} and M. P. {Owen}}, +booktitle={IEEE/AIAA Digital Avionics Systems Conference (DASC)}, +title={Adaptive stress testing of airborne collision avoidance systems}, +year={2015}, +volume={}, +number={}, +pages={6C2-1-6C2-13}, +keywords={aircraft;collision avoidance;Monte Carlo methods;tree searching;adaptive stress testing;airborne collision avoidance systems;reinforcement learning formulation;Monte Carlo tree search;MCTS;aircraft collision avoidance system;mid-air collisions;Lead;Atmospheric modeling;Quality of service}, +doi={10.1109/DASC.2015.7311450}, +ISSN={2155-7209}, +month={9},} + + +@INPROCEEDINGS{ast_av, +author={M. {Koren} and S. {Alsaif} and R. {Lee} and M. J. {Kochenderfer}}, +booktitle={IEEE Intelligent Vehicles Symposium (IV)}, +title={Adaptive Stress Testing for Autonomous Vehicles}, +year={2018}, +volume={}, +number={}, +pages={1-7}, +keywords={decision making;learning (artificial intelligence);Markov processes;Monte Carlo methods;stochastic processes;tree searching;vehicles;autonomous vehicles;collision scenarios;Markov decision process;failure scenarios;Monte Carlo Tree Search;MCTS;Deep Reinforcement Learning solutions;DRL;Monte Carlo sampling;reinforcement learning algorithms;adaptive stress testing;stochastic element perturbation;Autonomous vehicles;Sensors;Testing;Markov processes;Roads;Stress;Monte Carlo methods}, +doi={10.1109/IVS.2018.8500400}, +ISSN={1931-0587}, +month={6},} + + +@inbook{dast_acasx, +author = {Ritchie Lee and Ole Mengshoel and Anshu Saksena and Ryan Gardner and Daniel Genin and Jeffrey Brush and Mykel J. Kochenderfer}, +title = {Differential Adaptive Stress Testing of Airborne Collision Avoidance Systems}, +booktitle = {AIAA Modeling and Simulation Technologies Conference}, +chapter = {}, +pages = {}, +year={2018}, +doi = {10.2514/6.2018-1923} +} + +@inproceedings{lee2018differential, + title={Differential adaptive stress testing of airborne collision avoidance systems}, + author={Lee, Ritchie and Mengshoel, Ole and Saksena, Anshu and Gardner, Ryan and Genin, Daniel and Brush, Jeffrey and Kochenderfer, Mykel J}, + booktitle={AIAA Modeling and Simulation Technologies Conference}, + pages={1923}, + year={2018} +} + +@incollection{ast_safety, + title={Adaptive Stress Testing of Safety-Critical Systems}, + author={Lee, Ritchie and Mengshoel, Ole J and Kochenderfer, Mykel J}, + booktitle={Safe, Autonomous and Intelligent Vehicles}, + pages={77--95}, + year={2019}, + publisher={Springer} +} + +@inproceedings{ast_traj_plan, + title={Adaptive Stress Testing of Trajectory Planning Systems}, + author={Lee, Ritchie and Puig-Navarro, Javier and Agogino, Adrian K and Giannakoupoulou, Dimitra and Mengshoel, Ole J and Kochenderfer, Mykel J and Allen, B Danette}, + booktitle={AIAA Scitech Forum}, + pages={1454}, + year={2019} +} + +@phdthesis{lee_thesis, + title={{AdaStress}: Adaptive Stress Testing and Interpretable Categorization for Safety-Critical Systems}, + author={Lee, Ritchie}, + year={2019}, + school={Carnegie Mellon University} +} + +@article{trustworthy_ai, + title={Efficient Black-box Assessment of Autonomous Vehicle Safety}, + author={Norden, Justin and O'Kelly, Matthew and Sinha, Aman}, + journal={arXiv preprint arXiv:1912.03618}, + year={2019} +} + +@INPROCEEDINGS{fms, +author={S. {Liden}}, +booktitle={AIAA/IEEE Digital Avionics Systems Conference (DASC)}, +title={The evolution of Flight Management Systems}, +year={1994}, +volume={}, +number={}, +pages={157-169}, +keywords={aircraft computers;decision support systems;aircraft displays;computerised navigation;flight management;commercial aircraft;avionic equipment;757/767 systems;747-400;MD-80;MD-90;A310/A300-A600;A320-A321;ARINC 739;A330/A340;Aircraft;Aerospace electronics;Crisis management;Computer displays;Cost function;Fuels;Software design;Navigation;Computer interfaces;Aerospace industry}, +doi={10.1109/DASC.1994.369487}, +ISSN={null}, +month={10},} + +@incollection{fms_workload, + title={Flight deck automation and pilot workload}, + author={Roscoe, Alan H}, + booktitle={Vigilance and performance in automatized systems/vigilance et performance de l’Homme dans les syst{\`e}mes automatis{\'e}s}, + pages={111--122}, + year={1989}, + publisher={Springer} +} + +@inproceedings{mcts_ucb, + title={Continuous upper confidence trees}, + author={Cou{\"e}toux, Adrien and Hoock, Jean-Baptiste and Sokolovska, Nataliya and Teytaud, Olivier and Bonnard, Nicolas}, + booktitle={International Conference on Learning and Intelligent Optimization}, + pages={433--445}, + year={2011}, + organization={Springer} +} + +@misc{mcts_wildfire, + title={A Comparison of {Monte Carlo} Tree Search and Mathematical Optimization for Large Scale Dynamic Resource Allocation}, + author={Dimitris Bertsimas and J. Daniel Griffith and Vishal Gupta and Mykel J. Kochenderfer and Velibor V. Mišić and Robert Moss}, + year={2014}, + eprint={1405.5498}, + archivePrefix={arXiv}, +} + +@article{julia, + title={Julia: A fresh approach to numerical computing}, + author={Bezanson, Jeff and Edelman, Alan and Karpinski, Stefan and Shah, Viral B}, + journal={SIAM Review}, + volume={59}, + number={1}, + pages={65--98}, + year={2017}, + publisher={SIAM} +} + +@article{arch_comp, + title={{ARCH-COMP} 2019 category report: falsification}, + author={Ernst, Gidon and Arcaini, Paolo and Donze, Alexandre and Fainekos, Georgios and Mathesen, Logan and Pedrielli, Giulia and Yaghoubi, Shakiba and Yamagata, Yoriyuki and Zhang, Zhenya}, + journal={EPiC Series in Computing}, + volume={61}, + pages={129--140}, + year={2019}, + publisher={EasyChair} +} + + +@article{pomdps_jl, + author = {Maxim Egorov and Zachary N. Sunberg and Edward Balaban and Tim A. Wheeler and Jayesh K. Gupta and Mykel J. Kochenderfer}, + title = {{POMDP}s.jl: A Framework for Sequential Decision Making under Uncertainty}, + journal = {Journal of Machine Learning Research}, + year = {2017}, + volume = {18}, + number = {26}, + pages = {1-5} +} + +@article{vincenty, + title={Direct and inverse solutions of geodesics on the ellipsoid with application of nested equations}, + author={Vincenty, Thaddeus}, + journal={Survey review}, + volume={23}, + number={176}, + pages={88--93}, + year={1975}, + publisher={Taylor \& Francis} +} + +@inproceedings{bayes_opt, + title={Generating adversarial driving scenarios in high-fidelity simulators}, + author={Abeysirigoonawardena, Yasasa and Shkurti, Florian and Dudek, Gregory}, + booktitle={International Conference on Robotics and Automation (ICRA)}, + pages={8271--8277}, + year={2019}, + organization={IEEE} +} + +@inproceedings{hill_climbing, + title={Multi-armed Bandits for Boolean Connectives in Hybrid System Falsification}, + author={Zhang, Zhenya and Hasuo, Ichiro and Arcaini, Paolo}, + booktitle={International Conference on Computer Aided Verification}, + pages={401--420}, + year={2019}, + organization={Springer} +} + +@article{rrts, + title={Rapidly-exploring random trees-based test generation for autonomous vehicles}, + author={Tuncali, Cumhur Erkan and Fainekos, Georgios}, + journal={arXiv preprint arXiv:1903.10629}, + year={2019} +} + +@inproceedings{bootstrap, + title={Analyzing neighborhoods of falsifying traces in cyber-physical systems}, + author={Diwakaran, Ram Das and Sankaranarayanan, Sriram and Trivedi, Ashutosh}, + booktitle={International Conference on Cyber-Physical Systems}, + pages={109--119}, + year={2017} +} + +@article{mc_limitations, + title={Improvements to and limitations of {Latin} hypercube sampling}, + author={Huntington, DE and Lyrintzis, CS}, + journal={Probabilistic engineering mechanics}, + volume={13}, + number={4}, + pages={245--253}, + year={1998}, + publisher={Elsevier} +} + +@misc{corso2020survey, + title={A Survey of Algorithms for Black-Box Safety Validation}, + author={Anthony Corso and Robert J. Moss and Mark Koren and Ritchie Lee and Mykel J. Kochenderfer}, + year={2020}, + eprint={2005.02979}, + archivePrefix={arXiv}, +} + +@misc{lee2018adaptive, + title={Adaptive Stress Testing: Finding Likely Failure Events with Reinforcement Learning}, + author={Ritchie Lee and Ole J. Mengshoel and Anshu Saksena and Ryan Gardner and Daniel Genin and Joshua Silbermann and Michael Owen and Mykel J. Kochenderfer}, + year={2018}, + eprint={1811.02188}, + archivePrefix={arXiv}, +} + +@article{silver2016mastering, + title={Mastering the game of {Go} with deep neural networks and tree search}, + author={Silver, David and Huang, Aja and Maddison, Chris J and Guez, Arthur and Sifre, Laurent and Van Den Driessche, George and Schrittwieser, Julian and Antonoglou, Ioannis and Panneershelvam, Veda and Lanctot, Marc and others}, + journal={Nature}, + volume={529}, + number={7587}, + pages={484--489}, + year={2016}, + publisher={Nature Publishing Group} +} + +@inproceedings{coulom2006efficient, + title={{Efficient selectivity and backup operators in Monte-Carlo tree search}}, + author={Coulom, R{\'e}mi}, + booktitle={International conference on computers and games}, + pages={72--83}, + year={2006}, + organization={Springer} +} + +@Book{dmubook, + author = {Mykel J. Kochenderfer}, + title = {Decision Making Under Uncertainty: Theory and Application}, + year = {2015}, + publisher = {MIT Press}, +} + +@article{rubinstein1999cross, + title={The cross-entropy method for combinatorial and continuous optimization}, + author={Rubinstein, Reuven}, + journal={Methodology and Computing in Applied Probability}, + volume={1}, + number={2}, + pages={127--190}, + year={1999}, + publisher={Springer} +} + + +@book{rubinstein2004cross, + title={The Cross-Entropy Method: A Unified Approach to Combinatorial Optimization, {Monte-Carlo} Simulation and Machine Learning}, + author={Rubinstein, Reuven Y and Kroese, Dirk P}, + year={2004}, + publisher={Springer} +} + +@article{ll_wildfire, + title={Automated dynamic resource allocation for wildfire suppression}, + author={Griffith, J. Daniel and Kochenderfer, Mykel J. and Moss, Robert J. and Mi{\v{s}}i{\'c}, Velibor V. and Gupta, Vishal and Bertsimas, Dimitris}, + journal={Lincoln Laboratory Journal}, + volume={22}, + number={2}, + year={2017} +} + +@book{sutton2018reinforcement, + title={Reinforcement learning: An introduction}, + author={Sutton, Richard S and Barto, Andrew G}, + year={2018}, + publisher={MIT Press} +} + +@inproceedings{chaslot2007progressive, + title={Progressive strategies for {Monte-Carlo} tree search}, + author={Chaslot, GMJB and Winands, Mark and Uiterwijk, JWHM and Van Den Herik, H and Bouzy, Bruno}, + booktitle={Joint Conference on Information Sciences (JCIS)}, + pages={655--661}, + year={2007} +} + +@article{abbas2013probabilistic, + title={Probabilistic temporal logic falsification of cyber-physical systems}, + author={Abbas, Houssam and Fainekos, Georgios and Sankaranarayanan, Sriram and Ivan{\v{c}}i{\'c}, Franjo and Gupta, Aarti}, + journal={ACM Transactions on Embedded Computing Systems (TECS)}, + volume={12}, + number={2s}, + pages={1--30}, + year={2013}, + publisher={ACM New York, NY, USA} +} + + +@inproceedings{aerts2018temporal, + title={Temporal logic falsification of cyber-physical systems: An input-signal-space optimization approach}, + author={Aerts, Arend and Minh, Bryan Tong and Mousavi, Mohammad Reza and Reniers, Michel A}, + booktitle={IEEE International Conference on Software Testing, Verification and Validation Workshops (ICSTW)}, + pages={214--223}, + year={2018}, + organization={IEEE} +} + + +@misc{do178c, + title={{Software Considerations in Airborne Systems and Equipment Certification}}, + author={RTCA}, + howpublished={DO-178C}, + month={12}, + year={2011} +} \ No newline at end of file diff --git a/references/pomdpstresstesting.bib b/references/pomdpstresstesting.bib new file mode 100644 index 0000000..65d00cd --- /dev/null +++ b/references/pomdpstresstesting.bib @@ -0,0 +1,158 @@ +@article{julia, + title={Julia: A fresh approach to numerical computing}, + author={Jeff Bezanson and Alan Edelman and Stefan Karpinski and Viral B. Shah}, + journal={{SIAM Review}}, + volume={59}, + number={1}, + pages={65--98}, + year={2017}, + publisher={SIAM}, + doi={10.1137/141000671} +} + + +@article{pomdps_jl, + author = {Maxim Egorov and Zachary N. Sunberg and Edward Balaban and Tim A. Wheeler and Jayesh K. Gupta and Mykel J. Kochenderfer}, + title = {{{POMDP}s.jl: A Framework for Sequential Decision Making under Uncertainty}}, + journal = {{Journal of Machine Learning Research}}, + year = {2017}, + volume = {18}, + number = {26}, + pages = {1-5} +} + +@incollection{ast, + title={{Adaptive Stress Testing of Safety-Critical Systems}}, + author={Ritchie Lee and Ole J. Mengshoel and Mykel J. Kochenderfer}, + booktitle={{Safe, Autonomous and Intelligent Vehicles}}, + pages={77--95}, + year={2019}, + publisher={Springer}, + doi={10.1007/978-3-319-97301-2_5} +} + +@INPROCEEDINGS{ast_acasx, +author={Ritchie Lee and Mykel J. Kochenderfer and Ole J. Mengshoel and Guillaume P. Brat and Michael P. Owen}, +booktitle={{IEEE/AIAA Digital Avionics Systems Conference (DASC)}}, +title={Adaptive stress testing of airborne collision avoidance systems}, +year={2015}, +volume={}, +number={}, +ISSN={2155-7209}, +month={9}, +doi={10.1109/DASC.2015.7311450} +} + + +@INPROCEEDINGS{ast_fms, +author={Robert J. Moss and Ritchie Lee and Nicholas Visser and Joachim Hochwarth and James G. Lopez and Mykel J. Kochenderfer}, +booktitle={{IEEE/AIAA Digital Avionics Systems Conference (DASC)}}, +title={{Adaptive Stress Testing of Trajectory Predictions in Flight Management Systems}}, +year={2020}, +volume={}, +number={}} + + +@INPROCEEDINGS{ast_av, +author={Mark Koren and Saud Alsaif and Ritchie Lee and Mykel J. Kochenderfer}, +booktitle={{IEEE Intelligent Vehicles Symposium (IV)}}, +title={{Adaptive Stress Testing for Autonomous Vehicles}}, +year={2018}, +volume={}, +number={}, +pages={1-7}, +ISSN={1931-0587}, +month={6}, +doi={10.1109/IVS.2018.8500400} +} + +@inproceedings{mcts, + title={{Efficient Selectivity and Backup Operators in Monte-Carlo Tree Search}}, + author={Coulom, R{\'e}mi}, + booktitle={{International Conference on Computers and Games}}, + pages={72--83}, + year={2006}, + organization={Springer}, + doi={10.1007/978-3-540-75538-8_7} +} + +@inproceedings{trpo, + title={{Trust Region Policy Optimization}}, + author={Schulman, John and Levine, Sergey and Abbeel, Pieter and Jordan, Michael and Moritz, Philipp}, + booktitle={{International Conference on Machine Learning}}, + pages={1889--1897}, + year={2015} +} + +@article{ppo, + title={{Proximal Policy Optimization Algorithms}}, + author={Schulman, John and Wolski, Filip and Dhariwal, Prafulla and Radford, Alec and Klimov, Oleg}, + journal={arXiv:1707.06347}, + year={2017} +} + +@article{cem, + title={{The Cross-Entropy Method for Combinatorial and Continuous Optimization}}, + author={Rubinstein, Reuven}, + journal={{Methodology and Computing in Applied Probability}}, + volume={1}, + number={2}, + pages={127--190}, + year={1999}, + publisher={Springer}, + doi={10.1023/A:1010091220143} +} + +@inproceedings{staliro, + title={{S-TaLiRo: A Tool for Temporal Logic Falsification for Hybrid Systems}}, + author={Annapureddy, Yashwanth and Liu, Che and Fainekos, Georgios and Sankaranarayanan, Sriram}, + booktitle={{Tools and Algorithms for the Construction and Analysis of Systems (TACAS)}}, + pages={254--257}, + year={2011}, + organization={Springer}, + doi={10.1007/978-3-642-19835-9_21} +} + +@inproceedings{breach, + title={{Breach, A Toolbox for Verification and Parameter Synthesis of Hybrid Systems}}, + author={Donz\'{e}, Alexandre}, + booktitle={{Computer Aided Verification}}, + pages={167--170}, + year={2010}, + organization={Springer}, + doi={10.1007/978-3-642-14295-6_17} +} + +@article{falstar, + title={{Two-Layered Falsification of Hybrid Systems Guided by {M}onte {C}arlo Tree Search}}, + author={Zhang, Zhenya and Ernst, Gidon and Sedwards, Sean and Arcaini, Paolo and Hasuo, Ichiro}, + journal={{IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems}}, + volume={37}, + number={11}, + pages={2894--2905}, + year={2018}, + publisher={IEEE}, + doi={10.1109/TCAD.2018.2858463} +} + +@article{gym, + title={{OpenAI} gym}, + author={Brockman, Greg and Cheung, Vicki and Pettersson, Ludwig and Schneider, Jonas and Schulman, John and Tang, Jie and Zaremba, Wojciech}, + journal={arXiv:1606.01540}, + year={2016} +} + +@misc{do178c, + title={{Software Considerations in Airborne Systems and Equipment Certification}}, + author={RTCA}, + howpublished={DO-178C}, + month={12}, + year={2011} +} + +@article{gym, + title={{OpenAI} gym}, + author={Brockman, Greg and Cheung, Vicki and Pettersson, Ludwig and Schneider, Jonas and Schulman, John and Tang, Jie and Zaremba, Wojciech}, + journal={arXiv:1606.01540}, + year={2016} +} \ No newline at end of file diff --git a/references/weakness_rec.bib b/references/weakness_rec.bib new file mode 100644 index 0000000..5e7f66b --- /dev/null +++ b/references/weakness_rec.bib @@ -0,0 +1,1649 @@ +@String { aaai = {AAAI Conference on Artificial Intelligence (AAAI)} } +@String { aamas = {International Conference on Autonomous Agents and Multiagent Systems (AAMAS)} } +@String { acc = {American Control Conference (ACC)} } +@String { aiaa_info = {AIAA Infotech@Aerospace Conference} } +@String { aiaa_is = {AIAA Scitech Intelligent Systems Conference (IS)} } +@String { aiaa_jacic = {Journal of Aerospace Computing, Information, and Communication} } +@String { allerton = {Allerton Conference on Communication, Control, and Compution} } +@String { atio = {AIAA Aviation Technology, Integration, and Operations Conference (ATIO)} } +@String { cacm = {Communications of the ACM} } +@String { cav = {International Conference on Computer Aided Verification (CAV)} } +@String { cdc = {IEEE Conference on Decision and Control (CDC)} } +@String { cvpr = {IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR)} } +@String { dasc = {Digital Avionics Systems Conference (DASC)} } +@String { ecml = {European Conference on Machine Learning (ECML)} } +@String { fm = {International Symposium on Formal Methods (FM)} } +@String { gnc = {AIAA Guidance, Navigation, and Control Conference (GNC)} } +@String { hscc = {ACM International Conference on Hybrid Systems: Computation and Control (HSCC)} } +@String { icaart = {International Conference on Agents and Artificial Intelligence (ICAART)} } +@String { icaps = {International Conference on Automated Planning and Scheduling (ICAPS)} } +@String { icassp = {International Conference on Acoustics, Speech, and Signal Processing (ICASSP)} } +@String { iccps = {International 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{Conference on Uncertainty in Artificial Intelligence (UAI)} } +@String {arxiv = {arXiv} } + + +@inproceedings{yaghoubi2019gray, + title={Gray-box adversarial testing for control systems with machine learning components}, + author={Yaghoubi, Shakiba and Fainekos, Georgios}, + booktitle=hscc, + pages={179--184}, + year={2019} +} + +@article{fainekos2009robustness, + title={Robustness of temporal logic specifications for continuous-time signals}, + author={Fainekos, Georgios E and Pappas, George J}, + journal={Theoretical Computer Science}, + volume={410}, + number={42}, + pages={4262--4291}, + year={2009}, + publisher={Elsevier} +} + +@inproceedings{tuncali2019rapidly, + author={C. E. {Tuncali} and G. {Fainekos}}, + booktitle={IEEE Intelligent Transportation Systems Conference (ITSC)}, + title={Rapidly-exploring Random Trees for Testing Automated Vehicles}, + year={2019}, + volume={}, + number={}, + pages={661-666} +} + +@article{suykens1999least, + title={Least squares support vector machine classifiers}, + author={Suykens, Johan AK and Vandewalle, Joos}, + journal={Neural Processing Letters}, + volume={9}, + number={3}, + pages={293--300}, + year={1999}, + publisher={Springer} +} + +@article{julian2020validation, + title={Validation of Image-Based Neural Network Controllers through Adaptive Stress Testing}, + author={Julian, Kyle D and Lee, Ritchie and Kochenderfer, Mykel J}, + journal=arxiv, + number={2003.02381}, + year={2020} +} + +@article{hochreiter1997long, + title={Long short-term memory}, + author={Hochreiter, Sepp and Schmidhuber, J{\"u}rgen}, + journal={Neural Computation}, + volume={9}, + number={8}, + pages={1735--1780}, + year={1997}, + publisher={MIT Press} +} + +@book{sutton2018reinforcement, + title={Reinforcement Learning: An Introduction}, + author={Sutton, Richard S and Barto, Andrew G}, + year={2018}, + publisher={MIT press} +} + +@book{lavalle2006planning, + title={Planning Algorithms}, + author={LaValle, Steven M}, + year={2006}, + publisher={Cambridge University Press} +} + +@inproceedings{deshmukh2015stochastic, + title={Stochastic local search for falsification of hybrid systems}, + author={Deshmukh, Jyotirmoy and Jin, Xiaoqing and Kapinski, James and Maler, Oded}, + booktitle={International Symposium on Automated Technology for Verification and Analysis (ATVA)}, + pages={500--517}, + year={2015}, + organization={Springer} +} + + +@inproceedings{wicker2018feature, + title={Feature-guided black-box safety testing of deep neural networks}, + author={Wicker, Matthew and Huang, Xiaowei and Kwiatkowska, Marta}, + booktitle=tacas, + pages={408--426}, + year={2018}, + organization={Springer} +} + +@article{plaku2009hybrid, + title={Hybrid systems: from verification to falsification by combining motion planning and discrete search}, + author={Plaku, Erion and Kavraki, Lydia E and Vardi, Moshe Y}, + journal={Formal Methods in System Design}, + volume={34}, + number={2}, + pages={157--182}, + year={2009}, + publisher={Springer} +} + +@book{mockus2012bayesian, + title={Bayesian Approach to Global Optimization: Theory and Applications}, + author={Mockus, Jonas}, + volume={37}, + year={2012}, + publisher={Springer Science \& Business Media} +} + +@inproceedings{adimoolam2017classification, + title={Classification and coverage-based falsification for embedded control systems}, + author={Adimoolam, Arvind and Dang, Thao and Donz{\'e}, Alexandre and Kapinski, James and Jin, Xiaoqing}, + booktitle=cav, + pages={483--503}, + year={2017}, + organization={Springer} +} + +@inproceedings{Mathesen2019falsification, +title = "Falsification of cyber-physical systems with robustness uncertainty quantification through stochastic optimization with adaptive restart", +author = "Logan Mathesen and Shakiba Yaghoubi and Giulia Pedrielli and Georgios Fainekos", +year = "2019", +month = "8", +doi = "10.1109/COASE.2019.8843005", +language = "English (US)", +publisher = "IEEE Computer Society", +pages = "991--997", +booktitle = "International Conference on Automation Science and Engineering (CASE)", +} + +@inproceedings{Balakrishnan2019specifying, +title = "Specifying and Evaluating Quality Metrics for Vision-based Perception Systems", +author = "Anand Balakrishnan and Puranic, {Aniruddh G.} and Xin Qin and Adel Dokhanchi and Deshmukh, {Jyotirmoy V.} and {Ben Amor}, Hani and Georgios Fainekos", +year = "2019", +month = "5", +day = "14", +doi = "10.23919/DATE.2019.8715114", +language = "English (US)", +publisher = "Institute of Electrical and Electronics Engineers Inc.", +pages = "1433--1438", +booktitle = "Design, Automation and Test in Europe Conference and Exhibition (DATE)", +} + 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+@book{baier2008principles, + title={Principles of Model Checking}, + author={Baier, Christel and Katoen, Joost-Pieter}, + year={2008}, + publisher={MIT Press} +} + +@book{kochenderfer2019algorithms, + title={Algorithms for Optimization}, + author={Kochenderfer, Mykel J and Wheeler, Tim A}, + year={2019}, + publisher={MIT Press} +} + +@article{corso2020scalable, + title={Scalable Autonomous Vehicle Safety Validation through Dynamic Programming and Scene Decomposition}, + author={Corso, Anthony and Lee, Ritchie and Kochenderfer, Mykel J}, + journal=arxiv, + number={2004.06801} +} + +@article{corso2020interpretable, + title={Interpretable Safety Validation for Autonomous Vehicles}, + author={Corso, Anthony and Kochenderfer, Mykel J}, + journal=arxiv, + number={2004.06805}, + year={2020} +} + +@article{koren2020adaptive, + title={Adaptive Stress Testing without Domain Heuristics using Go-Explore}, + author={Koren, Mark and Kochenderfer, Mykel J}, + journal=arxiv, + number={2004.04292}, + year={2020} +} + +@article{hahn1972sample, + title={Sample sizes for {M}onte {C}arlo simulation}, + author={Hahn, GJ}, + year={1972}, + journal={IEEE Transactions on Systems, Man, and Cybernetics}, +} + +@book{Clarke2018, + author= {Edmund M. Clarke and Thomas A. Henzinger and Helmut Veith and Roderick Bloem}, + title={Handbook of Model Checking}, + publisher = {Springer}, + year= {2018} +} + +@article{Mnih2013, + title={Playing {A}tari with deep reinforcement learning}, + author={Mnih, Volodymyr and Kavukcuoglu, Koray and Silver, David and Graves, Alex and Antonoglou, Ioannis and Wierstra, Daan and Riedmiller, Martin}, + journal=arxiv, + number={1312.5602}, + Year= {2013} +} + +@Article{Silver2017, + title={Mastering the Game of {G}o without Human Knowledge}, + author={Silver, David and Schrittwieser, Julian and Simonyan, Karen and Antonoglou, Ioannis and Huang, Aja and Guez, Arthur and Hubert, Thomas and Baker, Lucas and Lai, Matthew and Bolton, Adrian and others}, + journal={Nature}, + volume={550}, + number={7676}, + pages={354}, + year={2017}, + publisher={Nature Publishing Group} +} + +@Article{Silver2016, + title={Mastering the Game of {G}o with Deep Neural Networks and Tree Search}, + author={Silver, David and Huang, Aja and Maddison, Chris J and Guez, Arthur and Sifre, Laurent and Van Den Driessche, George and Schrittwieser, Julian and Antonoglou, Ioannis and Panneershelvam, Veda and Lanctot, Marc and others}, + journal={Nature}, + volume={529}, + number={7587}, + pages={484--489}, + year={2016}, + publisher={Nature Research} +} + +@Book{dmubook, + author = {Mykel J. Kochenderfer}, + title = {Decision Making Under Uncertainty: Theory and Application}, + year = {2015}, + publisher = {MIT Press}, +} + +@inproceedings{He2017, + title={Mask {R-CNN}}, + author={He, Kaiming and Gkioxari, Georgia and Doll{\'a}r, Piotr and Girshick, Ross}, + booktitle={International Conference on Computer Vision (ICCV)}, + organization={IEEE}, + pages={2961--2969}, + year={2017} +} + +@inproceedings{Higgins2017, + title={Beta-{VAE}: Learning Basic Visual Concepts with a Constrained Variational Framework}, + author={Higgins, Irina and Matthey, Loic and Pal, Arka and Burgess, Christopher and Glorot, Xavier and Botvinick, Matthew and Mohamed, Shakir and Lerchner, Alexander}, + booktitle=iclr, + volume={3}, + year={2017} +} + +@Article{Kochenderfer2012next, + author = {Kochenderfer, Mykel J and Holland, Jessica E and Chryssanthacopoulos, James P}, + title = {Next-Generation Airborne Collision Avoidance System}, + year = {2012}, + volume = {19}, + number = {1}, + pages = {17--33}, + journal = {Lincoln Laboratory Journal}, + publisher = {{MIT} {L}incoln {L}aboratory}, +} + +@Article{LeCun2015, + author = {LeCun, Yann and Bengio, Yoshua and Hinton, Geoffrey}, + title = {Deep Learning}, + year = {2015}, + volume = {521}, + number = {7553}, + pages = {436--444}, + journal = {Nature}, + publisher = {Nature Research}, +} + +@Book{Bishop2007, + Title={Pattern Recognition and Machine Learning}, + Author={Christopher M. Bishop}, + Publisher={Springer}, + Year={2006}, + Address={New York}, + ISBN={0387310738}, +} + +@Book{Russell2020, + Title={Artificial Intelligence: A Modern Approach}, + Author={Stuart Russell and Peter Norvig}, + Publisher={Prentice Hall}, + Year={2020}, + Edition= {4} +} + +@book{Sutton2018, + title={Reinforcement Learning: An Introduction}, + author={Sutton, Richard S and Barto, Andrew G}, + year={2018}, + publisher={MIT {P}ress} +} + +@inproceedings{Pillai2019, + title={Superdepth: Self-Supervised, Super-Resolved Monocular Depth Estimation}, + author={Pillai, Sudeep and Ambru{\c{s}}, Rare{\c{s}} and Gaidon, Adrien}, + booktitle=icra, + pages={9250--9256}, + year={2019}, + organization={IEEE} +} + +@article{Vinyals2019, + title={Grandmaster Level in StarCraft II using Multi-Agent Reinforcement Learning}, + author={Vinyals, Oriol and Babuschkin, Igor and Czarnecki, Wojciech M and Mathieu, Micha{\"e}l and Dudzik, Andrew and Chung, Junyoung and Choi, David H and Powell, Richard and Ewalds, Timo and Georgiev, Petko and others}, + journal={Nature}, + volume={575}, + number={7782}, + pages={350--354}, + year={2019}, + publisher={Nature Publishing Group} +} + + +@techreport{reactis2013, + title={{Testing and Validation of Simulink Models with Reactis}}, + institution={Reactive Systems Inc.}, + number={RSITR 1.11}, + month={10}, + year=2013 +} + +@techreport{reactis2011, + title={{Finding Bugs in C Programs with Reactis for C}}, + institution={Reactive Systems Inc.}, + number={RSITR 2.5}, + month={8}, + year=2011 +} + +@inproceedings{Platzer2008, + title={{KeYmaera}: A Hybrid Theorem Prover for Hybrid Systems (System Description)}, + author={Platzer, Andr{\'e} and Quesel, Jan-David}, + booktitle={International Joint Conference on Automated Reasoning (IJCAR)}, + pages={171--178}, + year={2008}, + organization={Springer} +} + +@book{Fitting2012, + title={First-Order Logic and Automated Theorem Proving}, + author={Fitting, Melvin}, + year={2012}, + publisher={Springer Science \& Business Media} +} + +@book{Schumann2001, + title={Automated Theorem Proving in Software Engineering}, + author={Schumann, Johann M}, + year={2001}, + publisher={Springer Science \& Business Media} +} + +@inproceedings{Katoen2016, + title={The Probabilistic Model Checking Landscape}, + author={Katoen, Joost-Pieter}, + booktitle={ACM/IEEE Symposium on Logic in Computer Science (LICS)}, + pages={31--45}, + year={2016}, + organization={ACM} +} + +@inproceedings{leitner2008simulink, + title={Simulink Design Verifier vs. SPIN: a comparative case study}, + author={Leitner-Fischer, Florian and Leue, Stefan}, + year={2008}, + booktitle={International Conference on Formal Methods for Industrial Critical Systems (FMICS)} +} + +@inproceedings{Lee2019a, + author={Lee, Ritchie and Mengshoel, Ole J. and Agogino, Adrian K. and Giannakopoulou, Dimitra and Kochenderfer, Mykel J.}, + title={Adaptive Stress Testing of Trajectory Planning Systems}, + booktitle=aiaa_is, + year={2019}, + organization={aiaa}, +} + +@techreport{DOT2018preparing, +title = {Automated Vehicles 3.0: Preparing for the Future of Transportation}, +institution={{U.S.} {D}epartment of {T}ransportation}, +year = {2018} +} + +@techreport{FAA2019forecast, +title = {{FAA} Aerospace Forecast Fiscal Years 2020--2040}, +institution={{F}ederal {A}viation {A}dministration}, +year = {2019} +} + +@inproceedings{annapureddy2011staliro, + title={{S-TaLiRo: A Tool for Temporal Logic Falsification for Hybrid Systems}}, + author={Annapureddy, Yashwanth and Liu, Che and Fainekos, Georgios and Sankaranarayanan, Sriram}, + booktitle=tacas, + pages={254--257}, + year={2011}, + organization={Springer} +} + +@article{ecoffet2019go, + title={Go-explore: a new approach for hard-exploration problems}, + author={Ecoffet, Adrien and Huizinga, Joost and Lehman, Joel and Stanley, Kenneth O and Clune, Jeff}, + journal=arxiv, + number={1901.10995}, + year={2019} +} + +@article{salimans2018learning, + title={Learning 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title={Tatar: Testweaver-a tool for simulation-based test of mechatronic designs}, + author={Junghanns, Andreas and Mauss, Jakob and Tatar, Mugur}, + booktitle={International Modelica Conference}, + year={2008}, + organization={Citeseer} +} + +@inproceedings{jin2014powertrain, + title={Powertrain control verification benchmark}, + author={Jin, Xiaoqing and Deshmukh, Jyotirmoy V and Kapinski, James and Ueda, Koichi and Butts, Ken}, + booktitle=hscc, + pages={253--262}, + year={2014} +} + +@inproceedings{schuler2016hybrid, + title={Hybrid modelling of a wind turbine (benchmark proposal)}, + author={Schuler, Simone and Adegas, Fabiano Daher and Anta, Adolfo}, + booktitle = {International Workshop on Applied Verification for Continuous and Hybrid Systems (ARCH)}, + editor = {Goran Frehse and Matthias Althoff}, + series = {{EPiC} Series in Computing}, + volume = {43}, + pages = {18--26}, + year = {2017}, +} + +@article{koren2020formulation, + title={The Adaptive Stress Testing Formulation}, + author={Koren, Mark and Corso, Anthony and Kochenderfer, Mykel J}, + journal=arxiv, + number={2004.04293}, + year={2020} +} + +@inproceedings{fehnker2004benchmarks, +title={Benchmarks for hybrid systems verification}, +author={Fehnker, Ansgar and Ivan{\v{c}}i{\'c}, Franjo}, +booktitle={International Workshop on Hybrid Systems: Computation and Control (HSCC)}, +pages={326--341}, +year={2004}, +organization={Springer} +} + +@inproceedings{hu2000towards, + title={Towards a theory of stochastic hybrid systems}, + author={Hu, Jianghai and Lygeros, John and Sastry, Shankar}, + booktitle={International Workshop on Hybrid Systems: Computation and Control (HSCC)}, + pages={160--173}, + year={2000}, + organization={Springer} +} + +@article{balkan2017underminer, + title={Underminer: A framework for automatically identifying nonconverging behaviors in black-box system models}, + author={Balkan, Ayca and Tabuada, Paulo and Deshmukh, Jyotirmoy V and Jin, Xiaoqing and Kapinski, James}, + journal={ACM Transactions on Embedded Computing Systems (TECS)}, + volume={17}, + number={1}, + pages={1--28}, + year={2017}, + publisher={ACM New York, NY, USA} +} + +@InProceedings{pnueli1977temporal, + Title = {The temporal logic of programs}, + Author = {Pnueli, Amir}, + Booktitle = {Foundations of Computer Science, 1977}, + Year = {1977}, + Organization = {IEEE}, + Pages = {46--57}, +} + +@article{kapinski2016simulation, + author={J. {Kapinski} and J. V. {Deshmukh} and X. {Jin} and H. {Ito} and K. {Butts}}, + journal={IEEE Control Systems Magazine}, + title={Simulation-Based Approaches for Verification of Embedded Control Systems: An Overview of Traditional and Advanced Modeling, Testing, and Verification Techniques}, + year={2016}, + volume={36}, + number={6}, + pages={45-64},} + +@article{koymans1990specifying, + title={Specifying real-time properties with metric temporal logic}, + author={Koymans, Ron}, + journal={Real-Time Systems}, + volume={2}, + pages={255--299}, + year={1990} +} + +@inproceedings{clarke1981design, + title={Design and synthesis of synchronization skeletons using branching time temporal logic}, + author={Clarke, Edmund M and Emerson, E Allen}, + booktitle={Workshop on Logic of Programs}, + pages={52--71}, + year={1981}, + organization={Springer} +} + + +@inproceedings{abbas2017relaxed, + title={Relaxed decidability and the robust semantics of metric temporal logic}, + author={Abbas, Houssam and O'Kelly, Matthew and Mangharam, Rahul}, + booktitle={Proceedings of the 20th International Conference on Hybrid Systems: Computation and Control}, + pages={217--225}, + year={2017} +} + +@inproceedings{kress2008automatically, + title={Automatically synthesizing a planning and control subsystem for the DARPA Urban Challenge}, + author={Kress-Gazit, Hadas and Pappas, George J}, + booktitle={International Conference on Automation Science and Engineering (CASE)}, + pages={766--771}, + year={2008}, + organization={IEEE}, + publisher = {IEEE Computer Society}, +} + +@article{hekmatnejad2020search, + title={Search-based Test-Case Generation by Monitoring Responsibility Safety Rules}, + author={Hekmatnejad, Mohammad and Hoxha, Bardh and Fainekos, Georgios}, + journal={arXiv preprint arXiv:2005.00326}, + year={2020} +} + +@inproceedings{lee2018interpretable, + title={Interpretable categorization of heterogeneous time series data}, + author={Lee, Ritchie and Kochenderfer, Mykel J and Mengshoel, Ole J and Silbermann, Joshua}, + booktitle={Proceedings of the 2018 SIAM International Conference on Data Mining}, + pages={216--224}, + year={2018}, + organization={SIAM} +} + +@misc{lee2018adaptive, + title={Adaptive Stress Testing: Finding Likely Failure Events with Reinforcement Learning}, + author={Ritchie Lee and Ole J. Mengshoel and Anshu Saksena and Ryan Gardner and Daniel Genin and Joshua Silbermann and Michael Owen and Mykel J. Kochenderfer}, + year={2018}, + eprint={1811.02188}, + archivePrefix={arXiv}, +} + +@misc{corso2020survey, + title={A Survey of Algorithms for Black-Box Safety Validation}, + author={Anthony Corso and Robert J. Moss and Mark Koren and Ritchie Lee and Mykel J. Kochenderfer}, + year={2020}, + eprint={2005.02979}, + archivePrefix={arXiv} +} + +@article{huang2005sampling, + title={Sampling for {Bayesian} computation with large datasets}, + author={Huang, Zaijing and Gelman, Andrew}, + journal={Available at SSRN 1010107}, + year={2005} +} + + +@article{ferrari2013handling, + title={Handling large datasets of hyperspectral images: Reducing data size without loss of useful information}, + author={Ferrari, Carlotta and Foca, Giorgia and Ulrici, Alessandro}, + journal={Analytica chimica acta}, + volume={802}, + pages={29--39}, + year={2013}, + publisher={Elsevier} +} + + +@inproceedings{chatzilygeroudis2017black, + title={Black-box data-efficient policy search for robotics}, + author={Chatzilygeroudis, Konstantinos and Rama, Roberto and Kaushik, Rituraj and Goepp, Dorian and Vassiliades, Vassilis and Mouret, Jean-Baptiste}, + booktitle={IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS)}, + pages={51--58}, + year={2017}, + organization={IEEE} +} + +@article{wehrens2004model, + title={Model-based clustering for image segmentation and large datasets via sampling}, + author={Wehrens, Ron and Buydens, Lutgarde MC and Fraley, Chris and Raftery, Adrian E}, + journal={Journal of Classification}, + volume={21}, + number={2}, + pages={231--253}, + year={2004}, + publisher={Springer} +} + +@article{ganin2016domain, + title={Domain-Adversarial Training of Neural Networks}, + author={Ganin, Yaroslav and Ustinova, Evgeniya and Ajakan, Hana and Germain, Pascal and Larochelle, Hugo and Laviolette, Fran{\c{c}}ois and Marchand, Mario and Lempitsky, Victor}, + journal={The Journal of Machine Learning Research}, + volume={17}, + number={1}, + pages={2096--2030}, + year={2016}, + publisher={JMLR. org} +} + +@inproceedings{hinton1994autoencoders, + title={Autoencoders, minimum description length and Helmholtz free energy}, + author={Hinton, Geoffrey E and Zemel, Richard S}, + booktitle={Advances in neural information processing systems}, + pages={3--10}, + year={1994} +} + +@article{lecun2010mnist, + title={{MNIST} handwritten digit database}, + author={LeCun, Yann and Cortes, Corinna and Burges, CJ}, + journal={ATT Labs [Online]. Available: http://yann.lecun.com/exdb/mnist}, + volume={2}, + year={2010} +} + +@inproceedings{srivastava2015unsupervised, + title={Unsupervised learning of video representations using lstms}, + author={Srivastava, Nitish and Mansimov, Elman and Salakhudinov, Ruslan}, + booktitle={International conference on machine learning}, + pages={843--852}, + year={2015} +} + + +@article{cohen2017emnist, + author = {Gregory Cohen and + Saeed Afshar and + Jonathan Tapson and + Andr{\'{e}} van Schaik}, + title = {{EMNIST:} an extension of {MNIST} to handwritten letters}, + journal = {CoRR}, + volume = {abs/1702.05373}, + year = {2017}, + archivePrefix = {arXiv}, + eprint = {1702.05373}, + timestamp = {Mon, 13 Aug 2018 16:48:00 +0200}, + biburl = {https://dblp.org/rec/journals/corr/CohenATS17.bib}, + bibsource = {dblp computer science bibliography, https://dblp.org} +} + + +@article{treiber2000idm, + title={Congested traffic states in empirical observations and microscopic simulations}, + volume={62}, + ISSN={1095-3787}, + url={http://dx.doi.org/10.1103/PhysRevE.62.1805}, + DOI={10.1103/physreve.62.1805}, + number={2}, + journal={Physical Review E}, + publisher={American Physical Society (APS)}, + author={Treiber, Martin and Hennecke, Ansgar and Helbing, Dirk}, + year={2000}, + month={Aug}, + pages={1805–1824} +} + +@misc{sun2019scalability, + title={Scalability in Perception for Autonomous Driving: Waymo Open Dataset}, + author={Pei Sun and Henrik Kretzschmar and Xerxes Dotiwalla and Aurelien Chouard and Vijaysai Patnaik and Paul Tsui and James Guo and Yin Zhou and Yuning Chai and Benjamin Caine and Vijay Vasudevan and Wei Han and Jiquan Ngiam and Hang Zhao and Aleksei Timofeev and Scott Ettinger and Maxim Krivokon and Amy Gao and Aditya Joshi and Yu Zhang and Jonathon Shlens and Zhifeng Chen and Dragomir Anguelov}, + year={2019}, + eprint={1912.04838}, + archivePrefix={arXiv}, + primaryClass={cs.CV} +} + +@misc{lyft2020, title = {One Thousand and One Hours: Self-driving Motion Prediction Dataset}, author = {Houston, J. and Zuidhof, G. and Bergamini, L. and Ye, Y. and Jain, A. and Omari, S. and Iglovikov, V. and Ondruska, P.}, year = {2020}, howpublished = {\url{https://level5.lyft.com/dataset/}} } + +@article{patraucean2015spatio, + title={Spatio-Temporal Video Autoencoder with Differentiable Memory}, + author={Patraucean, Viorica and Handa, Ankur and Cipolla, Roberto}, + journal={arXiv:1511.06309}, + year={2015} +} + +@article{salzmann2020trajectron++, + title={Trajectron++: Dynamically-Feasible Trajectory Forecasting With Heterogeneous Data}, + author={Salzmann, Tim and Ivanovic, Boris and Chakravarty, Punarjay and Pavone, Marco}, + journal={arXiv:2001.03093}, + year={2020} +} + +@mastersthesis{Krizhevsky09learningmultiple, + author = {Alex Krizhevsky}, + title = {Learning multiple layers of features from tiny images}, + school = {University of Toronto}, + year = {2009} +} + +@article{Flux.jl-2018, + author = {Michael Innes and + Elliot Saba and + Keno Fischer and + Dhairya Gandhi and + Marco Concetto Rudilosso and + Neethu Mariya Joy and + Tejan Karmali and + Avik Pal and + Viral Shah}, + title = {Fashionable Modelling with {Flux}}, + journal = {CoRR}, + volume = {abs/1811.01457}, + year = {2018}, + archivePrefix = {arXiv}, + eprint = {1811.01457}, + timestamp = {Thu, 22 Nov 2018 17:58:30 +0100}, + biburl = {https://dblp.org/rec/bib/journals/corr/abs-1811-01457}, + bibsource = {dblp computer science bibliography, https://dblp.org} +} + +@article{moss2020adaptive, + title={Adaptive Stress Testing of Trajectory Predictions in Flight Management Systems}, + author={Robert J. Moss and Ritchie Lee and Nicholas Visser and Joachim Hochwarth and James G. Lopez and Mykel J. Kochenderfer}, + year={2020}, + journal=dasc +} + +@misc{kingma2017adam, + title={Adam: A Method for Stochastic Optimization}, + author={Diederik P. Kingma and Jimmy Ba}, + year={2017}, + eprint={1412.6980}, + archivePrefix={arXiv}, + primaryClass={cs.LG} +} + +@article{kramer1991nonlinear, + title={Nonlinear principal component analysis using autoassociative neural networks}, + author={Kramer, Mark A}, + journal={AIChE journal}, + volume={37}, + number={2}, + pages={233--243}, + year={1991}, + publisher={Wiley Online Library} +} \ No newline at end of file diff --git a/suthesis-ms-2e.sty b/suthesis-ms-2e.sty new file mode 100644 index 0000000..caff7a7 --- /dev/null +++ b/suthesis-ms-2e.sty @@ -0,0 +1,572 @@ +% Stanford University PhD thesis style -- modifications to the report style +% This is unofficial so you should always double check against the +% Registrar's office rules +% +% People are free to borrow as long as they change the name and date +% in the \typeout lines, the name of the file, and acknowledge the +% work that has been done by previous people. Ideally they should +% comment their changes. + +% Original version by Joseph Pallas back in 1989 +% Modified by Emma Pease 5/7/92 +% added singlespace environment from doublespace.sty +% added switches for variant title pages +% modified the figure environment according to changes in latex.tex +% corrected the signature page due to University rule changes +% added an optional third reader to signature page +% Corrected a spacing problem with style changes 5/14/92 - Emma +% Modified by Emma Pease 1/10/95 +% Modified for latex2e 5/17/95 +% changed \@xfloat and \@footnotetext to reflect latex2e changes +% Modified for latex2e 6/22/95 (Emma Pease) +% changed singlespace environment so it would work (taken from doublespace.sty) +% Modified 9/8/95 (Emma Pease) +% removed doublespace.sty commands and explicitely inputted +% doublespace +% Modified 12/17/96 (Emma Pease) +% added optional \coprincipaladvisor (\coprincipaladviser) +% Modified 5/29/98 +% replaced the required doublespace.sty by setspace.sty +% Modified 8/21/98 +% added a \businessthesis for the school of business +% Modified 8/22/98 +% added a \lawthesis +% Modified 8/23/98 +% spelling error in \businessthesis def corrected +% Modified 5/14/1999 by Emma Pease +% 'By' dropped from title page +% Modified 7/26/1999 by Emma Pease +% copyright page fixed +% Modified 9/28/99 by Emma Pease +% more copyright page fixings +% Modified 10/28/99 by Emma Pease +% and more copyright page fixings plus a minor mod on bibliography +% need to start thinking of overhauling to standard package format +% Modified 11/26/99 +% fixed copyrightyear so that all Fall quarter theses are next +% year's copyright + +% Modified 5/31/01 by Emma Pease +% fixed certification statement. Setup for twoside option. +% Modified 6/4/01 by Emma Pease +% emphasized that it is unofficial +% Modified 8/3/01 by Emma Pease +% setup so that on twoside if the intro material (page numbered with +% roman numerals) ends on an odd page an extra blank page is included so +% the main body (page numbered with arabic numbers) starts on an odd +% absolute page (explanation modified 5/28/02) +% Modified 5/28/02 by Emma Pease +% made first and second reader optional (not that the first reader +% should ever be missing but someone managed to avoid a second reader) +% If they aren't defined, they won't appear +% Modified 7/13/2003 by Emma Pease +% dropped signature line for ``Approved for the University Committee +% on Graduate Studies'' on signature page. Also made sure the next +% section starts on an odd page if two sided. +% Modified 11/19/03 by Emma Pease +% fixed the bibliography so the addcontentsline works correctly with +% hyperref. Thanks to Peter Sturdza for pointing out this +% Modified 2/14/04 by Emma Pease +% Changed documentation on how to change line spacing +% Modified 6/29/04 by Emma Pease +% Correction to humanitiesthesis definition + +% Modified 11/9/2004 by Emma Pease +% Reformatted Signature Page to fit requirements +% Reformatted Title page to fit requirements + +% Modified 8/26/2005 by Emma Pease +% Modified \language to \languagemajor so as not to interfere with +% babel. + +% Modifed 10/31/2005 by Emma Pease +% added an optional fourth reader to signature page (Biology) +% added a length \signaturespace + +% Modified 8/23/2006 by Emma Pease +% added () around names on signature page + +% Modified 5/7/2007 by Emma Pease +% redefined \@endpart so that blank page after part has page number +% as per thesis office requirements + +% Modified 9/17/2008 by Emma Pease +% changed copyright year calculations so September theses are summer + +% November 2009 by Emma Pease +% changing to use online or hardcopy options for the new online +% submission possibility. + +% Modified May 2010 by Emma Pease +% added command \onlinesignature which creates a signatue page +% for the online version. This should be the last command before the +% \end{document} + +% Modified May 2014 by Emma Pease +% fixed error in the signature page (Stanford University Committee not just University Committee) + +% Modified Feb 2021 by Robert Moss +% modified for master of science degree (renamed to suthesis-ms-2e.sty) +% changed "dissertation" to "thesis" +% removed "committee of graduate studies" mentions + +%%%%% +%%%%% PRELIMS +%%%%% + +\ProvidesPackage{suthesis-ms-2e}[2014/05/26] + + + +%%\typeout{Document Style Option `suthesis' for latex2e <$Date: 9/17/2008 $>.} +\typeout{Note that this tries to fulfill the Stanford Thesis + requirements but it is unofficial} + +% First thing we do is make sure that report has been loaded. A +% common error is to try to use suthesis as a documentstyle. +\@ifundefined{chapter}{\@latexerr{The `suthesis' option should be used +with the `report' document style}{You should probably read the +suthesis documentation.}}{} + +%%%%% +%%%%% SETUP DOUBLESPACING +%%%%% + +% include doublespace.sty for some of the stuff below + +\RequirePackage{setspace} + +% default to hardcopy submission +\newif\ifonline +\onlinefalse +\DeclareOption{online}{\onlinetrue} +\DeclareOption{hardcopy}{\onlinefalse} +\ProcessOptions + + +% Use 1.3 times the normal baseline-to-baseline skip +\setstretch{1.3} + + +%%%%% +%%%%% DOCUMENTATION +%%%%% + +\long\def\comment#1{} +\comment{ + + Example of use: + \documentclass{report} + +\usepackage{suthesis-2e} +\dept{Computer Science} + + + \begin{document} + \title{How to Write Theses\\ + With Two Line Titles} + \author{John Henry Candidate} + \principaladviser{John Parker} + \firstreader{John Green} + \secondreader{John BigBooty} + \thirdreader{Jane Supernumerary} %if needed + \fourthreader{Severus Snape} %if needed + + \beforepreface + \prefacesection{Preface} + This thesis tells you all you need to know about... + \prefacesection{Acknowledgments} + I would like to thank... + \afterpreface + + \chapter{Introduction} + ... + \chapter{Conclusions} + ... + \appendix + \chapter{A Long Proof} + ... + \bibliographystyle{plain} + \bibliography{mybib} + \end{document} + +Documentation: + This style file modifies the standard report style to follow the + Graduate Degree Support Section of the Registrar's Office's + "Directions for Preparing Doctoral Dissertations". It sets the + margins and interline spacing and disallows page breaks at + hyphens. + + The \beforepreface command creates the title page, a copyright page + (optionally), and a signature page. Then the user should put + preface section(s), using the \prefacesection{section title} + command. The \afterpreface command then produces the tables of + contents, tables and figures, and sets things up to start + the main body (on arabic page 1). + + The following commands can control what goes in the front matter + material: + + \title{thesis title} + \author{author's name} + \dept{author's department} + - Computer Science if omitted +The following switches allow for special title pages (not all are current) + \committeethesis - for a thesis in a committee (no dept.) + use \dept{committee name} + \programthesis - for a thesis in a program (no dept.) + use \dept{program name} + \educationthesis - for the School of Education. \dept doesn't matter + \businessthesis - for the GraduateSchool of Business. \dept doesn't matter + \lawthesis - for the School of law. \dept doesn't matter + \humanitiesthesis - for a thesis also submitted to the Graduate + Program in Humanities + \specialthesis - for a Graduate Special thesis + \industrialthesis - for a thesis in Industrial Engineering + \dualthesis - for a thesis in a dual language department. + Also define \languagemajor{language}. + e.g., \dept{French and Italian} + \languagemajor{Italian} + \principaladviser{the principal advisor's name} + (or \principaladvisor, if you prefer advisor spelled with o) + \coprincipaladviser{optional second principal advisor's name} + (or \coprincipaladvisor, use only if you have two principal + advisors only for the second one) + \firstreader{the first reader's name} + \secondreader{the second reader's name} + \thirdreader{optional third reader's name} + \fourthreader{optional fourth reader's name} + \setlength{\signaturespace}{.5in} + - default is .5in, can be adjusted to fit all + signatures in one page + \submitdate{month year in which submitted to GPO} + - date LaTeX'd if omitted + \copyrightyear{year degree conferred (next year if submitted + in Fall quarter)} + - year LaTeX'd (or next year, in December) if omitted + \copyrighttrue or \copyrightfalse + - produce or don't produce a copyright page (true by default) + \thesiscopyrighttrue or \thesiscopyrightfalse + - produces the style of copyright page listed by the + Thesis Office or the style that everyone else uses + (Thesis office by default). + \figurespagetrue or \figurespagefalse + - produce or don't produce a List of Figures page + (true by default) + \tablespagetrue or \tablespagefalse + - produce or don't produce a List of Tables page + (true by default) + +This style uses interline spacing that is 1.3 times normal, except +in the figure and table environments where normal spacing is used. +That can be changed by doing: + \setstretch{1.6} +(or whatever you want instead of 1.6) + +This command should be put before the \begin{document} command but +after loading the packages + +You can also set any particular section in singlespacing mode by using +the singlespace environment. For example + +\begin{quote} +\begin{singlespace} +... +\end{singlespace} +\end{quote} + +makes the quote singlespaced. See the documentation for setspace.sty +for more information. + +The example at the beginning shows the 12pt substyle being used. This +seems to give acceptable looking results, but it may be omitted to get +smaller print. + +} + + + +%%%%% +%%%%% SETUP MARGINS AND PENALTIES NEEDED FOR STANFORD THESIS +%%%%% + +% We need 1" margins except on the binding edge, where it is 1 1/2" +% Theses may be either single or double sided + \if@twoside + \setlength\oddsidemargin {36.1\p@} + \setlength\evensidemargin {0\p@} + \setlength\marginparwidth {40\p@} + \else + \setlength\oddsidemargin {36.1\p@} + \setlength\evensidemargin {36.1\p@} + \setlength\marginparwidth {40\p@} + \fi + +\marginparsep 10pt +%\oddsidemargin 0.5in \evensidemargin 0in +%\marginparwidth 40pt + + +\topmargin 0pt \headsep .5in +\textheight 8.1in \textwidth 6in + +% Disallow page breaks at hyphens (this will give some underfull vbox's, +% so an alternative is to use \brokenpenalty=100 and manually search +% for and fix such page breaks) +\brokenpenalty=10000 + +%%%%% +%%%%% SETUP COMMANDS PECULIAR TO THESES +%%%%% + +% \author, \title are defined in report; here are the rest of the +% front matter defining macros +\def\dept#1{\gdef\@dept{#1}} +\def\advis@r{Adviser} % default spelling +\def\principaladviser#1{\gdef\@principaladviser{#1}} +\def\principaladvisor#1{\gdef\@principaladviser{#1}\gdef\advis@r{Advisor}} +\def\coprincipaladvisor#1{\gdef\@coprincipaladviser{#1}\gdef\advis@r{Co-Advisor}} +\def\coprincipaladviser#1{\gdef\@coprincipaladviser{#1}\gdef\advis@r{Co-Adviser}} +\def\firstreader#1{\gdef\@firstreader{#1}} +\def\secondreader#1{\gdef\@secondreader{#1}} +\def\thirdreader#1{\gdef\@thirdreader{#1}} +\def\fourthreader#1{\gdef\@fourthreader{#1}} +\def\submitdate#1{\gdef\@submitdate{#1}} +\def\copyrightyear#1{\gdef\@copyrightyear{#1}} % \author, \title in report +% needed only for dual language departments to choose the language +\def\languagemajor#1{\gdef\@languagemajor{#1}} \def\@language{babel} +\def\jointprogram#1{\gdef\@jointprogram{#1}} +\def\@title{}\def\@author{}\def\@dept{computer science} +\def\@principaladviser{}\def\@firstreader{*}\def\@secondreader{*} +\def\@coprincipaladviser{*} +\def\@thirdreader{*} +\def\@fourthreader{*} +\def\@submitdate{\ifcase\the\month\or + January\or February\or March\or April\or May\or June\or + July\or August\or September\or October\or November\or December\fi + \space \number\the\year} +% Stanford says that Fall quarter theses should have the next year as the +% copyright year +\ifnum\month>9 + \@tempcnta=\year \advance\@tempcnta by 1 + \edef\@copyrightyear{\number\the\@tempcnta} +\else + \def\@copyrightyear{\number\the\year} +\fi +\newif\ifcopyright \newif\iffigurespage \newif\iftablespage +\newif\ifthesiscopyright + + +\copyrighttrue +\thesiscopyrighttrue + +\figurespagetrue \tablespagetrue + + +\def\@standardsub{submitted to the department of \uppercase\expandafter{\@dept}} +\def\@standardend{} + +\def\committeethesis{\let\@whichsub=\@committeesub} +\def\programthesis{\let\@whichsub=\@programsub} +\def\educationthesis{\let\@whichsub=\@educationsub} +\def\businessthesis{\let\@whichsub=\@businesssub} +\def\lawthesis{\let\@whichsub=\@lawsub} +\def\humanitiesthesis{\let\@whichsub=\@humanitiessub% +\let\@whichend=\@humanitiesend} +\def\specialthesis{\let\@whichsub=\@specialsub% +\let\@whichend=\@specialend} +\def\industrialthesis{\let\@whichsub=\@industrialsub% +\let\@whichend=\@industrialend} +\def\dualthesis{\let\@whichsub=\@dualsub% +\let\@whichend=\@dualend} + + +\def\@committeesub{SUBMITTED TO THE COMMITTEE ON \uppercase\expandafter{\@dept}} +\def\@programsub{SUBMITTED TO THE PROGRAM IN \uppercase\expandafter{\@dept}} +\def\@educationsub{SUBMITTED TO THE GRADUATE SCHOOL OF EDUCATION} +\def\@businesssub{SUBMITTED TO THE GRADUATE SCHOOL OF BUSINESS} +\def\@lawsub{SUBMITTED TO THE GRADUATE SCHOOL OF LAW} + +\def\@humanitiessub{SUBMITTED TO THE DEPARTMENT OF\\ \uppercase\expandafter{\@dept}} +\def\@humanitiesend{\\IN\\ \uppercase\expandafter{\@jointprogram} AND HUMANITIES} + +\def\@specialsub{SUBMITTED TO THE COMMITTEE ON GRADUATE STUDIES} +\def\@specialend{\\IN\\ \uppercase\expandafter{\@dept}} + + +\def\@dualsub{SUBMITTED TO THE DEPARTMENT OF \uppercase\expandafter{\@dept}} +\def\@dualend{\\IN\\ \uppercase\expandafter{\@languagemajor}} + + +\let\@whichend=\@standardend +\let\@whichsub=\@standardsub + + +\def\titlep{% + \thispagestyle{empty}% + \null\vskip1in% + \begin{center} + \large\uppercase\expandafter{\@title} + \end{center} + \vfill + \begin{center} +\large +% \sc a dissertation\\ +% \lowercase\expandafter{\@whichsub}\\ +% of stanford university\\ +% in partial fulfillment of the requirements\\ +% for the degree of\\ +% doctor of philosophy \uppercase\expandafter{\@whichend} + A THESIS\\ + \uppercase\expandafter{\@whichsub}\\ + OF STANFORD UNIVERSITY\\ + IN PARTIAL FULFILLMENT OF THE REQUIREMENTS\\ + FOR THE DEGREE OF\\ + MASTER OF SCIENCE \uppercase\expandafter{\@whichend}\\ + WITH A DISTINCTION IN RESEARCH + \end{center} + \vfill + \begin{center} + \rm \@author\\ + \@submitdate\\ + \end{center}\vskip.5in\newpage} + +\def\thesiscopyrightpage{% + \null\vfill + \begin{center} + \large + \copyright\ Copyright\ by \@author\ \@copyrightyear\\ + All Rights Reserved + \end{center} + \vfill\newpage} + +\def\tradcopyrightpage{% + \null\vfill + \begin{center} + \large + Copyright\ \copyright\ \@copyrightyear\ by \@author\\ + All Rights Reserved + \end{center} + \vfill\newpage} + + + + +\newlength{\signaturespace} +\setlength{\signaturespace}{.5in} + + +\long\def\signature#1{% +\begin{flushright} +\begin{minipage}{5in} +\parindent=0pt +I certify that I have read this thesis and that, in my opinion, +it is fully adequate in scope and quality as a thesis for the degree +of Master of Science. +\par +\vspace{\signaturespace} +%\hbox to 4in{\hfil\shortstack{\vrule width 3in height 0.4pt\\ #1}} +\hbox to 5in{\hfil\begin{tabular}{@{}l@{}}\vrule width 3in height + 0.4pt depth 0pt\\ #1\end{tabular}} +\end{minipage} +\end{flushright}} + +\long\def\ucgssignature{% +\begin{flushright} +\begin{minipage}{5in} +\parindent=0pt +\hfill Approved for the Stanford University Committee on Graduate Studies +\par +\vspace{\signaturespace} +\hbox to 5in{\hfil\begin{tabular}{@{}l@{}}\vrule width 3in height + 0.4pt depth 0pt\end{tabular}} +\end{minipage} +\end{flushright}} + + +\def\signaturepage{% +\ifonline +\setcounter{page}{0} +\def\thepage{} +\thispagestyle{myheadings} +\markboth{\rm \@author}{\rm \@author}\fi +\signature{(\@principaladviser)\quad Principal \advis@r} + \vfill +% if second principal advisor + \if*\@coprincipaladviser \else + \signature{(\@coprincipaladviser)\quad Principal \advis@r} + \vfill\fi + \if*\@firstreader \else + \signature{(\@firstreader)} + \vfill\fi + \if*\@secondreader \else + \signature{(\@secondreader)} + \vfill\fi +% if thirdreader then do \signature\@thirdreader \vfill + \if*\@thirdreader \else + \signature{(\@thirdreader)} + \vfill\fi +% if fourthreader then do \signature\@fourthreader \vfill + \if*\@fourthreader \else + \signature{(\@fourthreader)} + \vfill\fi +} + +\def\onlinesignature{ +\cleardoublepage +\@twosidetrue +\signaturepage +} + +\def\beforepreface{ + \pagenumbering{roman} + \pagestyle{plain} + \titlep +% online version has no copyright or signature pages but page counter +% must be incremented +% signature page should come at end + \ifonline\setcounter{page}{4}\else + \ifcopyright\ifthesiscopyright\thesiscopyrightpage\else\tradcopyrightpage\fi\fi + \signaturepage\fi + \cleardoublepage} + + +\def\prefacesection#1{% + \chapter*{#1} + \addcontentsline{toc}{chapter}{#1}} + +\def\afterpreface{\newpage + \tableofcontents + \iftablespage + \listoftables + \fi + \iffigurespage + \listoffigures + \fi + \cleardoublepage + \pagenumbering{arabic} + \pagestyle{headings}} + +% Redefine \thebibliography to go to a new page and put an entry in the +% table of contents +\let\@ldthebibliography\thebibliography +\renewcommand{\thebibliography}[1]{\newpage + \@ldthebibliography{#1}% +\addcontentsline{toc}{chapter}{\bibname}} + +% redefine \@endpart so the blank page after part has a page number +\def\@endpart{\vfil\newpage + \if@twoside + \if@openright + \null + \thispagestyle{plain}% + \newpage + \fi + \fi + \if@tempswa + \twocolumn + \fi} + + +% Start out normal +\pagestyle{headings} \ No newline at end of file