07_Classification_TP.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 07 / 08. TP Classification"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### enseignant: Anastasios Giovanidis 2022 - 2023\n",
    "#### date: 08 / 15 Novembre 2022 "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### student name or binome:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is the TP related to classification. We will need to import the following libraries."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import math"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this class we will learn how to use PYTHON for classification, applying the following techniques:\n",
    "\n",
    "- KNN\n",
    "- Logistic Regression (multivariate)\n",
    "- LDA\n",
    "- QDA"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Preparation: Generating \"synthetic\" data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let us first create a reasonable dataset related to $\\mathrm{Default}$. The predictors are:\n",
    "\n",
    "- Balance ('x')\n",
    "- Income ('z')\n",
    "- Student[Yes]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There are two classes: \n",
    "\n",
    "- Class A: $\\mathrm{Default}=Yes$, \n",
    "- Class B: $\\mathrm{Default}=No$.\n",
    "\n",
    "We assume that the (balance, income) tuple follows for each class a bi-variate normal distribution\n",
    "with different mean vector and covariance matrix. \n",
    "\n",
    "E.g. for class A: $\\mu_A = [\\mu_{A}(x),\\ \\mu_{A}(z)]$,\n",
    "$\\mathbf{\\Sigma}_A = \\left[\\ [Var_A(x,x),Cov_A(x,z)],\\  [Cov_A(z,x),Var_A(z,z)] \\right]$, and similarly for class B."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "muA = [700, 3000]\n",
    "muB = [1350, 3000]\n",
    "SigmaA = [[70000,0], [0,900000]]\n",
    "SigmaB = [[70000,0], [0,900000]]\n",
    "n = 300 # sample size"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The covariance is the same for the two classes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "np.random.seed(100)\n",
    "xA, zA = np.random.multivariate_normal(muA, SigmaA, n).T\n",
    "# Avoid negatives\n",
    "xA = list(np.multiply(xA>0,xA))\n",
    "zA = list(np.multiply(zA>0,zA))\n",
    "#\n",
    "xB, zB = np.random.multivariate_normal(muB, SigmaB, n).T\n",
    "# Avoid negatives\n",
    "xB = list(np.multiply(xB>0,xB))\n",
    "zB = list(np.multiply(zB>0,zB))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(xA, zA, 'x')\n",
    "plt.plot(xB, zB, 'o')\n",
    "balanceMAX = 2700\n",
    "incomeMAX = 6200\n",
    "plt.axis([-1, balanceMAX, -1, incomeMAX])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let us plot the histogram for the xA."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "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": [
    "countA, binsA, ignoredA = plt.hist(xA, 15, density=True)\n",
    "countB, binsB, ignoredB = plt.hist(xB, 15, density=True)\n",
    "plt.plot(binsA, 1/( np.sqrt(2 * np.pi * SigmaA[0][0])) * np.exp( - (binsA - muA[0])**2 / (2 * SigmaA[0][0]) ), linewidth=2, color='b')\n",
    "plt.plot(binsB, 1/( np.sqrt(2 * np.pi * SigmaB[0][0])) * np.exp( - (binsB - muB[0])**2 / (2 * SigmaB[0][0]) ), linewidth=2, color='r')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The actual data-trace will look as follows:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = xA+xB\n",
    "z = zA+zB\n",
    "defaultA = list(np.zeros(len(xA)))\n",
    "defaultB = list(np.ones(len(xB)))\n",
    "default = defaultA + defaultB\n",
    "for i in range(len(default)): \n",
    "    default[i] = int(default[i]) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Generate Student[Yes] predictor. We give a higher probability for someone with high $x$ (Balance) to be a student, because we assume that students tend to borrow money from a bank for their studies (tendency for higher balance)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "Student = list()\n",
    "Mx = max(x)\n",
    "for i in range(len(x)):\n",
    "    p = x[i]/max(x)/2\n",
    "    Student.extend(np.random.binomial(1, p, 1))\n",
    "#"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Percentage of students in the data set\n",
    "muS = sum(Student)/len(Student)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.23666666666666666\n"
     ]
    }
   ],
   "source": [
    "print(muS)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Create a Dictionary of DATA"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "DATA = {}\n",
    "for i in range(len(x)):\n",
    "    DATA[i] = {}\n",
    "    DATA[i]['predictors'] = [x[i],z[i],Student[i]]\n",
    "    DATA[i]['Default'] = default[i]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'predictors': [633.2117025413584, 4093.865807946399, 0], 'Default': 0}\n"
     ]
    }
   ],
   "source": [
    "print(DATA[1])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "or put everything in a pandas structure:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>balance</th>\n",
       "      <th>income</th>\n",
       "      <th>student[Yes]</th>\n",
       "      <th>y-Default[Yes]</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>790.664713</td>\n",
       "      <td>1340.026720</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>633.211703</td>\n",
       "      <td>4093.865808</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>836.049517</td>\n",
       "      <td>3930.962641</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>416.893146</td>\n",
       "      <td>3209.829458</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>767.467041</td>\n",
       "      <td>2820.228470</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>595</th>\n",
       "      <td>1255.148641</td>\n",
       "      <td>2372.074801</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>596</th>\n",
       "      <td>1375.892328</td>\n",
       "      <td>2932.481878</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>597</th>\n",
       "      <td>1539.465139</td>\n",
       "      <td>4679.803405</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>598</th>\n",
       "      <td>1791.358794</td>\n",
       "      <td>2760.898896</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>599</th>\n",
       "      <td>1658.278123</td>\n",
       "      <td>2209.289884</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>600 rows × 4 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "         balance       income  student[Yes]  y-Default[Yes]\n",
       "0     790.664713  1340.026720             0               0\n",
       "1     633.211703  4093.865808             0               0\n",
       "2     836.049517  3930.962641             0               0\n",
       "3     416.893146  3209.829458             1               0\n",
       "4     767.467041  2820.228470             0               0\n",
       "..           ...          ...           ...             ...\n",
       "595  1255.148641  2372.074801             0               1\n",
       "596  1375.892328  2932.481878             0               1\n",
       "597  1539.465139  4679.803405             0               1\n",
       "598  1791.358794  2760.898896             1               1\n",
       "599  1658.278123  2209.289884             1               1\n",
       "\n",
       "[600 rows x 4 columns]"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import pandas as pd\n",
    "data1 = {'balance': x, 'income': z, 'student[Yes]': Student , 'y-Default[Yes]': default}\n",
    "df_DATA = pd.DataFrame(data=data1)\n",
    "df_DATA"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exercise 1 (KNN)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Use the K-Nearest-Neighbours classification method, to build a $\\mathrm{Default}=\\left\\{Yes,No\\right\\}$ classifier, based on the DATA available. For the moment you can ignore the $\\mathrm{Student}$ predictor, and only use the pair of predictors $(\\mathrm{Balance},\\mathrm{Income})$.\n",
    "\n",
    "### Part A\n",
    "\n",
    "For $K=1,3,10,40$\n",
    "\n",
    "- Train the KNN classifier using the entire data-set (no train-test split).\n",
    "- Plot a 2D map of the areas where $\\mathrm{Default}=Yes$.\n",
    "\n",
    "Discuss your observations.\n",
    "\n",
    "### Part B\n",
    "\n",
    "- Using the function **from sklearn.model_selection import cross_validate** do a cross-validation for the DATA set (balance, income) and estimate the Test Classification error for each $K$. Then average over all the ways that the set was split to derive the average Test error per $K$. Use as scores: **scoring=('accuracy', 'roc_auc','neg_mean_absolute_error')** and plot the mean scores over $1/K$.  What is your conclusion about the optimal $K$ value among the values you checked? Take **$K=1,\\ldots, 100$**.\n",
    "\n",
    "I want to see 3 plots, in each plot two curves, one for Train and the other for Test. The x-axis should be in logarithmic scale. The y-axis in linear scale."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Answer: (Part A)**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First create input vector X01 containing only the 0 and 1 entry of each vector."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.neighbors import KNeighborsClassifier"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Answer: (Part B)**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.model_selection import cross_validate\n",
    "from sklearn.metrics import SCORERS\n",
    "Kmax = 100\n",
    "Train_accuracy = list()\n",
    "Test_accuracy = list()\n",
    "Train_roc = list()\n",
    "Test_roc = list()\n",
    "Train_error = list()\n",
    "Test_error = list()\n",
    "#\n",
    "for K in range(1,Kmax):\n",
    "    neigh = KNeighborsClassifier(n_neighbors=K)\n",
    "    #TODO..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "#To check the SCORERS do:\n",
    "#print(SCORERS.keys())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "#To check the keys for cross validats scores, print the keys()\n",
    "#print(cv_results.keys())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "#print(cv_results['test_roc_auc'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The best fitting value for K-NN is for $K=$..."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exercise 2 (Logistic Regression)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- Split the original data set into a train and a test set, so that Test-set is 30\\% of the whole Data entries. Use the Logistic Regression classifier, to derive the prediction for the first entry of the $Xtest$ set.\n",
    "\n",
    "Use **logistic.predict(X_test[0])** and **logistic.predict_proba([X_test[0]])**. What do you observe?\n",
    "\n",
    "Use **logreg.score(X_test,D_test)** to find the mean prediction error.\n",
    "\n",
    "- Split in several ways the original data set into train-test sets. For each, calculate the error, and the average over all ways. What is the value of the Test error rate in Logistic Regression (averaged over all splits)? Compare with the error rate from the optimal KNN classifier above. What do you see?\n",
    "\n",
    "- Use the confusion matrix of the last split to evaluate the correctness of the predictor for the last Train-Test split. Find the Accuracy (ACC), True-Positive rate (TPR), False-Positive rate (FPR) and the Precision (PPV). \n",
    "\n",
    "- Repeat the whole processes using Cross Validation (**cross_validate**)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.linear_model import LogisticRegression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The Logistic coefficients for the last Train-Test split are as follows:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "#print('logreg1.classes_ =', logreg1.classes_)\n",
    "#print('logreg1.coef_ =', logreg1.coef_) #b1 and b2 coefficients\n",
    "#print('logreg1.intercept_ =', logreg1.intercept_) #b0 coefficient"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Compare the logistic regression score with the mean accuracy. What do you observe?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "#logreg.score(X_test,Y_test)\n",
    "#np.sum(np.abs(logreg.predict(X_test) - Y_test))/len(Y_test)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can also see the confusion matrix with False/True Positives/Negatives."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "ename": "NameError",
     "evalue": "name 'D_test' is not defined",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mNameError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-21-f8eded58307c>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m      1\u001b[0m \u001b[0;32mfrom\u001b[0m \u001b[0msklearn\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mmetrics\u001b[0m \u001b[0;32mimport\u001b[0m \u001b[0mconfusion_matrix\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 2\u001b[0;31m \u001b[0mCM\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mconfusion_matrix\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mD_test\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mD_esti\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      3\u001b[0m \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'confusion_matrix=\\n'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mCM\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      4\u001b[0m \u001b[0;31m# x-axis is Known Truth, y-axis is Prediction.\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mNameError\u001b[0m: name 'D_test' is not defined"
     ]
    }
   ],
   "source": [
    "from sklearn.metrics import confusion_matrix\n",
    "CM = confusion_matrix(D_test, D_esti)\n",
    "print('confusion_matrix=\\n', CM)\n",
    "# x-axis is Known Truth, y-axis is Prediction."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 128,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Latest Test-Set Total Error= 0.133\n"
     ]
    }
   ],
   "source": [
    "TE = (CM[1][0]+CM[0][1])/(CM[0][0]+CM[0][1]+CM[1][0]+CM[1][1])\n",
    "print('Latest Test-Set Total Error= %.3f' %TE)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Latest Test-Set False Positive= 0.000\n",
      "Latest Test-Set True Positive= 0.000\n"
     ]
    }
   ],
   "source": [
    "FPR = 0#TODO\n",
    "print('Latest Test-Set False Positive= %.3f' %FP)\n",
    "TPR = 0#TODO\n",
    "print('Latest Test-Set True Positive= %.3f' %TP)\n",
    "ACC = 0#TODO\n",
    "PPV = 0#TODO"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Using Cross Validation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Test_error = []\n",
      "Test ROC curve surface = []\n",
      "Test accuracy = []\n"
     ]
    }
   ],
   "source": [
    "Logi_Train_accuracy = list()\n",
    "Logi_Test_accuracy = list()\n",
    "Logi_Train_roc = list()\n",
    "Logi_Test_roc = list()\n",
    "Logi_Train_error = list()\n",
    "Logi_Test_error = list()\n",
    "#\n",
    "logregCV = LogisticRegression()\n",
    "# TODO\n",
    "#\n",
    "print('Test_error =', Logi_Test_error)\n",
    "print('Test ROC curve surface =', Logi_Test_roc)\n",
    "print('Test accuracy =', Logi_Test_accuracy)\n",
    "#print('logregCV.coef_ =', logregCV.coef_)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exercise 3 (Discriminant Analysis LDA & QDA)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- Use the $\\mathrm{LinearDiscriminantAnalysis}$ (LDA) and $\\mathrm{QuadraticDiscriminantAnalysis}$ (QDA) method to fit the Train Data and predict the Test Data.\n",
    "\n",
    "- Again find the average Test Error using several Train-Test splits.\n",
    "\n",
    "- Compare the Average Test Error for LDA, QDA, Logistic and KNN. Order the methods for the specific dataset."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Answer:**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.discriminant_analysis import LinearDiscriminantAnalysis , QuadraticDiscriminantAnalysis"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exercise 4 (Uniform) -- Bonus*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Generate again an artificial dataset where the (Balance,Income) tuple is generated from two independent uniform distributions. The ranges are:\n",
    "\n",
    "- Class A (no Default): Income is $[100,6000]$ and the range of Balance is $[10,1500]$, number of samples 300.\n",
    "\n",
    "- Class B (yes Default): Income is $[100,6000]$ and the range of Balance is $[1000,2500]$, number of samples 100.\n",
    "\n",
    "(A) Find the Accuracy and the Mean Test Error using Cross Validation, for K-NN ($K=1,\\ldots,100$), Logistic Regression, LDA, QDA.\n",
    "\n",
    "(B) Order the methods by their quality. Which one is better? Why?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Answer:**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We first generate the uniform \"synthetic\" data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "nA = 300 # sample size per class\n",
    "nB = 120"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "zA = np.random.uniform(100,6000,nA)\n",
    "xA = np.random.uniform(10, 1500,nA)\n",
    "#\n",
    "zB = np.random.uniform(100,6000,nB)\n",
    "xB = np.random.uniform(1000,2500,nB)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "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": [
    "plt.plot(xA, zA, 'x')\n",
    "plt.plot(xB, zB, 'o')\n",
    "balanceMAX = 2700\n",
    "incomeMAX = 6200\n",
    "plt.axis([-1, balanceMAX, -1, incomeMAX])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = list(xA)+list(xB)\n",
    "z = list(zA)+list(zB)\n",
    "defUA = list(np.zeros(len(xA)))\n",
    "defUB = list(np.ones(len(xB)))\n",
    "defU = defUA + defUB\n",
    "for i in range(len(defU)): \n",
    "    defU[i] = int(defU[i]) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "XU01 = list()\n",
    "for i in range(len(defU)):\n",
    "    XU01.append([x[i],z[i]])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exercise 5 (Class related covariance matrix $\\Sigma_m$) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Generate again an artificial dataset where the (Balance,Income) tuple is generated from a binormal distribution. The data from the two classes have different means and covariances for their predictors:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [],
   "source": [
    "muSA = [700, 3000]\n",
    "muSB = [1350, 3000]\n",
    "SigmaSA = [[70000,-100], [-100,900000]]\n",
    "SigmaSB = [[70000,+200], [+200,900000]]\n",
    "nS = 300 # sample size"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [],
   "source": [
    "xSA, zSA = np.random.multivariate_normal(muSA, SigmaSA, nS).T\n",
    "# Avoid negatives\n",
    "xSA = list(np.multiply(xSA>0,xSA))\n",
    "zSA = list(np.multiply(zSA>0,zSA))\n",
    "#\n",
    "xSB, zSB = np.random.multivariate_normal(muSB, SigmaSB, nS).T\n",
    "# Avoid negatives\n",
    "xSB = list(np.multiply(xB>0,xB))\n",
    "zSB = list(np.multiply(zB>0,yB))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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gcxdXyNW7vI709sH6rXYE4fTq4XT2ga6aK+eO4UJHp5/P/KXsn8cZN7QvbxkT26sHm6nytlJZWsDCKSUs23YkZXn/NRlMNpeVjBAt9C3EMz+OnepFvTdvUimThxdQ2/wZI/pfTu2J0yycUuL3GSUgnfjElw/K48G1+1i965KRVxVXqWloDxvUFM7oGjgmgNwcD5Wl+eZkpHYCsyuK2Xv0FLMriniv6bSZDG7Ztg9YsaOe5+8bq3X7mvji5rw6LpyMtMtmAMnILbN6l5elW2qZVVHEzsOtZtZM67UidVMMdk716GQ8TlxA7VwxF6zbD8DiW8v8rqkeJw8vZIOh23/67usdjUejcYxb8+oEZhIFX0BYEmo9aJfNCEh0uH+Vt5Vl247wyPQRPH13hVkJa+GUEj9DbKRuivMmlTKroogN1Y2UFfb2E7pOdgtOXUDtdjIzygcyo3ygbfbPhVNKeO3gCWZXFLOx+niX3Uikqh6dcVPTBbfm1XFpjWNtyA0gUPi1fHaOmaOL4hYYVNPQ7qfisKp/YlnxVnlb2Xm4lRuH9uWdo6eYXVFsCuHK0gJz52BNoqbGEWjwDeUCatfHp+4s79KmPrdofbU53i8V9WHpllrea/yUnYdbo9pFOTVOa7KIZCdvc4pLJyO90rdgl1tmc00TC9btj1sO+WgDjUKtcK2eMXUtZ8xVdY7nkvC1Bo09NLnUbxyJKnkYeF7rbsTxLipAJ1p55g3HQV96V5AluDWvjkuTvGmhb8FO+K2cO4YZ5QNTXhs3lJG5pqHdT5Xz9N3X88j0ESzbdsQvY2YwYZmoiNfA86rdiOMo4iAGusozbzhSwbmhmL0mCbi1RrJLJyNtyHVIqmvjQmgjs1PDbzzHEYmxOapcPEEMdGd7F1F5drkj43RYw7wuoadJJCn6/wplyM0Koa+Ek9JfB+qzw+nTo/HoSVSSsFiEdrw9kyIR5FHdjyDVlToRvD23zvHk0eWeWQtuI/yv4cmFHn3gi1N6EtCkLVnvvaO2+YFpAtTrUNt9JVSmjexvRtYqlUEw/fCzO73muZVqQeXTj0W1EEuSNatwvKxHN9N/3qr6CKbrjjX4C6K0ZQTRfZ7vPTCiGgDWe3b49ectKiPoMql0XoAvTuI6f28rLvT91qQPWSH0lWDw+YwXsHRLLZOHF3bxjbdDCbaZo4tYtL6aTQcaWTilhE0HGs0JI1BgqsjbhVNKeHDtPu557m2WbqllydRh5uo0lipX0RQwsdorrP2raWgPq+sOpRtPqItrEJ1oz2k/9msKNnnY3bPLdy/t6kYXChe42PmR6kAkPeGkPY7VO0KIHGAfcFxKOUMIcQ3wO6Af8FdgrpTyvBCiB/BrYAzQBtwtpTxqnONh4EGgA1gspdwa6prx1umrbb5ya4xURaICkS50dJKb4/HLOROsgHhhnx58cOI0N5Xl8+J3JkSdVz5WFZXdWCJR9QQ7Ph4qo5Cqn777o9aJ2p1XPn4lwrYgdygSVKw7GlIZiJTCYCNNZMRLvfN94H3L658BT0sphwGn8AlzjMdTUsoy4GnjOIQQXwK+CYwEbgP+jzGRJIVLaQKKjDQBkWd+rCwt4P7KoZy90MmFjk7e9rYFFeCVpQVMHl7ABydOc+2APuyua+MHv6+O2vtHqUesq27r60jVRpGu0O2Oj1f5xJBeNuV3+YTZ45/4HiMQLnYqJRGNu1yq/b2tpNL326XBRnr3ERmOhL4QYhAwHXjOeC2AW4A/GIf8CphlPL/DeI3x/q3G8XcAv5NSnpNS/h2oA26MxyDCYfVj33m4lUemj2Dn4ZYuem0n51H6YSCkwFy9y8vG6kZmVxTRcvocE8vy2VDdyOThXbNhRkKsxUmUfj4wa+Ydv3wrpE+7nT0hXv79sY4pImxURp3S0Oz36gc53f2Pd4GLnR+p9P12Y7BRqtVdofrl0onI6Ur//wX+G6ASqecDn0gpLxqvG4Bi43kxcAzAeL/dON5st/lMQlHCyS5NgFMhZTXo9unVjU4JuTmCNVVHWb3LawpT9ahSLVw74ApuH9XfTKf82sFm8/hosVt1Ow1EKh+Ux4J1+1mwbj/PzKlgQmk+AIdPnA4ahBa4op82sj8L1u33U52oa0Xr319ZWsBPSt7jrre+zv6Of6LylSmJ+aFYfLolgkYKeHX4E4zJ+QNV39gLd/zSff7eVlLp++3GYCM37j7cOhEZhE3DIISYAXwspdwvhJiimm0OlWHeC/UZ6/XmA/MBhgwZEq57jlBCyLpytOafd7KiVBPHocZ2lm6pZc74wbxyoImywt7m61Vv1puTiEo9sHqXl/V7jjFn/GAG9+vN5Gt9+eYfmT4i6vEErronlOY7Tk+gcuVsrmnibW+bXz58ZZxW+vlpI/v7jV2dV7HpQKNZI0AZxVX/IrUxHH79eW458m/08pz3NagfCsRf6JbfRVXvW8z7M720gL7m/bqFyh+4SMgHou5FKmILbv1Xe51+KndCqd592PnhB5uIXv2hK2JCwhpyhRBPAXOBi0BP4ApgAzANGCClvCiE+ArwuJRymhBiq/H8P4UQ3YATQCHwIwAp5VPGec3jgl3bTcFZCuWOqTyBNlY3MrEsn/0ffmKbNth6vBKmsRQSCeUbDwQ1qgYaNZVRe2JpPr+ZN8E8v9WnPTAHj9211D14ZPoI5k0q7dI/p2Maum48Rdio2ewMlGECXpzEBOhi61HitmA2Nxq2nXqHJdAIHpMhV0r5sJRykJRyKD5D7BtSym8BfwG+YRx2L/An4/krxmuM99+QvpnlFeCbQogehufPMOCdKMeUMMKpSR6aXEpHJ0a64EazYMhtowbYqokemlzKvEmlfuqYeZNKoxYsofToVrVPoO0gx+Orwav0+WuqjtIz10PN8XY/lY51BwEE1bWra22obmRWRRErdtRHrY+vaWhnIG32bwau2BxsnZ2kX9DF1qMkBsN6QkiluivYit6pf0qK1FCx+On/EFgihKjDp7N/3mh/Hsg32pdwaYV/CHgJeA94DfielLIjhuvHDaugVwLDqqcPFBg5HthYfZybygrYe/SUWfowJ8jdjCWoyto3tTpVz9W51erU6qG0sbrRL43xih31fKW0H9/51T4eWLsXgBfuG8fiW8vMAix2njiArZePdUw7D7eaBdCj8dV/aHJpcK+awHYHOtykGoY1qSWReXfCGWODqZBkR9eJKBgpMIJnRRqGcASqJAILklgFRpW3lQfX7qOytB9v1LYwsSyf3XVt3DKikCrvyS4qHqsBGKDEyHWvVCSbDjRydX7voCvMQJWKKlgyo3xgl3MtWLefksLe/PC2EabtYVZFMX9+v5mSwt7MKB/Iz179gIudksW3lNGnVzeWbTvCkqnD2F3XxvybS7r0fdOBRrYeavZTGQFB7lcxOw+3RCdgw/iAm5PbX8Zgl5rBzpfeDfmSNGmKk5iEUKolpdtXarDzZ4xIb5tjE6CGyvo0DOEIXBmu2FEfNAVwTUM7S6YOo8p7kollBbxV18bEsgKqvCdZMnVYFxWPNaJ3c00Ty7fXmRG996/Zy8bq4367iECPG5VBc9H6at72tnHuYidnzl3kP71tLN1Sy8IpJQD8j40HOXex08wIOrIoj1kVxWyoPs6FDl/78u11dO/moWeuh1/u8PKkESU8b1Ipa+/3ec8GevtsPdS1du+mA41+en5V9/faAX2i9tW386o5fOOTpsA3d1sOdwTBdlcZk27ZxS6BSSHR43fiFRRKtRSoBrv9Z67JuKmLqBhY9eGzjRWr1TtGCX7rinzpllpuHNqX3XWtpiEzEOvxK+eOYcG6/fxi22EAPAK6WXRCdh43St00eXgBy9+o46ayfN6qa+No2+fcVJbP8u11nL3QwcUOafahvuUMD67diwR65nrIzfFwtPUM5y920r2bh1EDruCdo6f8+ml37XD2A7tjgC7HOKb8Lii/C1HzEv22PsaA3f/Mp/v+J5vP38Uz93zfdz4HHiSBOzerQTojirAErkIT6emkrucm420yxu/EKygST6pUel0FoNU7BurHP3l4IRurj4f0Rrl0bAEbjAAsp5WglMoB8POQCZXGQKlPxg3ty96jp8jN8SUSuNAh8QhfcNHsiiKevrvCPP7JLbXmNfr06saTW2r51vjBfH6+kw3Vx7lxaF/+drydDgkP3VySsHrAEWOzrb7g6UnurP996QcSo/dOvLONhh1PvH/oyfRYSXbqBSf3Kxnjd2vdXYdo9U4YHn65xgxWunZAHx6ZPoLl2+t4+OUa2yhTpXJRBUFUIfJwQV5Wr5meuR7WVB0F7A2l1s/41E3FvGMI/B65OcwoLwJ8Av/aAX3YebjVVFvUt5yhV66Hbh7Bip1elm+v49HpI2hqP8uG6uOMLLqCupYzLJk6HI8IHVmcdGy21bmdZzm79bFLDWE8SMJ55iQ0SZyi5iX42TXw8rz4B+kk0zc9mcFPToOakjF+lxZAiQda6Afw0ORSRhb557EJdOVTWSqtuu4VO+rDpmhWRtgX7hvHC/eNA+DBtXtZU3U0qGdPTUM71w/O48/vN1NZmk+P3Bz+r9ED2Vh9HIBuHsHR1jMsnFLCgnX7eWDtO2w91Mzz941j5uiBXOiQnL3gc5J660gbl3XP4dHp1/HMnAqWb69DAJWl+by45yMefrkmrL47lE48LvryID/c7meaIrcTBCEWbypHKOFlZ7iLh8BMZmSsmyYYpccPljAvnuN3azWuOKCFPr7C3ivnjvFz8Vs5d4xtwW8IresORk1DOzPKB7Jy7hjTz33xrWV0SJ8nTrCEZeWD8thr6N8X3VLG4lvL+M2eY0igRzcPP7z9Wrp38/D060e42NFJ25nzpn565+FWZlcUcbFD8tyuv9Mj18Nz9/p7F82qKGb9vAmO6wGH8oGPS3nCEDn0Y63Za+1TrEniQmInvKzEKjCTuQp1ywTjtwuwIRHjd1tMQpzQOn0LyXbxe3anlw/bzjBzdJGZPyfH41PPKDfOh1+u4b2mT5lRPpAVO+q5bkAf9vz9JKOKr+C6gVew9VAzk4cXsKXmBP84ppin7izvYof4we/fZUP1cWZXFPP03deb11Z6b6v/v3LRnDy8gNcONttGGdvpxFWKZ7gUFbym6igzygcGnTxtcahDjjaiNimRuEEqfpmIHJj9bGxCJFnG1WTq9EPp0SG4wFcukhkilOOB1uk7IOFbfhsemlzKzNFFZnBU+aA8lm+vY3NNEzken61h66FmU+BPHl7Ibm8bM0cX8dHJL5g5usiMin1ocokpXANz5ew83MLsimJeO3jCHJdV7/1h2xlT9fTUneWmgbr/FT26CEeVVC1QJ65W+XDJRnGho5OZo4tC3oMuKqHyuzh845Oc7jGQUNvqaHcVSYnEDbcKlh2x6/ZjXYU6dXlMppoj1A4m6O5IZNQqPBnolT5RFu2OI9bgpj+/30xHp6RTSrNQizUASnnwPDJ9BCOL8kJ6oVgDw5TwtbonWr1ZlND/6nX92Vh9HI8HOjux9WJS57ErqKKKzAB+/Q9GLPc+qV44kWC3OrYjVZ4gbi6GEmwHk+beNMkm6wujhyPVybee3enlrSMtvFXXxo1D+1JzvJ2zFzqpLM1n/bxL1basLqJ/fv9jAFOo2glLq9rGKrCVCifQDfW+F97hfIeke45g7QM3+kX1qkhb67ns/NwfWLuXsxc6bRO2BSMW4e3aqFur8Aqq6omhIlcs6p10FKBunqhciFbvhCFVybeUaiPHA7vr2rh2wOW8c/QU5y920jPXw9+MZGh2LqLjhvZlRnnoAuFqXNaI47e9bV0EvqLTkE0ejy8L9rxJpWZUr1LjWFVHyitHXXfTgUY8QpjeQNb3QhGtC2UqVHKOsapflE46kGiNobHma091OuJoKL8LRs+5lMxM5Phea4EfMVropxBV0GT59jrmjB/MByc+A3zC9x9vKDY9iqz56pXHybvH2rvoy0NNVKEEq1LL9Oqew+JbysjN8bBg3X5W7/L6RSZXeVv9JkirHr98UJ5hixAsuqXML2FbuMkzGuGdFC+cWLDqzM+fAU+u//uxeJvE6jvvxmIo4ah5CQ6s99lDwPd4YH32pZ+IA1rox5lIfNVVQZOOTskf/3qcHGOFfVNZAaBdekAAACAASURBVC//tRHwrZR/u+cYC6eU+K3qF04pYdWb9Y768uxOL6t3ec0MnKt3/d2vetemA75rrZw7hiVTr2Xl3DFc7Ojk51sPhxSq1h3EL40oY6tLqpNVfrTCO16lGhNC4Er8i5MghK8cYzyMobGu1NMx8MiNFbLSFC3040ykXiVP3VnO9YOv5OyFTnJzBItvKeO9pk/5Smk/Nh1opLK0gH+bPYoVO+p5YO07ZgDVih31zL+5JGTwk+rLsZNnWLqllttH9Wfn4VbuvKGIpVtqzVTQV+f39jO4VpYWMKuimH+8oTisUFU7iN3eNu6vHOq3g7DuPAJTRKu8/qramGp3KrxdnQ/fTkB1nIfuvePj8x3rSj0dA4/SUSXlUrQhNwE4NUwqv/zl233ujbk5HhbfWkZ9yxk21zQBdPHe6ZYj6JmbY5Y4DGcoVamgx1x9Jbvr2sx00U6rd8Urj02wFNFOx5FWBPXTj8FwayUbjZrpaHxOIdqQmwSsK1mr/nzEgD5BBVmOB9MNUxU0WbqllpJC38pbpUm2pnu+0CG50NHJ2942vzz9Vqyr/8rSAuZNuoa36toYN7SvmS7aafWuUDuXSFQzgaqgi4ZbpxqHk9xF4XBN2uRE68zTZaUez/TH6aiScila6McJFeBkLUfYPUew/8NTQfXTHYYf/LvH2nnb22bmpe/o9AnJp+4st5Q/LDS9d+BSkrSZo4tCqpMuVdMqZu/RU8yuKIrI0yVUFapI9epWVdDFTslXr7vKLO24fHsdH7adieieBxKXNBDxIBkCyu0pAmL1MAokXSa6NECrd+KE8oC52NGJBAS+XPmLby0zPW+CrfiD+ZrbpXseWZRnBkCp4CcIHiylVtErdtR3eXSiTlHqnbe9bX4F00PFMARTCVlTPGyo9hmPbxzal3eOnuKy7jld8gJFQyh1U1LjMdyWgz7ZaHVMStHqnSRQWVrAyrljjKyWPsG/cu4Y5k0qDbn6DeauaI2m7ZnrMdM9L1i3n8W3ljG7othU/8Cl1AfXDehjnlutxOtbzjBtZH+zLx2dzvzn4ZJbqcoEuqbqKAvW7Q+5erZbcS9Yt5/NNU08M6eCfxo7mF65vn+9d46eons3j+m5FAl26hyAEQP62LqmJnUn4PaVeLwIpsLRhlfXooV+nOmW01V4BfMqUXn8p43sz4TSfJ6ZU8GCdft5+OUaNh1oNNMnbD3UzMiiPGaUD2Tc0L6s2FHPzNFFPHVnOc/MqWDTgUZz4qg53m6qmdQ1tx5qNn36VV8C+xRMH67cOSPBTiVkzTDqKzk5nO7GvfIIWHxrWcQ6/WCTy9+Ot9v6/IdSVYW6B2lXSjFZhFLhpGMsQJaghX6cUAInN8fjF+DkRHdeUtibReurOdToE3rNn541BbVVUBVe3oN3j3UtT2itY7ty7hjOXezkwbV7/QQbdK1/q1BeRCrxG/jyAT24dh/Nn55lRvlA7q8cyvI36ri/cigr546hpqE9pJAMDAZ76s5yv6Cu5dvr6JF7KRhs+fY6Xj3YZF5fsXqXl/vWvGPb70AhbvUIChVbECxIzTU2gXQhlO+8nV0D4ZsYsrGmr4vQQj9O2AU4WdvtUHn8VQbNpVtq+ep1V3UR7KEElZ0x9V+mDedChzSPB2yFlxLaqiiM8t+f8vO/sHRLLXfeUMS7x9pp/vSsX6EX8AnID9vOhPTsCRZlG+xeefB5M1knnqVbaplYlh/0HlrvTXlxXpd4g0A1Vqh+hdsJZATx9KgJpcLxM7yCz8pl2A/jVUFMExXakBsnYjESKkOuMmoGM+g6TUjmNNul1W5QUtib5dvrOHPuIp0SBvftRetn51kydRjLt1+KtgV7H3tr31RbsOyeq970BZbZ3SurG6vKJmpXcD6ae+M0o6drk7jFSrz9+50aa7VRN+loQ24CCFRtWCNPFUpvHkoNEs6lMtI0Ber4lXPHMH9SCWcvdJrCPxC1st1c08Qvth3mi/M+gZ/fuzvHTn3BmKuvpKPTJ9xVHqC3vW0AZrI3u12I2n0od1LAtD0sWl/dReBb79W8SaWMMya/cUP7OhL4Tu+NExdTVydxi5V4pzJw6pqqjbquQgv9KIlE/xvs2BwPpkvlzsMtPDJ9hBktq46P1BdeHQ+Ywis3x8OmA41BvV3Ki/M4e6GTi52+FX7bmfP0v6IHb9W1cezkGVO4Tx5eyPI36vhycZ5ZsMVOSAbL7vmH/Q3cPqq/n8AP1Nk/sPYd9h49xY3GSn/1rkv5g4KN1em9eWhyKTUN7V1UOuWD8sx74+okbrESb+Hr1HdeG3VdhVbvxEA0qoV7xg9h9a6/s2TqMDo6fROCUmtYX6tHIGK1UTA1RqB/vjW24EKHr3BLp4SbyvI50NDO2fMdXOiUfGv8YIYW9GbpllpycwQSmDSsgO9MKgmbpx8uqUtuKstnd12bGYB27OQZ1u85ZqpwHt1Qw2/2HKNXrofn7xtn5vPvabyOh249lIpH3fdU1VVIOKlSs2Rj2ogUE1MRFSFET+BNoAfQDfiDlPIxIcQ1wO+AfsBfgblSyvNCiB7Ar4ExQBtwt5TyqHGuh4EHgQ5gsZRya6hrp0roR6Kfj0T/q46dbSlKEo8CKIH9Vd441tw6qv9q16Fq2IJPVVNS2Jufbz2MlJKeuTlmDqA/7m/gfIfvf6RXroclU4ezbNthzl7opKSwN9+8cbBZweuZORUcamxnd10bE0rybWvmlhX25t1j7Vzb/3Jqmz/jW+MH8+RsX13fbz//DnePG8T08iLLBFnP8AF9+NP3borqu7xvzTtMLMv3UxM9uqGG3+9t4LtTSt1VcSvRpFL4ZnuwWpIJJfS7Ofj8OeAWKeVnQohc4C0hxKvAEuBpKeXvhBDP4hPmK4zHU1LKMiHEN4GfAXcLIb4EfBMYCRQBfxZCDJdSJch2D0owBqsOpQhUbUwozQ+ZWM167O2j+vPg2n3Mm3SNreB59WAT//7nwzx/3zjTf//z8xcBwboHb7R1NVTnsL5W1y8flGdOAEoHf2WvXL53S6kptNfe71tdb65pMncEhZf3YLmRNjn/8h4s315nrsJ//tphfr71MEhY+8A44FLef+hq8F1TdZS6ljOmwB/R/3JePdhMfu8PeHHPR/zaMi7Vx1iNqRPL8lm6pRbwFYVZvcvL+j3HmFhWYJ4/KwQ+XBKyqRC+5XcFv46eEJJKWKEvfVuBz4yXucafBG4B5hjtvwIexyf07zCeA/wBeEYIIYz230kpzwF/F0LUATcC/xmPgcQTqy46XP1Z1R6qNKDySFFqjD69uhmuiPaC59mdXkYVXUHNsXYeXLuXeZNKTK+am8r62RpBrf1dsdPLXWMH+fnFP7h2L1de1p0HbhrKmqqj9Mz1cO5iB0+/foRh/S83BbVVaG860MjmmiZ65nq40NFJw6kvzICqeZNKea/xNBuqj9O9m4e3vW1d7tOM8oFsrmky31s5dwxbahr5zZ5jps5+Yll+l3vgdDJ1glrhL91Sy+uHmtl79BRzxg/m1YPNcTl/2hFK+KaCwN2HcucEd/Uzg3BkyBVC5Agh3gU+Bl4HvMAnUsqLxiENQLHxvBg4BmC83w7kW9ttPuM6AjNlWnl2p5fndtUzbaS/UXLayP62RkSVWG3FjnozY+ac8YPZ/+EpWy+R8kF5vHqwmTnjB/PFhU6Wv1FHp4RRRVfwXtPpoFksVX/HX9OP9XuOmf7uhxp9NXdbT5/jyS21dHRKXrhvHEumDufz8x0caf7MzHZpFdoqvfM/Tx3OZd270T1HcL5D8uDavfzg99VsrD7O7IpiPALbGIKn7iw3g7ruGT+EQ43trN9zjEenj+ClhyqZM34wb9W1cVNZvnkPEmFMtXoEDR/g2124zlgbT//5dEIXR0k6joS+lLJDSnk9MAjf6vw6u8OMR7skKjJEux9CiPlCiH1CiH0tLS1OupcQrKvNv1lSG4Bv5f6X2hZKCnubx1rLBgaeB3yC51LGzAJePdjM8/eNtRU8auX+yoEm8zwCeGT6dX7HWr1xrK6f+z/8hDnjB7N0Sy13PVtl7jLGXdMPgE4pzayej04fwfWDr+witGsa2plRPtBMGLdy7hj+ccwgKgbnce5iJxuqG5lVUcSXivogJfTM9bCm6qif8AxcsW+uaTJ3O1XeVl492My3xg+mW47HHNemA42mUbXK2+rnkRNtSoTVu7ymR9AHJz7z8yByWrTFMdEI73hnpEwnMtmd06UTeUQum1LKT4AdwATgSiGEUg8NAlToaQMwGMB4Pw84aW23+Yz1GquklGOllGMLCwsj6V7cCFxtWoOS1ErdunJXxwZLc/xh2xmzXOHiW8p47WAzt4+6tCsIJni+OO/bSOX37g7Ag2v3ApeSpSndvUqZ4KuM1cKSqcN49WAzg/r25J2jpyju6/Olrj1x2i8183UD+jCyKM9st+44HppcylN3lpvJ2SpLC5g5uoi6ljN4hGBk0RW8dvAES7fU8l+nDeeF+8aZCeCCrdiPnfyCkUW+SVG5Wz45u5y1999o3oOr83v72SWU4FevI02JoKJ6HzF2F49OH+G3C1L3Py7eOdEK72xe7WaqO6eLJ/KwQl8IUSiEuNJ43gv4KvA+8BfgG8Zh9wJ/Mp6/YrzGeP8Nwy7wCvBNIUQPw/NnGGCfVCXF2Pl/r5w7hvLiPHNFbF25qxVysDD+kkKfu+PCKSUsmXotS6YOY/2eY2a5QnUNq+D5+Wu1XOz01cuVwJzxgzl7oZPndtX7JU17Zk4Fy7YdYczVV7LeqKU7b1IpFYPzOHbqLCP6X07DqS940rj+hNJ8c8u19+hJFqzbb6vqULsIa1nCQ43tnLvYSa/uOdw64io6jBX+yCKfe+nM0UXmhFTT0O5XGCXwtW0w25k3eOivd8DjV1L5yhR+N+GjiFIi2MUhbK5p4h9GFJq6/XmTSnlk+gh217VF/o8RjmiFdyavdsORqcVRXDyRO1npDwT+IoSoAfYCr0spNwM/BJYYBtl84Hnj+OeBfKN9CfAjACnlIeAl4D3gNeB7bvTcAfv6qwDvW1bE1pW7dYVsF6Fqp9NXvup2VHlb+dvxT/nW+MG8+J3xPDOnwtTxdwYoxKyVsWZVFLFiRz33PPc222tb+Nb4wbz2g8ncMsK3Y/pfWw/zwNq9dMvx8Oj0EVxXdEWXcwXuIqy7lmXbjvAv04abevqHbi7h+fvG+R2v7p/K56NW5oGvuwSz2ayMhr/zKD8pea9LymjrfbJOGnZ9PnbyC74zqcTvc/MmlbL2/hvtb34sRCu8M3W164RMLY7i4olcB2c5INBTx6oyUPppaw6bFTvqTa8fay1apz794eIErO9bC628dvAEt40awIbq4z7j6HcmmJ9fvcvLL//i5ZPPL/hdP1TwkV3wGdgXbAl2vJ3Hk+37QQKHGingd5X/YcYUqBxCwfLmRJqnyAmO4zaiDX7SwUuZR4rzDencOzESqO5RK3e1Ulcr5OZPz/qpcRZOKWHpllpyPJHldLHbaVjVP1ZdvjWNw503FJkeNYFePiOL8vAIYbszCabPDty1AF309IEG6GDZQMO+H2QFNJA2W7tKMHVPuD5Eg+OUG9GqKjJ1tZvNuFhtpVf6xK+MngrCClzp17ec8YuiDbZKjaRPVd5WHly7j9tG9Tfz9ahSiCqdgzVAy0l2yUACV80qa2aoPsV7pW9dGVV5W3nmjTqqvG22u6Vg998amezk3jq5F0HvXbYFGmXbeCMhhfcm1EofKaVr/8aMGSOTwe66FlnxxDa5u67F9nWk/GJrrbz6h5vlL7bWSimlXLGjrsu5dte1yBU76qLqkzqf9To/+uMB+aM/HrC9hjre2g/ra7t+RHpPwh0f2P9Vb9b5vf/Btufk+R9fJeVjV1z6+7f+Uh74fZdr/GJrrW1fVr1ZJ4f+cLNc9Wad7etox6YI/F6zngO/931HIb4zTWoA9skgcjXn8ccfT8rMEw2rVq16fP78+Qm/zuB+l/FlY2V85txFfvraB1Hrgqu8rfz0tQ/M9ApfHpTH7IpBDO53WZdrjh3aL6o+ne/oZMG6/bx77BMeurmEZ9+s573jnzJj9EDGXN3P7MemA41ceVl3HppcyuB+l3G+o5NF66v5srHKVa/vnziULX9r4nxHp9nPLX9ror7lM+pbPuOO64vN/jy3q54N1ceZVVHMszu95me2/K2J+ycONT87u2IQXzaSxo0d2s98X133iU3vs3BKCSfaz3G+o5MHXv2Cr35lLPmfvgfnTvtW+Lf91FwZWXcnd40bYt6bLw/KM/u89+gpJl9bwIod9Zw5d5EXdh81E9tZ73U037f1e239zxeZuPd7dHv9v0P1i9C7APqPjPh/Je1Zfzd8HuAF1XkRGt+Fr3w3NX3SAPDjH/+46fHHH19l956T3DtZgVUXHG0+lkhSM0TTJ7sAomOnvkB2Si50SpZtO2z6wQfmvVHns6ZrUNk+Vd+UfUCph/79z4epb/HFGMybVMqhxnb+UutLAQ3+KiSrekeplJQbK/irVwL7oT4zvPRr8LUHbe9FqDTKgdc4/cVF854Fy8cfyfft972eeYMOz2pyzui0AcE9VGzUdBrXkDWG3HBFr+NRPCPS/O7hCOyTyr+/6UAjK+eO4avX9WdD9XFmjC7i0ekj6JTwwNq9PGAEcdlVy7IKu9tG9WfFjnozAEoZnj84cZpF66uZVVHcJbJ3zvjBXQzYTn3prd+BtR/XDegTdlIMZ9wOds9CFZtx+n37fa/bnyCnw53+10knqEupcEUQksaerBH6oTwwYs33YhfIpCaUaKI9n93pNT1zVJ8WTilh2bYjLJxSwtZDzfx/+46Znjo7D7cwsiiPBTf7KmWdvdDJ/ZVDbQWpVdhZC7ao+IFZFcVsqD7OPeOHMHN0Ea8ebGb4gMv98tZ82HbGVniPsAhvu0lWFV9/+OUaVu/ymonfao63s3qXN6oUC4Fjc/I9Rvp9+004Lva/Tjq3/itBs6tk4ySYJmSN0A+1Ko11hR5JFS2n51MCXnnbrNhRb+qnJw8vMHPfXDugDwunlLBg3X6ee+vv9Mz10L2bh2d31jsSdqoou8oJtPNwC5Wl+aZf/O2j+vPBic/I751r5q2ZObqIB9fuM6taKeFd/dEpHn65Jug9UWP407uNfonfFt9aZrq2RoOaYKzfo/V14PcY0/edzYFUgZTfhU36LB/ZOAmmCVnnshmPotd2Ln+rd3lZtu1I0Pz4kRLMRdDOVXP59jrOX+xESviX24azfHsdHZ2SHI9g5dwxfpW4rEFdqmLXsm1HuG1UfzZWN/LI9BG+XcO6/Zy/2Mn5i52MLLqCg42fMqroCg41fmrq9JduqaVbjjCLrlgLqFtdQwPHMGf121R52+iZ62H+pJKgrpWR3qtIXVKjQgdS+aOLnrsSHZxlEA+9PQRfxd42qn9MQUHBdN5KbaKE2fP3jeXpuyvMlfq4oX2REqaXDzQzYj5371hmlA/0S5EQGMWrfNqfv28s1w64wkwVAb5c+Bc6Ornqih4cavyU2RVFfHjyc64fnMfuujbmTSrlS0VXcKFDct2APuZ11SQTOIbJwwvNa9eeOM3simIudki/XEbRJj2L1LYQEzqQyh8XByFp7MmalX68V4OBq1gVHBVL+H+g98uCdfu50NFJbo6HGeUDAZg5usgU5OArdHJ1fm8+OOEraBJsB2O36g5VE7Z8UB73vfAO5zsksyuK+aexg7p4BC1aX01ZYW/eOXqK2RXFPH339bbXnDy8kI3Vx83iJWp3crGjEwnk5nhsjc6REo9dnCYKdICW64ipRm4qiafQDxWFCZEXH4fIat46pcrb6ifsrekHANvXqoD4rIB+BI79bW+bKRQnlOaHjUC9f81epJR4PMKvL6pOr5rolFBXuYjU5wPzFT25pdYsum4di21B9QgFSSJy7miykHhPYCmaEGOtkZsR2Ak35UceahcQDKuqKNDf3c6H3CmVpQWUF+ex29vG/Ekl5udnlA+k+dOzpmADuNjRyZNb3ue9xk/5hxGF9Mz1mN441pKHAL/8i0/fvviWMtZUHWVN1VE/H/7AsS1aX82a+8eZE4W1fypNsiqtWFlawJeK+rBs2xFGFuXZGsc7OuGmsnzeqmujsjSfRUZe/5qGdp66s5yZo1sv3a8IS+hVeVvZ/OK/U3XZH+hZ1cR3ew/kiRe/Afd8P3mCP5tXu5ky9niXbnRpKcis0ukHI1KdsDKmqsRqz983lhU76v3cDq0qGOvnwrklVnlb/VI4Kx3/zNFFvHusncnDfXV1v3rdVUjgUOOnzKoo4juTSthc08Ty7XUsnFLCpgONLFi3n801TWaFL6cogQ2Xirnn5njMCeShyaV+xVXAl674+fvG+uXLt96/HA/srmtjdkURtSdOc6ix3c/Dyc+1NcJc5J/v+y0/8aym55lGQNLzTCM/8azm832/jWjcUePighkJJ5PGHu8c+C7Nqa+FvkEk2RlrGtpZMnVYl8CmZduO+OWPd+rGqQy4D79cYxY1mVCaz7SR/Vmwbj8Pv1xjXmNjdSOD+vZiQ3UjAkx/+0ON7abe/xfbDrOh+jjgU6F0dPoeVR78LxfnsfhW/wjfKm8r9615x4w3gEsRupf16MbKuWPYeqjZHI/TYCl1blVDYOfhViYPLzSzkdre5wh94b/auLJLwFROxxd8tXGl/XnijUt/3Ekh2rG7sZRgvGMwXBrToYW+QaSpj+dNKvXbHSgvmEAVj5Pdg5ogmj89C2Cugq0rdCU4Z1UU03Dq0o9sQmm+GUlbUtib+yuHdgnQemhyKZsONLKm6qhZ83f59jpyPJcmnEXrq5lYlm9OVKverOd2I2JX2TsWTilh1Zv1Ed/bmoZ2po3sz8iiPO4ZP8TM3VPfcsZ+5xPE5/1s74F+r82dU6p/XKm+fiqJZuxu3R3EOwbDpTEdWugTeYSmIqb88QHHPTOngnePtfPV665i6ZZaJg8vNN0gn7qz3NSjq+Cpy7rnAPDMG3XmKrq+5Qxrqo7SzSPo3u1SofIqbyt/ereRcxc6mVCab6z+JU9aUi48M6fCbyLre1l3s/yiNUBs/s0ltmMIxUOTS5k5uogF6/abE8+f329mc02TfQCbjRtgR04vnvj8G/Y7p1T/uFJ9/VQSzdjdujOKt/upS91ZtdAn+gjNcLuDSPO7TB5eyIbqRsYN7cuG6uNMHl7o512kDKfr503guXvHIoEqbxv3jB/CyKI8Ntc0AfDD26+lRzcPHZ3SF6m7q54cj+BfbhvOovXVvO1tI8fjK26uUi5Yx25djQcWf3diGLVLwXCosZ3zF4PUhwzExhc+547lzLjn+/Y7J4c/rnD5l5yMw/Z4l/64k0I0Y0/Ezige6qJ4x2C4NKYja7x3QhHKsycY4TJqRppxM8cDG6uPc1NZAbvrWrmpLN90g4SuE9OmAz6d/sTSfF7c8xEtn51j3NC+9L+iJ/MmlVLfcoaN1ccZ0q83/+k9yfP3+by3rhvQx3AzLWLn4VZzQppQmm/22zpRKcNxJJlHrdk3K0sLePjlGv741+P8y7ThZgbM2RXFvrw7wTycyu/q8uOoBPvMmOq4MB4kgf0K56Xl+HiH189Iohl73qAgUbxR7ozi6SVj838XE/E+XxzIGj/9eBNJHVu7960oYXL7qP6s33OMiWX57K5rM4OZ7CpQhfLbVwLqgbV7OXuh0/TLV8d89bqrzJQL1hq/gW6YqhbwLGOCCOb/Hyy4S7mXqjw+i28tY9m2I4y5ui+761r9ru+kSlk8fPEjPUdM18wUV8Z4E+9UFjoVRBd0cJbLUcKzpqGdD058yobqRmZXFHHtgCvMdrtyf4CfYJ1RPpCn7iwH/IO8ADxC+OXiUSkYrKvYVW/6dPbWVa1d+UVrJtFQuxtrhGyfXt1YuqW2y4QWONEEI54R1ZFG7kYV6atz9IQmnhPi41din/hNwOOfxNLLtEUL/TQhmlWlnUCyCkQVXNXNI/jh7df6FRUJtcJ2ulMJlRgusL7u2Qsd5oSmXDdfO3jCz+vJjmd3evmw7Yxffd4qb6uZgiKSnD1JW+nr1Wfy0Pe6CzrhmgsJNBKqlfm0kf0dexAFMxTbBVf16p5DfcsZv8/b+dU7rQ2gjvNPquaLxLXzhtpc08Sf3//YjCvwGa2PM2/SNWGFaPmgPLYeavYb96L11cwcXRSVwHfqpRWtVxeQ3W6cySYaY7Ib4wSSRMYK/Ug9NZJNYPCWinadOboICO9BFEogWYOr1PuBwVVO+xUsqEwdt3qXlxf3fMTsiiI2VjeS4+lqdFbMKB9oFoRRBWCcZDuNVxbNSL20dN79KEm2QI3US8atcQJJImPVO051wJEYXONNLEbCeBqSo+3XJUOvL9FbMP28tS9ObAXBSKssmtmq00+HcWeBOihrdfpOhFesBkKrETawQImdETYQtwoyJ/16dqe3S0rncBNLtJNRWmbRzEbvnXQQqFlg+I1Jpy+EGCyE+IsQ4n0hxCEhxPeN9n5CiNeFEEeMx75GuxBCLBdC1AkhaoQQN1jOda9x/BEhxL3xGmAwnETEhlIdOFERqZWqKlquatuq16FKJkYSvJVMnParfFAeOw+3+B0XLP+OIpKcPQprTiKlylI5iVxN+V0+Qff4J77HTBf4kB62jGxWveFMp38R+Gcp5XXABOB7QogvAT8CtksphwHbjdcAtwPDjL/5wArwTRLAY8B44EbgMTVRJAqnwivY5OBEv60mDV9e+QK/FArhMnXGUow9UTjtV6r7/3V28d/e/0ZWGuJcTSIEarxtBNkcQY0DoS+lbJJS/tV4fhp4HygG7gB+ZRz2K2CW8fwO4NfSx9vAlUKIgcA04HUp5Ukp5SngdeC2uI7GQiRCKdjk4NSAeCl1waUUCk4ydcZSjD1ROO1XMvv/1J3lrJw7xvweNr/47yzNeY6+F5qJmyEui7054kq8BWoijK4uTY+QDkgTMwAAEmNJREFULCLS6QshhgJvAqOAj6SUV1reOyWl7CuE2Az8VEr5ltG+HfghMAXoKaX8N6P9fwBfSCn/V7DrxaLTj9TPPJROP5x+W31m8vACNlY3Bq1g5TYSZcRO1HnV91CTt4Qrzp3oekC0euN0MD6mE/G0ZaSDjcCFxMVPXwhxOfBH4L9IKT8NdahNmwzRHnid+UKIfUKIfS0tLU671wWnuuNwK1YnSdWUN8rOw61GzvgWs4JVqtU1oYgk578iEjtHJOcNh/V7uPxcs/1B0eqN3Zr1MV2Jpy0jHWwEaYYjoS+EyMUn8H8jpXzZaG421DYYjx8b7Q3AYMvHBwGNIdr9kFKuklKOlVKOLSwsjGQsURFqcnCiIlKThqokpdITq9fJVtdEEp8Qjf97JHaOSP3qg/X94Zdr/L6H8wF59U2i1RtrweJestzomgiceO8I4HngfSnlMstbrwDKA+de4E+W9m8bXjwTgHYpZROwFZgqhOhrGHCnGm0JI9YALSd6azVpWCcP6+tE+/oHEukq22nOf+vxkdg5nJ43VN/BvzRjz2k/piMnjnpjLVgSR6y2kiw3uiYCJyv9icBc4BYhxLvG39eBnwJfE0IcAb5mvAb4D6AeqANWA98FkFKeBH4C7DX+njDaEkasaoZo3AtTTWVpgVlm0SqUAdvJLhq3UScCPdrz2k0oT91Z7n+N8rvIuSOOhrh4CRZtDPYnHkbYLDe6JoKMDs6CNA3qiRG7tMp2K/JoA9PC3dNYA96cBobF1Vgcq/FRG4O7oo2wKSOrE65Fo2bIBHJzPPTM9bBqV70Z2BQ4djv11bSR/c08QAqrSiwSO0c07pyRBIbF1Vgcq/FRG4O7kgm2kgzcvWW80Hdr1CuEtzmo963HWV8HU9csWl/NyrljmD+phLMXOs2c+oHYqa9mji7yS8wWKEwDBbqq3WsV6Cr9hBUnarFIYivilYQtbmSCgIs36W4rydDEbBkt9FMdNRqOcKvVaFI82KVVzs3xdFm9ByOcMA2cKFTtXtWXWFbcke4QXLWLi0TAZeDq0ZZ0N8Jm6O4to3X6qcyg6RSn+vHJwwvZWH08aOlCu3PGUmUqkkRwibSbOC3JmHJ7jVOdfrbp/tM56VwaJ2bLWp1+OnjfhFutXkrxcNxI8dDod5ydimjTgUamjewfdYqESFViiVxxB9sNqd2Oa3ZxTr1MMnT1GBRlK7lzle/1y/PTZ3cTD/WUC3d1GS30U4nTGAEnEb++IiXF7D16itkVRX7H2QnFjdWNlBT2jqrf0ajEEmk3CaZuUsFvrspd5MQYnI26/3TVjceqnnLpuDNW6Ke6cpYT75JwAtY/xUOLkeKh1S/Fg51QXDJ1GCt21Efl2RKpR08y7CZ2O4l02MXZku7GzWhI191NrDECLh13xgr9ROR/iQQn3iU1De1MG9m/y2c2HWjk2Z1exykeAoWiOi4az5ZIPXqSkW3TzR5YEZPuxs1oSOfdTSyuvC4dd7eUXj2BWIVuqgx9VmG8+JayLtcOzO+j3t96qLmLILWeM7A9UChOKM0Pe+1IxxHsXtqdN1h7NATen2CBZmmDEhrpatyMhrxBQYK0Mnh3A64dd8au9CH+BsZIVUZOVqix+psHU6+oguXxWh2nyj3SrXUHYiKdK2pFY5jMxt0NuHbcGS30460WiERlFGmgUbQC1U4oLpxSwrJtR5g2sj8TSvP9rh2tXSNVKpa01d0rXOi9ETXRGiazNX+OS8edsX768fBVD3XecCqjSGIE4u3nrq4Nl9wawefKGag6ckKi7mXKSJbveKb55OtcOmlDKD/9jBX6iQzMiiRwKVx/AgVxvAVqPCaUdAhyc0wyBXGmCck0DlbKNrIyOCtRagGnao5A/X/5oDwWrNvPwy/XmOexyxUfb511oOqopqE9YlfWtFexWEmmG51LvTeiJlvcTTNJJWdDxgr9RBCJnj5Q/6/YXNMUOlc88RWogZOUimRNlStrykmmIM40IelSw2RccWlAVTzRQj8CIvEksfPKWTl3DPdXDk2aB4zdJLViR70Z3OWK7JTJJpmCONOEpEsNk3HFpQFV8SRjdfpuwar/Vz7myYobCKWL//zcRVu7REbp7+1ItnE1nROORUomjDVD7BahdPoZG5zlBqyqlTVVR1lTdZSVc8ckLcjITkiray1aX90lmAsuqaXsDMvhCJwwnt3pJccDHZ2X+pLyCSTZwVHld6Wf4IuGwMlUqUUgvcbv0oCqeKLVOwkiULUyo3yg3/upCjIKZ5eIJVgs0I6R44GlW2rJ8fhfO+X2g3QOjnIrmaIWyTSVnA1avZMg3KomCdUvwHxPqaVmVxRz7YA+Zp/DjSvQRXThlBJW7Kh3R857TeLIELUIkBFqKq3eSQHBVCupFnih+mXN6qnSOW+sPs4j00eYx4ZT/wTm/Jk3qZTTX1yMSw4gTRQkS4BFohZxu1DNcJWcFvoak5qGdm4f1Z+lW2qNCl0tzBk/mGXbjjCyKM+cHEIlsgt0Ee3Tq5ttMjhNEkiUnt1OaN/6r/YG8kC1SKbo/tMYrdPXmJQPyuPlvzYysayADdWNTB5eyKsHm1kydZif7SFYrqBAe8HCKSUs3VLLwikl7qhulW0kQs8ezI8ddOWwNEGv9DUmlaUFLJk6jKVbarlxaF9TtTNvUtdcQXar98A4ho5OeGT6CDo6L51fGa8Tttp3u+ogmUQbiBbqHoYS2k6M4smOUtb/D13QQl9jUuVtZcWOemZVFLGhupHZFUWs2FFvqnbUMcHy2wfaC5Ju19CqA3+icT8Mdw9jFdrJdInU/w+2aPWOxqSmod0ozdjK4lvKzNKMVtWOq/Pba9WBP9G4H4a7h7FGNEfrEhlNPpxEqbfSPC+PXulrTAI9c6yreIVbvZKAzEtwFivRBKKFu4dODbbx7FO0K/Z4/z9kyM4h7EpfCPGCEOJjIcRBS1s/IcTrQogjxmNfo10IIZYLIeqEEDVCiBssn7nXOP6IEOLexAwne0hE4XdXr+KdkGkJzuJBpIFo4e5hPPLvRNqnaFfs8f5/yJCdpBP1zlrgtoC2HwHbpZTDgO3Ga4DbgWHG33xgBfgmCeAxYDxwI/CYmig00ZGIwu9pn0I5C6IpE46Te5jsiOZoV+zx/n/IkJ1kWKEvpXwTOBnQfAfwK+P5r4BZlvZfSx9vA1cKIQYC04DXpZQnpZSngNfpOpFkFbGu1GOtrZuRZEMWyETjxnsY7Yo93mPJkJ1ktDr9/lLKJgApZZMQ4iqjvRiwmuYbjLZg7V0QQszHt0tgyJAhUXbP/cSS2EwRGP2a1QJfkeHRlEnBbfcwFjtCPMcSqz3DJcTbe0fYtMkQ7V0bpVwlpRwrpRxbWFgY1865iXis1FNVrFyjSSpu2X24pR8xEu1Kv1kIMdBY5Q8EPjbaG4DBluMGAY1G+5SA9h1RXjtjcLpSt0tytnqXl2XbjvD8fWOTlqo54ehAGk0w3LL7cEs/YiDalf4rgPLAuRf4k6X924YXzwSg3VADbQWmCiH6GgbcqUZbVuN0pW5ntF227QhLpg5LX0+bQLKgTF3WkgG+7ZlE2NTKQojf4lulFwDN+LxwNgIvAUOAj4B/klKeFEII4Bl8RtrPgfullPuM8zwAPGKc9kkp5ZpwnUvn1MrhCIxsDXwd7PiMTVH89KggkZqDfR4imvQk2ZXKNEDo1Mo6n36KiCbfvrX0orXEYUaQSfnYNZfQk3lK0Pn0XUikka3BkpxlDFlQpi4ryRDf9kxC595JA8KVOMwIdGBVZpIhvu2ZhBb6CSReqRLSPj2CEzLEHU4TgJ7MXYfW6SeQSI21Gk3CSKU7rHbFTfo90IbcFJLxXjfxJB4/jGjP4fRz6SjAtAdNdMTru07B/Q8l9LV6J8EEKy2oCSAefvrRnsPp59I1liBDskMmlc1L4OX58fmuXXb/tdBPMDpVQmhMu0c8fhjRnsPp51z243WM9qCJjJqXYN8LdHEhjva7dtn910I/gWSF102MqGhjGY8fRrTncPo5l/14HaM9aCJj+xMESQ0W3XftsvuvhX4CyQqvmxhR96SJfPsDIvlhRPvjcvq5RP54E5mqQHvQREYowR7Nd+2y+6+FfgJxS1GSRFTZiieVpQVUD1vM57K7/xuR/jCi/XE5/VyifryJthVod9jICCrYRXTftcvuv/beyQLc7jqq+vOTkveoOLKcgbQhssl7R6cqcBd23jYIGPsAzFiWsm5FgnbZ1LjWddTtE1JS0HmH3Ec6uuZa0Ll3NK6tshXK7uGWPiYcJ3mH0lwIpR0ZkDc/GFqnn4HY6fBX7/KyetffXec66ha7R0oJZytI1/gAjSvRQj8DCSy6snqXl6VbalkydZh2HXUj4Qx9bokPsHoY/ewa358ujJJ2aJ1+hmLV4a/e9XeWTB3GvEmlfu+Hyt2vcRFu0PnbGjct6LQOrkKnYchCrDr8eZOu8RP46n0t8NMENwT32O02rKRDZLIG0EI/Y9HpHzIINwT3OIlEdXtkMuh6vWihn5Ho9A8ZhhuCe5zsKtye1kEbxAGt089Ioqm/q9GEJBN0+lkUBKf99LOMSOvvajRhsXoStR8D4QHZ6Wvr1Q9u/5m7BT4kL2Gey2MqtHpHo9E4o/yuS/YFJfABLoYw8DohWXr2eBnEQ/U3DVRIWuhrNBrnxDtmIJlCMh4G8XD9dUtMRQi00NdoNM6Jt4okmUIyHgbxcP1Ng5oLWqev0Wic4yRPUCQkW0jGmlMnXH/jfX8SgF7pazQa58Q7ZsANgWeREK6/boipCEPShb4Q4jYhxAdCiDohxI+SfX2NRhMD8Y4ZSAMh6Ue4/rohpiIMSfXTF0LkAIeBrwENwF7g/5ZSvmd3vPbT12iyAJe7OHYhDfrrJj/9G4E6KWU9gBDid8AdgK3Q12g0WUC65a5Pt/4GkGyhXwxYrRwNwHjrAUKI+cB84+U5IURmhco5owDIxpwJetzZhR534rg62BvJFvrCps1PvySlXAWsAhBC7Au2Rclk9LizCz3u7CLV4062IbcBGGx5PQhoTHIfNBqNJmtJttDfCwwTQlwjhOgOfBN4Jcl90Gg0mqwlqeodKeVFIcQiYCuQA7wgpTwU4iOrktMz16HHnV3ocWcXKR23q1MrazQajSa+6IhcjUajySK00NdoNJoswrVCP9PTNQghjgoh/iaEeFcIsc9o6yeEeF0IccR47Gu0CyHEcuNe1Aghbkht750jhHhBCPGxNd4imnEKIe41jj8ihLg3FWOJhCDjflwIcdz4zt8VQnzd8t7Dxrg/EEJMs7Sn1e9ACDFYCPEXIcT7QohDQojvG+0Z+52HGLM7v28ppev+8Bl5vUAJ0B04AHwp1f2K8xiPAgUBbf8T+JHx/EfAz4znXwdexRfnMAHYk+r+RzDOm4EbgIPRjhPoB9Qbj32N531TPbYoxv048F9tjv2S8T/eA7jG+N/PScffATAQuMF43gdf2pUvZfJ3HmLMrvy+3brSN9M1SCnPAypdQ6ZzB/Ar4/mvgFmW9l9LH28DVwohBqaig5EipXwTOBnQHOk4pwGvSylPSilPAa8DtyW+99ETZNzBuAP4nZTynJTy70Advt9A2v0OpJRNUsq/Gs9PA+/ji8TP2O88xJiDkdLv261C3y5dQ6ibmI5IYJsQYr+RegKgv5SyCXz/SMBVRnum3Y9Ix5lJ419kqDFeUCoOMnTcQoihQAWwhyz5zgPGDC78vt0q9MOma8gAJkopbwBuB74nhLg5xLHZcD8g+DgzZfwrgFLgeqAJ+IXRnnHjFkJcDvwR+C9Syk9DHWrTlpZjtxmzK79vtwr9jE/XIKVsNB4/Bjbg29o1K7WN8fixcXim3Y9Ix5kR45dSNkspO6SUncBqfN85ZNi4hRC5+ITfb6SULxvNGf2d243Zrd+3W4V+RqdrEEL0FkL0Uc+BqcBBfGNUXgr3An8ynr8CfNvwdJgAtKutcpoS6Ti3AlOFEH2NLfJUoy2tCLDDzMb3nYNv3N8UQvQQQlwDDAPeIQ1/B0IIATwPvC+lXGZ5K2O/82Bjdu33nWrLdwiL+NfxWcG9wKOp7k+cx1aCzzJ/ADikxgfkA9uBI8ZjP6NdAL807sXfgLGpHkMEY/0tvq3tBXwrmQejGSfwAD6DVx1wf6rHFeW41xnjqsH3Yx5oOf5RY9wfALdb2tPqdwDchE8lUQO8a/x9PZO/8xBjduX3rdMwaDQaTRbhVvWORqPRaBKAFvoajUaTRWihr9FoNFmEFvoajUaTRWihr9FoNFmEFvoajUaTRWihr9FoNFnE/w9bgdeVWs/DCwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(xSA, zSA, 'x')\n",
    "plt.plot(xSB, zSB, 'o')\n",
    "balanceMAX = 2700\n",
    "incomeMAX = 6200\n",
    "plt.axis([-1, balanceMAX, -1, incomeMAX])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [],
   "source": [
    "xS = xSA+xSB\n",
    "zS = zSA+zSB\n",
    "defaultSA = list(np.zeros(len(xSA)))\n",
    "defaultSB = list(np.ones(len(xSB)))\n",
    "defaultS = defaultSA + defaultSB\n",
    "for i in range(len(defaultS)): \n",
    "    defaultS[i] = int(defaultS[i])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [],
   "source": [
    "XUS01 = list()\n",
    "for i in range(len(defaultS)):\n",
    "    XUS01.append([xS[i],zS[i]])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "(A) Find the Accuracy and the Mean Test Error Rate (using the average of several Train-Test splits) for all the above methods (K-NN ($K=1,\\ldots,100$), Logistic Regression, LDA, QDA).\n",
    "\n",
    "(B) Order the methods by their quality. Which one is better? Why?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exercise 6 (non-linear predictors) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Generate again an artificial dataset where the (Balance,Income) tuple is generated from two Normal distributions as the first dataset. You can also use non-zero covariance between the variables.\n",
    "\n",
    "Then, suppose that the values of (Balance, Income) are not observed, but rather the triplet of predictors: \n",
    "\n",
    "($\\mathrm{Balance^2},\\mathrm{Income^2}, \\mathrm{Balance\\times Income}$).\n",
    "\n",
    "(A) Find the Mean Test Error Rate (using the average of several Train-Test splits) for all the above methods and specifically: 1NN, 3NN, 10NN, LR, LDA, QDA.\n",
    "\n",
    "(B) Order the methods by their quality. Which one is better? Why?"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.12"
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 },
 "nbformat": 4,
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