Functions_Demo.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy import stats\n",
    "import numpy as np\n",
    "import CombinedFCToolBox as cfc  #import the combinedFC toolbox\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Demo for CombinedFC Toolbox functions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### For more information and details about the functions and methods implemented here refer to: Sanchez-Romero, R., and Cole, M.W. (2021) \"Combining multiple functional connectivity methods to improve causal inferences\" Journal of Cognitive Neuroscience. https://doi.org/10.1162/jocn_a_01580"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Content\n",
    "1. Apply combinedFC to a single empirical dataset\n",
    "2. Apply combinedFC to group data\n",
    "3. Simulate networks and data\n",
    "4. Alternative implementations of combinedFC\n",
    "5. Simulate and apply combinedFC to a high-dimensional dataset (nodes >> datapoints)\n",
    "***"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1. Apply combinedFC to a single empirical dataset"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Load data from the hcp_data directory"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Subject 100206 dataset with 2390 datapoints and 360 nodes\n"
     ]
    }
   ],
   "source": [
    "#Load data for a single subject\n",
    "\n",
    "#NOTE: Here we are using the \"hcp_data\" directory included in the repository\n",
    "#which includes 100 subjects resting-state fMRI from the HCP, parcellated into 360 regions\n",
    "\n",
    "#IMPORTANT: The user need to format her own datasets as:\n",
    "#matrix with dimensions [datapoints x nodes] and no headers.\n",
    "\n",
    "#NOTE: The following are steps to read and load data in h5 format\n",
    "#(http://docs.h5py.org/en/stable/)\n",
    "\n",
    "#The user should adjust the script according to her own datasets\n",
    "#For example, to load a txt file the user can use the numpy loadtxt function\n",
    "#(https://docs.scipy.org/doc/numpy/reference/generated/numpy.loadtxt.html)\n",
    "#eg., for a comma separated file with headers in the first row use:\n",
    "#data = np.loadtxt('datafile.txt',comments='None', delimiter=',',skiprows=1)\n",
    "\n",
    "\n",
    "import h5py\n",
    "datadir = 'hcp_data'  #directory path for the datasets\n",
    "subject_id = '100206'  #just select one of the subjects. The directory has 100.\n",
    "#HCP data includes 4 resting state fMRI datasets per subjects,\n",
    "#select how many of these you want to concatenate\n",
    "#In this example, we just use 2 of the datasets            \n",
    "restRuns = ['rfMRI_REST1_RL','rfMRI_REST1_LR'] #,'rfMRI_REST2_RL', 'rfMRI_REST2_LR']\n",
    "#Read the h5 file\n",
    "h5file = h5py.File(f'{datadir}/{subject_id}_data.h5','r')\n",
    "#initialize the variable where the data will be concatenated\n",
    "rest_data = []\n",
    "#loop through the resting state fMRI datasets that were selected in restRuns\n",
    "for run in restRuns:\n",
    "    #extract the resting-state data from the h5 file, [:] loads it as an array\n",
    "    tmp = h5file[f'{run}/nuisanceReg_resid_24pXaCompCorXVolterra'][:]\n",
    "    #concatenate the resting state datasets (transpose to get [nDatapoints x nNodes])\n",
    "    rest_data.extend(tmp.T)\n",
    "    \n",
    "#save the nDatapoints x 360 nodes dataset (1195 datapoints per run)\n",
    "rest_data = np.asarray(rest_data)\n",
    "#IMPORTANT: close the h5 file\n",
    "h5file.close()\n",
    "\n",
    "print(f'Subject {subject_id} dataset with {rest_data.shape[0]} datapoints and {rest_data.shape[1]} nodes')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Apply combinedFC"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Important: the dataset input has to be a matrix [datapoints x nodes], and without header.\n",
    "#see the function code for more details.\n",
    "\n",
    "#Returns the symmetric combinedFC connectivity matrix [nodes x nodes]\n",
    "Mcfc_subj = cfc.combinedFC(dataset = rest_data,  \n",
    "            methodCondAsso = 'partialCorrelation', #method used to compute conditional associations\n",
    "            methodParcorr='inverseCovariance',     #if Partial Correlation, choose \"inversecovariance\" or \"regression\"\n",
    "            alphaCondAsso = 0.01,                  #alpha cutoff for conditional association\n",
    "            methodAsso = 'correlation',            #method used to compute bivariate associations\n",
    "            alphaAsso = 0.01,                      #alpha curtoff for bivariate association\n",
    "            equivalenceTestAsso = False,           #True for equivalence test, False for non-significance criterion\n",
    "            lower_bound = -0.2,                    #lower bound for equivalence test\n",
    "            upper_bound = +0.2                     #upper bound for equivalence test\n",
    "            )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Plot the combinedFC weighted connectivity matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Plot the combinedFC symmetric weighted connectivity matrix\n",
    "#with a colorbar with red for positive and blue for negative values\n",
    "fig, ax = cfc.plotConnectivityMatrix(ConnMat = Mcfc_subj,         #input weighted connectivity matrix\n",
    "                           methodTitle='CombinedFC\\n Connectivity Matrix',    #title for the plot\n",
    "                           )  \n",
    "fig.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#This function will also plot the HCP data connectivity matrix ordering \n",
    "#the 360 Glasser parcellation nodes (https://www.nature.com/articles/nature18933)\n",
    "#using the functional networks defined in Ji et al., (2019)\n",
    "#https://www.sciencedirect.com/science/article/pii/S1053811918319657\n",
    "\n",
    "fig, ax = cfc.plotConnectivityMatrix(ConnMat = Mcfc_subj,                   #input matrix\n",
    "                                methodTitle='CombinedFC\\n Ordered Connectivity Matrix',    #title for the plot\n",
    "                                functionalNetworks = True,   #True, if using Ji et al., (2019) functional networks order\n",
    "                                networkColorBar_x = True,   #include color marks in x axis for the functional networks\n",
    "                                networkColorBar_y = True,    #do not include color marks in y axis\n",
    "                                networkLabels = True)        #include labels for the Ji et al., networks\n",
    "fig.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2. Apply combinedFC to group data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Load data for all the subjects in the group, from the hcp_data directory"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "group_restData contains a list of 100 subjects\n",
      "Each subject dataset contains 1195 datapoints and 360 nodes\n"
     ]
    }
   ],
   "source": [
    "#IMPORTANT: The individual subjects data has to be saved as a list to input to combinedFC\n",
    "#recall that each individual dataset has to be in a matrix with dimentions [datapoints x nodes]\n",
    "#Here we show how we did it for the hcp_data directory datasets saved in h5 format.\n",
    "\n",
    "#If the user has her datasets in txt files in a directory the following pseudocode using numpy\n",
    "#loadtxt could be used:\n",
    "# group_data = []   #initialize a list\n",
    "# for each subject.txt file in your directory do:\n",
    "#   data = np.loadtxt('subject.txt')\n",
    "#   group_data.append(data)   #to save the individual data as a list\n",
    "\n",
    "\n",
    "import h5py\n",
    "#directory of the hcp data in h5 format\n",
    "datadir = 'hcp_data'\n",
    "#labels for the pool of 100 hcp subjects\n",
    "subjects = ['100206','108020','117930','126325','133928','143224','153934','164636','174437',\n",
    "            '183034','194443','204521','212823','268749','322224','385450','463040','529953',\n",
    "            '587664','656253','731140','814548','877269','978578','100408','108222','118124',\n",
    "            '126426','134021','144832','154229','164939','175338','185139','194645','204622',\n",
    "            '213017','268850','329844','389357','467351','530635','588565','657659','737960',\n",
    "            '816653','878877','987074','101006','110007','118225','127933','134324','146331',\n",
    "            '154532','165638','175742','185341','195445','205119','213421','274542','341834',\n",
    "            '393247','479762','545345','597869','664757','742549','820745','887373','989987',\n",
    "            '102311','111009','118831','128632','135528','146432','154936','167036','176441',\n",
    "            '186141','196144','205725','213522','285345','342129','394956','480141','552241',\n",
    "            '598568','671855','744553','826454','896879','990366','102513','112516','118932',\n",
    "            '129028']\n",
    "\n",
    "#just use one resting state run per subjects             \n",
    "restRuns = ['rfMRI_REST1_RL'] #'rfMRI_REST1_LR','rfMRI_REST2_RL', 'rfMRI_REST2_LR']\n",
    "\n",
    "#initialize the list that will contain the nSubjects datasets\n",
    "group_restData = []\n",
    "\n",
    "#extract individual datasets and populate the list\n",
    "#loop through all the subjects\n",
    "for subject in subjects:\n",
    "    h5file = h5py.File(f'{datadir}/{subject}_data.h5','r')\n",
    "    rest_data = []\n",
    "    for run in restRuns:\n",
    "        #extract the resting-state data, [:] loads it as an array\n",
    "        tmp = h5file[f'{run}/nuisanceReg_resid_24pXaCompCorXVolterra'][:]\n",
    "        #concatenate the resting state datasets from restRuns\n",
    "        rest_data.extend(tmp.T)\n",
    "    #save the nDatapoints x 360 nodes dataset as an array (1195 datapoints per run)\n",
    "    rest_data = np.asarray(rest_data)\n",
    "    #important, save the h5 file\n",
    "    h5file.close()\n",
    "    #append to the group data list\n",
    "    group_restData.append(rest_data)\n",
    "    \n",
    "print(f'group_restData contains a list of {len(group_restData)} subjects')\n",
    "print(f'Each subject dataset contains {group_restData[0].shape[0]} datapoints and {group_restData[0].shape[1]} nodes')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Apply combinedFC at the group level and use an equivalence test for the zero correlations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "#IMPORTANT: The input is a list containing the subjects individual datasets with dimensions [datapoints x nodes]\n",
    "#The output is a group combinedFC connectivity matrix with dimensions [nodes x nodes]\n",
    "\n",
    "#See the manuscript for information about computation and interpretation of the group matrix\n",
    "#In sum, each entry in the matrix represents the group average significant connectivity weight\n",
    "\n",
    "#See the manuscript for meaning and use of the equivalence test in group analysis\n",
    "\n",
    "Mcfc_group = cfc.groupCombinedFC(groupData = group_restData,   #list containing the subjects individual datasets \n",
    "                    alpha = 0.01,                          #alpha level for partial correlation\n",
    "                    methodParcorr ='inverseCovariance',    #method to compute the partial correlation\n",
    "                    equivalenceTest = True,                #If True, compute an equivalence test for zero correlations\n",
    "                    lower_bound = -0.2,                    #lower and upper bound representing the minimum correlation of\n",
    "                    upper_bound = +0.2,                    #interest for the equivalence test\n",
    "                    alphaEqTest = 0.01                      #alpha level for the equivalence test\n",
    "                    )                   "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Plot the group combinedFC weighted connectivity matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = cfc.plotConnectivityMatrix(ConnMat = Mcfc_group,   #input group weighted matrix       \n",
    "                                methodTitle='Group CombinedFC\\n Ordered Connectivity Matrix',   \n",
    "                                functionalNetworks = True,   #order in functional networks from Ji et al.,(2019)\n",
    "                                networkColorBar_x = True,    #include color marks in x axis for the functional networks\n",
    "                                networkColorBar_y = True,    #do not include color marks in y axis\n",
    "                                networkLabels = True)        #include labels for the Ji et al., networks\n",
    "fig.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3. Simulate networks and data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Simulate a directed network model: adjusted Erdos-Renyi or adjusted Static Power Law"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "directed network with 200 nodes and 893 edges\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#the graphModel function requires installation: \"conda install -c conda-forge python-igraph\"\n",
    "#or \"pip install python-igraph\"\n",
    "#https://igraph.org/python/\n",
    "\n",
    "#This function is now loaded by default, so we need it to call it directly as:\n",
    "from CombinedFCToolBox import graphModel\n",
    "\n",
    "model = 'ErdosRenyi'  #or StaticPowerLaw\n",
    "edgedensity = 900 #aprox. number of edges\n",
    "nNodes = 200 #number of nodes\n",
    "\n",
    "#returns a binary directed network encoded as column(source) -> row(target)\n",
    "#for example, the entry Cij, implies that j -> i (j is a directed cause of i)\n",
    "C = graphModel.graphModel(model,edgedensity*2,nNodes)\n",
    "\n",
    "#Note: the user can define her own model as long as it is a binary\n",
    "#directed matrix encoded as column(source) -> row(target).\n",
    "\n",
    "#plot the network model\n",
    "real_nEdges = np.sum(C==1) #get the real number of edges\n",
    "print(f'directed network with {nNodes} nodes and {real_nEdges} edges')\n",
    "plt.spy(C,markersize=3)\n",
    "plt.xlabel('sources',fontsize=14)\n",
    "plt.ylabel('targets',fontsize=14)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Simulate data for the network, using the linear model X = WX + E, and pseudoempirical noise terms E"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "#use the network model defined above\n",
    "network = C \n",
    "#Connectivity coefficients are sampled from a Uniform(min,max) distribution\n",
    "min_coefficient = -1\n",
    "max_coefficient = 1\n",
    "number_datapoints = 1200\n",
    "\n",
    "#returns a dataset X [datapoints x nodes] and a coefficient matrix W [nodes x nodes]\n",
    "X, W = cfc.simulateData.pseudoEmpiricalData(network, \n",
    "                                            min_coeff = min_coefficient, \n",
    "                                            max_coeff = max_coefficient, \n",
    "                                            nDatapoints=number_datapoints\n",
    "                                            )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### An alternative to the pseudoEmpirical noise terms is to sample E from a Standard Gaussian (or Beta)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "#network model defined above\n",
    "network = C \n",
    "#Connectivity coefficients are sampled from a Uniform(min,max) distribution\n",
    "min_coefficient = -1\n",
    "max_coefficient = 1\n",
    "number_datapoints = 1200\n",
    "type_distribution = 'Gaussian' #standard Gaussian(mean=0,std=1) or \"nonGaussian\" a Beta(1,5)\n",
    "\n",
    "X, W = cfc.simulateData.syntheticData(network, \n",
    "                                      min_coeff = min_coefficient, \n",
    "                                      max_coeff = max_coefficient, \n",
    "                                      nDatapoints = number_datapoints,\n",
    "                                      distribution = type_distribution\n",
    "                                      )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Apply combinedFC to the simulated data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Important: the dataset input has to be a matrix [datapoints x nodes], and without header.\n",
    "#see the function code for more details.\n",
    "\n",
    "#Returns the symmetric combinedFC connectivity matrix [nodes x nodes]\n",
    "Mcfc = cfc.combinedFC(dataset = X,  \n",
    "            methodCondAsso = 'partialCorrelation', #method used to compute conditional associations\n",
    "            methodParcorr='inverseCovariance',     #if Partial Correlation, choose \"inversecovariance\" or \"regression\"\n",
    "            alphaCondAsso = 0.01,                  #alpha cutoff for conditional association\n",
    "            methodAsso = 'correlation',            #method used to compute bivariate associations\n",
    "            alphaAsso = 0.01,                      #alpha curtoff for bivariate association\n",
    "            equivalenceTestAsso = False,           #True for equivalence test, False for non-significance criterion\n",
    "            lower_bound = -0.2,                    #lower bound for equivalence test\n",
    "            upper_bound = +0.2                     #upper bound for equivalence test\n",
    "            )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Apply partial correlation to the simulated data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "#returns the symmetric partial correlation connectivity matrix [nodes x nodes]\n",
    "M_parcorr = cfc.partialCorrelationSig(dataset =X, \n",
    "                                      alpha = 0.01, \n",
    "                                      method = 'inverseCovariance'   #\"inverseCovariance\" or \"regression\"\n",
    "                                      )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Apply bivariate correlation to the simulated data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "#returns the symmetric bivariate correlation connectivity matrix [nodes x nodes]\n",
    "M_corr = cfc.correlationSig(dataset = X,\n",
    "                            alpha=0.01  #alpha cutoff for the significance test: two-sided z-test\n",
    "                            )   "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Accuracy of the methods in the simulation, using precision and recall\n",
    "We want to quantify the accuracy of a method to recover the adjacencies of the true model.\n",
    "<br>\n",
    "precision = true positives / (true positives + false positives)\n",
    "<br>\n",
    "recall = true positives / (true positives + false negatives)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "combinedFC accuracy:\n",
      "precision: 0.596\n",
      "recall: 0.77\n",
      " \n",
      "partial correlation accuracy:\n",
      "precision: 0.378\n",
      "recall: 0.829\n",
      " \n",
      "bivariate correlation accuracy:\n",
      "precision: 0.085\n",
      "recall: 0.898\n"
     ]
    }
   ],
   "source": [
    "# the true model is the simulated network C\n",
    "trueModel = C\n",
    "\n",
    "#estimated models\n",
    "estimatedModel = Mcfc\n",
    "precision = cfc.precision(estimatedModel,trueModel)\n",
    "recall = cfc.recall(estimatedModel,trueModel)\n",
    "#print results\n",
    "print(f'combinedFC accuracy:')\n",
    "print(f'precision: {round(precision,3)}')  #round up result to 3 decimals\n",
    "print(f'recall: {round(recall,3)}')\n",
    "print(' ')\n",
    "\n",
    "\n",
    "estimatedModel = M_parcorr\n",
    "precision = cfc.precision(estimatedModel,trueModel)\n",
    "recall = cfc.recall(estimatedModel,trueModel)\n",
    "print(f'partial correlation accuracy:')\n",
    "print(f'precision: {round(precision,3)}')\n",
    "print(f'recall: {round(recall,3)}')\n",
    "print(' ')\n",
    "\n",
    "estimatedModel = M_corr\n",
    "precision = cfc.precision(estimatedModel,trueModel)\n",
    "recall = cfc.recall(estimatedModel,trueModel)\n",
    "print(f'bivariate correlation accuracy:')\n",
    "print(f'precision: {round(precision,3)}')\n",
    "print(f'recall: {round(recall,3)}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 4. Alternative implementations of combinedFC"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Implement combinedFC with the regression approach for partial correlation and an equivalence test for zero correlations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "Mcfc_eq = cfc.combinedFC(dataset = X,  \n",
    "                methodCondAsso = 'partialCorrelation', #method used to compute conditional associations\n",
    "                methodParcorr='regression',            #for Partial Correlation, \"inversecovariance\" or \"regression\"\n",
    "                alphaCondAsso = 0.01,                  #alpha cutoff for conditional association\n",
    "                methodAsso = 'correlation',            #method used to compute bivariate associations\n",
    "                alphaAsso = 0.01,                      #alpha curtoff for bivariate association\n",
    "                equivalenceTestAsso = True,            #True for equivalence test, False for non-significance criterion\n",
    "                lower_bound = -0.2,                    #lower bound for equivalence test\n",
    "                upper_bound = +0.2                     #upper bound for equivalence test\n",
    "                )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Accuracy of combinedFC with the regression approach for partial correlation and an equivalence test for zero correlations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "combinedFC with regression approach for partial correlation and an Equivalence test, accuracy:\n",
      "precision: 0.708\n",
      "recall: 0.701\n"
     ]
    }
   ],
   "source": [
    "trueModel = C\n",
    "estimatedModel = Mcfc_eq\n",
    "precision = cfc.precision(estimatedModel,trueModel)\n",
    "recall = cfc.recall(estimatedModel,trueModel)\n",
    "print(f'combinedFC with regression approach for partial correlation and an Equivalence test, accuracy:')\n",
    "print(f'precision: {round(precision,3)}')\n",
    "print(f'recall: {round(recall,3)}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Implement combinedFC with simple regression and multiple regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "#returns the symmetric combinedFC connectivity matrix [nodes x nodes]\n",
    "Mcfc_reg = cfc.combinedFC(dataset = X,  \n",
    "                   methodCondAsso = 'multipleRegression', #use multiple regression for conditional associations  \n",
    "                   alphaCondAsso = 0.01,                  #alpha cutoff for the multiple regression coefficients\n",
    "                   methodAsso = 'simpleRegression',       #use simple regression for the bivariate associations        \n",
    "                   alphaAsso = 0.01,                      #alpha cutoff for the simple regression coefficients \n",
    "                    )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Accuracy of combinedFC with simple regression and multiple regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "combinedFC with simple and multiple regression, accuracy:\n",
      "precision: 0.596\n",
      "recall: 0.77\n"
     ]
    }
   ],
   "source": [
    "trueModel = C\n",
    "estimatedModel = Mcfc_reg\n",
    "precision = cfc.precision(estimatedModel,trueModel)\n",
    "recall = cfc.recall(estimatedModel,trueModel)\n",
    "print(f'combinedFC with simple and multiple regression, accuracy:')\n",
    "print(f'precision: {round(precision,3)}')\n",
    "print(f'recall: {round(recall,3)}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 5. Simulate and apply combinedFC to a high-dimensional dataset (nodes >> datapoints)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "directed network with 800 nodes and 1718 edges\n"
     ]
    }
   ],
   "source": [
    "#define a directed network\n",
    "from CombinedFCToolBox import graphModel\n",
    "model = 'StaticPowerLaw'  #or ErdosRenyi\n",
    "edgedensity = 1000 #aprox. number of edges\n",
    "nNodes = 800 #number of nodes\n",
    "#call the function to generate the network\n",
    "C = graphModel.graphModel(model,edgedensity*2,nNodes)\n",
    "\n",
    "real_nEdges = np.sum(C==1)\n",
    "print(f'directed network with {nNodes} nodes and {real_nEdges} edges')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "X_hd dataset has 800 nodes and 400 datapoints\n"
     ]
    }
   ],
   "source": [
    "#generate the high-dimensional dataset using the above directed network\n",
    "network = C #network model defined above\n",
    "#Connectivity coefficients are sampled from a Uniform(min,max) distribution\n",
    "min_coefficient = -1\n",
    "max_coefficient = 1\n",
    "#number of nodes of the network\n",
    "nNodes = network.shape[1]\n",
    "#define number of datapoints to be half of the number of nodes (nodes >> datapoints)\n",
    "number_datapoints = np.round(nNodes/2).astype(int) #round and define as integer\n",
    "\n",
    "#generate data using Gaussian noise terms E\n",
    "type_distribution = 'Gaussian'  #standard Gaussian(mean = 0,std =1)\n",
    "X_hd, W_hd = cfc.simulateData.syntheticData(network, \n",
    "                                            min_coeff = min_coefficient, \n",
    "                                            max_coeff = max_coefficient, \n",
    "                                            nDatapoints = number_datapoints,\n",
    "                                            distribution = type_distribution\n",
    "                                            )\n",
    "print(f'X_hd dataset has {X_hd.shape[1]} nodes and {X_hd.shape[0]} datapoints')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Implement combinedFC with a high-dimensional method to compute partial correlations\n",
    "The method used is glasso, a regularized solution to the inverse covariance approach for high-dimensional datasets."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "#the glasso implementation uses as default a cross-validation with 10 kfolds to choose the regularization parameter\n",
    "Mcfc_hd = cfc.combinedFC(dataset = X_hd,  \n",
    "                    methodCondAsso = 'partialCorrelation', #method for conditional associations\n",
    "                    methodParcorr = 'glasso',              #use glasso as method for partial correlations\n",
    "                    alphaCondAsso = 0.01,                  #alpha cutoff for the multiple regression coefficients\n",
    "                    methodAsso = 'correlation',            #use simple regression for the bivariate associations        \n",
    "                    alphaAsso = 0.01,                      #alpha cutoff for the simple regression coefficients\n",
    "                    )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Apply partial correlation using glasso to the high-dimensional dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "#the glasso implementation uses as default a cross-validation with 10 kfolds to choose the regularization parameter\n",
    "Mparcorr_hd = cfc.partialCorrelationSig(dataset =X_hd, \n",
    "                                      alpha = 0.01, \n",
    "                                      method = 'glasso'   #use glasso for high-dimensional datasets\n",
    "                                      )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Apply correlation to the high-dimensional dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [],
   "source": [
    "Mcorr_hd = cfc.correlationSig(dataset = X_hd,\n",
    "                            alpha=0.01  #alpha cutoff for the significance test: two-sided z-test\n",
    "                            )   "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Precision and recall of the methods for the high-dimensional problem"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "combinedFC using glasso to compute partial correlations, accuracy:\n",
      "precision: 0.635\n",
      "recall: 0.513\n",
      " \n",
      "partial correlation using glasso, accuracy:\n",
      "precision: 0.47\n",
      "recall: 0.532\n",
      " \n",
      "bivariate correlation accuracy:\n",
      "precision: 0.203\n",
      "recall: 0.565\n"
     ]
    }
   ],
   "source": [
    "# the true model is the simulated network C\n",
    "trueModel = C\n",
    "\n",
    "estimatedModel = Mcfc_hd\n",
    "precision = cfc.precision(estimatedModel,trueModel)\n",
    "recall = cfc.recall(estimatedModel,trueModel)\n",
    "print(f'combinedFC using glasso to compute partial correlations, accuracy:')\n",
    "print(f'precision: {round(precision,3)}')\n",
    "print(f'recall: {round(recall,3)}')\n",
    "print(' ')\n",
    "\n",
    "estimatedModel = Mparcorr_hd\n",
    "precision = cfc.precision(estimatedModel,trueModel)\n",
    "recall = cfc.recall(estimatedModel,trueModel)\n",
    "print(f'partial correlation using glasso, accuracy:')\n",
    "print(f'precision: {round(precision,3)}')\n",
    "print(f'recall: {round(recall,3)}')\n",
    "print(' ')\n",
    "\n",
    "estimatedModel = Mcorr_hd\n",
    "precision = cfc.precision(estimatedModel,trueModel)\n",
    "recall = cfc.recall(estimatedModel,trueModel)\n",
    "print(f'bivariate correlation accuracy:')\n",
    "print(f'precision: {round(precision,3)}')\n",
    "print(f'recall: {round(recall,3)}')"
   ]
  }
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