Cancer de la Prostate.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Chargement des librairies et des données"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# coding: utf-8\n",
    "%matplotlib inline  \n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "from sklearn import linear_model\n",
    "from sklearn.linear_model import Ridge, RidgeCV\n",
    "\n",
    "import warnings\n",
    "warnings.filterwarnings(action='ignore')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "raw_data = pd.read_csv('prostate_dataset.txt', delimiter='\\t')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>col</th>\n",
       "      <th>lcavol</th>\n",
       "      <th>lweight</th>\n",
       "      <th>age</th>\n",
       "      <th>lbph</th>\n",
       "      <th>svi</th>\n",
       "      <th>lcp</th>\n",
       "      <th>gleason</th>\n",
       "      <th>pgg45</th>\n",
       "      <th>lpsa</th>\n",
       "      <th>train</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
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       "      <td>-1.386294</td>\n",
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       "      <td>-0.162519</td>\n",
       "      <td>T</td>\n",
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       "      <th>2</th>\n",
       "      <td>3</td>\n",
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       "      <td>2.691243</td>\n",
       "      <td>74</td>\n",
       "      <td>-1.386294</td>\n",
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       "      <td>-1.203973</td>\n",
       "      <td>3.282789</td>\n",
       "      <td>58</td>\n",
       "      <td>-1.386294</td>\n",
       "      <td>0</td>\n",
       "      <td>-1.386294</td>\n",
       "      <td>6</td>\n",
       "      <td>0</td>\n",
       "      <td>-0.162519</td>\n",
       "      <td>T</td>\n",
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       "      <th>4</th>\n",
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       "      <td>-1.386294</td>\n",
       "      <td>6</td>\n",
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       "      <td>T</td>\n",
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       "    <tr>\n",
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       "      <td>6</td>\n",
       "      <td>-1.049822</td>\n",
       "      <td>3.228826</td>\n",
       "      <td>50</td>\n",
       "      <td>-1.386294</td>\n",
       "      <td>0</td>\n",
       "      <td>-1.386294</td>\n",
       "      <td>6</td>\n",
       "      <td>0</td>\n",
       "      <td>0.765468</td>\n",
       "      <td>T</td>\n",
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       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>7</td>\n",
       "      <td>0.737164</td>\n",
       "      <td>3.473518</td>\n",
       "      <td>64</td>\n",
       "      <td>0.615186</td>\n",
       "      <td>0</td>\n",
       "      <td>-1.386294</td>\n",
       "      <td>6</td>\n",
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       "      <td>0.765468</td>\n",
       "      <td>F</td>\n",
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       "      <th>7</th>\n",
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       "      <td>58</td>\n",
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       "      <td>-1.386294</td>\n",
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       "      <td>-1.386294</td>\n",
       "      <td>6</td>\n",
       "      <td>0</td>\n",
       "      <td>1.047319</td>\n",
       "      <td>F</td>\n",
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       "      <th>9</th>\n",
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       "      <td>0.223144</td>\n",
       "      <td>3.244544</td>\n",
       "      <td>63</td>\n",
       "      <td>-1.386294</td>\n",
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       "      <td>-1.386294</td>\n",
       "      <td>6</td>\n",
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       "      <td>1.047319</td>\n",
       "      <td>F</td>\n",
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      ],
      "text/plain": [
       "   col    lcavol   lweight  age      lbph  svi       lcp  gleason  pgg45  \\\n",
       "0    1 -0.579818  2.769459   50 -1.386294    0 -1.386294        6      0   \n",
       "1    2 -0.994252  3.319626   58 -1.386294    0 -1.386294        6      0   \n",
       "2    3 -0.510826  2.691243   74 -1.386294    0 -1.386294        7     20   \n",
       "3    4 -1.203973  3.282789   58 -1.386294    0 -1.386294        6      0   \n",
       "4    5  0.751416  3.432373   62 -1.386294    0 -1.386294        6      0   \n",
       "5    6 -1.049822  3.228826   50 -1.386294    0 -1.386294        6      0   \n",
       "6    7  0.737164  3.473518   64  0.615186    0 -1.386294        6      0   \n",
       "7    8  0.693147  3.539509   58  1.536867    0 -1.386294        6      0   \n",
       "8    9 -0.776529  3.539509   47 -1.386294    0 -1.386294        6      0   \n",
       "9   10  0.223144  3.244544   63 -1.386294    0 -1.386294        6      0   \n",
       "\n",
       "       lpsa train  \n",
       "0 -0.430783     T  \n",
       "1 -0.162519     T  \n",
       "2 -0.162519     T  \n",
       "3 -0.162519     T  \n",
       "4  0.371564     T  \n",
       "5  0.765468     T  \n",
       "6  0.765468     F  \n",
       "7  0.854415     T  \n",
       "8  1.047319     F  \n",
       "9  1.047319     F  "
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "raw_data.head(10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(97, 11)"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "raw_data.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "C’est un jeu de données assez classiques relativement petit, avec 97 observations et 9 variables. Nous allons ici définir comme target y la quantité d’expression de l’antigène qui est associée à la détection de ce cancer (la colonne lpsa du dataset). Les autres variables sont des constantes associées.\n",
    "\n",
    "On récupère nos variables explicatives pour la régression, qu'on place dans une matrice X et notre variable expliquée y à part. On ne récupère pas la dernière colonne du dataset qui est un booléen associé à la présence du cancer, car on ne traite pas les variables discrètes dans ce TP."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "X_train = raw_data.iloc[:60,1:-3]\n",
    "y_train = raw_data.iloc[:60,-2]\n",
    "X_test = raw_data.iloc[60:,1:-3]\n",
    "y_test = raw_data.iloc[60:,-2]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Baseline : régression linéaire classique"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.864149965701444\n"
     ]
    }
   ],
   "source": [
    "# On crée un modèle de régression linéaire\n",
    "lr = linear_model.LinearRegression()\n",
    "\n",
    "# On entraîne ce modèle sur les données d'entrainement\n",
    "lr.fit(X_train,y_train)\n",
    "\n",
    "# On récupère l'erreur de norme 2 sur le jeu de données test comme baseline\n",
    "baseline_error = np.mean((lr.predict(X_test) - y_test) ** 2)\n",
    "\n",
    "print(baseline_error)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Régression ridge"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "On appelle alpha le coefficient de régularisation.\n",
    "On va en tester un certain nombre afin de déterminer celui qui est le plus optimal."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "n_alphas = 200\n",
    "alphas = np.logspace(-5, 5, n_alphas)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "On peut maintenant tester toute les régressions ridges avec les différentes valeur de l'hyperparamètre α . On récupère les poids des différents coefficients de la régression associées ainsi que l'erreur quadratique."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "ridge = linear_model.Ridge()\n",
    "\n",
    "coefs = []\n",
    "errors = []\n",
    "for a in alphas:\n",
    "    ridge.set_params(alpha=a)\n",
    "    ridge.fit(X_train, y_train)\n",
    "    coefs.append(ridge.coef_)\n",
    "    errors.append([baseline_error, np.mean((ridge.predict(X_test) - y_test) ** 2)])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "On peut afficher l'évolution de la valeur des différents poids associés aux paramètres :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "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": [
    "ax = plt.gca()\n",
    "\n",
    "ax.plot(alphas, coefs)\n",
    "ax.set_xscale('log')\n",
    "plt.xlabel('alpha')\n",
    "plt.ylabel('weights')\n",
    "plt.title('Ridge coefficients as a function of the regularization')\n",
    "plt.axis('tight')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "La valeur de alpha diminue les poids de tous les paramètres de la régression. \n",
    "Etudions maintenant la valeur de l'erreur quadratique :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "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": [
    "ax = plt.gca()\n",
    "\n",
    "ax.plot(alphas, errors)\n",
    "ax.set_xscale('log')\n",
    "plt.xlabel('alpha')\n",
    "plt.ylabel('error')\n",
    "plt.axis('tight')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Comme on peut le voir, la régularisation diminue l'erreur sur le jeu de données test. Vers alpha=10, le minimum semble se trouver pour la régression ridge. On peut récupérer la valeur minimum:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[2.864149965701444, 2.064827060795022]"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "min(errors)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "La première valeur correspond à l'erreur avec la régression linéaire classique et la seconde valeur correspond à l'erreur avec la régression Ridge."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Régression Lasso"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "On teste aussi un certain nombre d'hyperparamètres pour appliquer le lasso"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "n_alphas = 300\n",
    "alphas = np.logspace(-5, 1, n_alphas)\n",
    "lasso = linear_model.Lasso(fit_intercept=False)\n",
    "\n",
    "coefs = []\n",
    "errors = []\n",
    "for a in alphas:\n",
    "    lasso.set_params(alpha=a)\n",
    "    lasso.fit(X_train, y_train)\n",
    "    coefs.append(lasso.coef_)\n",
    "    errors.append([baseline_error, np.mean((lasso.predict(X_test) - y_test) ** 2)])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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YQkpFLs2rD3D4jveof3znoA5bpXpc/OxTS/j0aVP5+at7+PYzmjjGm6QmDRG5QES2i8guEbktxvyviMgWEdkoIqtFZGoy4lRq3EnJhOsehZRs+P21eDL8TPj0XIq+soSMUybSuq6a6h+t5dgfthM+5o+5isD+Jhr/so9IU/c9E5clfPPSk7lhRTn3/3UvP35hx0iMSI2QpF09JSIuYAdwPlAFvAdca4zZ0qXPucA7xpg2Efk8cI4x5hN9rVevnlJqAKrWwq8+AjPOhWsf7XihU6QlSPOrVbS8dQgMZCwrJvu8MlxZXowxtL59mIY/7QHbIB6LzLNKyP5QmfOGxCjbNnz98U08uqaSf75gNp8/Z0ayRqniEO/VU308NjPhlgO7jDF7AETk98ClQEfSMMa83KX/28CnRjRCpca7kiVw4R3wzD/C6z+Es78GgCvTS+5F08laOYWmlw7Q+u5h2tbVkHV2CZGWIK1vHSZ1dj7Zq8pofq2K5tUHCB1qoeBTczsSh2UJ371iPv5whO//eRuFWSlctaQkmaNVwyCZSWMKUNmlXgWc2kf/G4HnYs0QkZuBmwHKysoGFYwJhfBt+qDLSrutv2vl+HK3O2x76xvnunpb30Di6VY+PoZe1zGQeLptov8/H7Es51+xltVR7mhzuZx4XK7O93+rkbP0Rtj3Brz2X84zqnJLO2a5clLIu7yCzJVTaPrzPppe2A9A5sop5Hx0GmIJBdfNobnsII1P76Hl7UNknTGlc3lL+O+PL+RoS4CvP76RqQXpLCvX+zjGsmQenroKuMAY89lo/dPAqcaYW2L0/RRwC3C2MSbQc35Xgz08FT52jJ0rhvbyGjVM2pNKeyKJmWgsRDoTjng8iNcDHo9Tbp/cPeqxptQUrLR0rPQ0rLQ0JC3t+Hp6OlZaGlZGBuIah89ZaqiEu5c47xy/7Ke9dgvsbyJ81Ef6KRO7JXdjDEd/vZng/iaKv7IEV073d3k0toW47J43aPSFePKLZ+irZEehsXB46iBQ2qVeEm3rRkRWAbcTR8IYCldmJqW//KVT6ZZIu5TN8WUTo63nYh2VXvr2u44BxNNtfd0W62cdvcbTyzo6ynGMyTZgbIxtQ8R2yhEbbBtjR5z5dqRjvjH2cW2xlulYNhLBhMOYUKj7FAhit7Qe3x4KQfTTjpYHwsrMxJWTg5WTjSsnB1d2Dq7sbFy5OVjZ2bjz8nAXFnZMrvz80Z9ockth+U3w9j2w4laYODtmt5Sp2aRMzT6uXUTIu3QGR368joan91DwyTnd5ueke/jl9Uu5/Kdv8NkH1/DHL6wgMyWZf/2owUrmnoYb50T4eTjJ4j3gOmPM5i59FgOP4eyR7IxnvXoiXA2UCYex/X7stjaMz4ft82G3+bB9x9ftllYiTY3YjY1EGpuINDY6U5NTjpmAXC7cBQVOEikqwlMyBW9JKZ7SErylpXhKSrBSR8HD/tqOwZ0LYdpZcM1vB7WKppcP0PT8fibcOI/Uirzj5r++s5brf/UuH1s4mR9/YpEeihxFRv2ehjEmLCK3AM8DLuBXxpjNIvJNYI0x5ingv4BM4H+jP1wHjDEfS1bManwStxtXZiauzKE9h8kYg/H5iNTXE66tJVRTQ7i2ttsUqqqi9e23MW3d74FwFxbiKStzkkhZKd7SMjyTJ+EuKsI9cSKWN853hg9Fej6c/kV45XtQvQWK5g54FVkrS2h9r5rGZ/aS8qVcxOqeFM6sKOTvV83iRy/sYMWMCVy9rLSXNanRSh9YqNQIM8YQOXaMUGUlwcoqQlWVBA9UEqw8QOhAJeGamuOWcRUU4CkqcpJIcRHe0jK85eV4y6fiLSlBhiuptB2DH8+D2RfBlb8Y3Co21nLskW3kXVFBxvLi4+ZHbMOn73+HdQfqefrWlcycqE/GHQ30KbdKjVG2z0fo4EFCR6oJVx8hVF1N+Eg1oeojzueRI9iNjZ0LWBaeKVPwlpeTUlFB6pzZpM6ejXfaNMQ9iIMJz9/unNu4dR3kTxvw4sYYau/dSLjOR/HXlmLFOHdR0+TnIz95jdL8dB7//ArcLn04RbJp0lBqHIs0NBDcv5/gvn0dn4F9+wju2o0JOndoS0oKKRUVpC2YT/rSpaQtWYqnaGL/K286DHcugEWfhEt+Mqj4AgeaqL1nA9kfmUr2ubEvg39m42G++Mg6/vH8Wdx6XsWgtqOGz6g/p6GUGjxXbi5pubmkLVzYrd2EQgT27iWwbRv+LVvxb91KwxNPUv/I7wDwlJaSvmQJ6aedSuZZZ+HOj3HPRPYkWHgtbPgdfOjfIKNgwPGllGWTOief5lcPknnaZKy04/+quWjBJJ77YBJ3vbSTVXOLmDPp+Kuy1OijexpKjXMmHMa/dStta9fiW7uWtjVridTXgwhpCxaQec7ZZJx1Fqlz5jj3wQDUbIV7ToPz/h3O/MdBbTd4qIWau9aT9aFScj5cHrNPfWuQVT96lakF6Tz2uRVYll5NlSx6eEopFZOxbfxbttLyyiu0vPoq/k2bAHDl55O+fDlp8+eRevI8Ujd+C1fLHvjyBufJuINQ99ut+LfXU/zPy3BlxF7HY2ur+Or/buB7V8zn2uWDe6KDGjpNGkqpuIRra2l9801a3ngD37r1hKqqOuZ5s8KkLl5K2jmXkL54MSkVFQM6uR6qbqX6x+vIXlVG9qrYD6k2xnDNfW+z7UgzL/3j2RRkpsTspxJLk4ZSalDC9fX4P9iMf9MmfE/9D74aiLTZAFjp6aQuXEDa/AWkVMx0rtKaObPPm/SOPhh9vMhty7G8se+M31ndzEd+8ho3nTWdr184J2YflVh6IlwpNSjuvDwyz1xJ5pkrYVEE8/zthC5/Al9lK77162l7fz11998PkQgA3vJysj96IdkXX0zK9OnHrS/rnFJqf7aB1nePkLVyynHzASqKsrhowWR++/YBvnDOTHLSBnc4TCWeXhytlOrdwmsRtxfv4T+Tc8nFFP/7vzH98ceZvX4d05/+E8Xf+AbuoiKO/uxe9lx8CbX33IOJJpN2KVOz8U7LpuX1g5iw3eumPnf2dFoCYR5+e3+iR6WGQJOGUqp3GQUw5xLY8HsIdb7BT7xeUmbOJO+aTzD1wQeoeO1Vsi+6iKN33U3lTTcRPnq022qyzi4l0hjAt+lozy10OHlyDmfPKuTXb+zFH4r02k8llyYNpVTfltwA/gbY+lSvXdyFhUz+wfeZ9O1v0bZ2HXsvvwJf9KosgNRZebgnpNHy5qE+N/X5c2ZwtCXIH9dV9dlPJY8mDaVU38rPhPzpsPaBPruJCLlXXUX5H/6AeL3s//Tf0Pzii848S8g8fRLBymaClc29ruPUafmcPDmbB9/cx3i7SGe80KShlOqbCJzyN7D/DTja/xsKUk+aRfmjvydl1iyqbv0SdQ88AED6kiIkxdXn3oaIcMOKcnZUt/DW7rrhGoEaRpo0lFL9W/RJsNz97m20c0+YwNQHHyDr/POpueP71N51N5LiImNJEW0ba4k0B3td9pKFk8nP8PLAm/uGJ3Y1rDRpKKX6lzkRTvoovP8IBFvjWsRKS2PKT35MzlVXcvSee6i9807STyuGiKF1bXWvy6V6XFyzrJQXt1ZTeayt134qOTRpKKXic/ot4DsGa34d9yJiWUz65jfJ/fhV1N37cxoevg/vtGza3jvS5zmLT53m3D3++/cODDlsNbw0aSil4lN2qvMq2DfuhEBL3IuJZVH8n/9J7tVXU3fffZjmbYTr/AT3Nva6zOTcNM6eVcgf1x4kYusJ8dFEk4ZSKn7n/Qe01sBffzSgxcSyKP7Gf5B90UUc+/V3wWVofa/3Q1QAH19aypEmP3/d1fu9HWrkadJQSsWvZCksuAbevBsOvT+gRcWymPS975K+ZBHBPa/TtqEG2xfutf95cyaSm+7hD2sqhxq1GkaaNJRSA/OR70L6BHjsMxDo/Z6LWCyvl5L/uRtCe8CGptVbeu2b4nZx2aIpvLC5moa23q+2UiNLk4ZSamAyCuCq+6F+Hzz9DwNe3JWdTcmd38Ruq6Hpz5uItPR+fuSqJSUEIzZ/2tD3neRq5GjSUEoN3NQVsPIrsOl/oW73gBf3TplC+pJJWJllHL79O71eSTVvSg4VEzN5euPhoUashokmDaXU4Cy53vnc9vSgFs+9eDEAgT1+6h96qNd+F86fxLv7jlHT7O+1jxo5mjSUUoOTWwaTFsLWwSUNd0Ea3rIsvLM/RM1//xD/ltjnNy6aPwlj4PnNfV9tpUaGJg2l1ODNuQSq3oWmwR0+Sl88EXHl4p4ym4Nf+Ufs1uPvNp9VlMmMwgye1UNUo4K+uU8pNXizL4GXvu0colp+04AXT5s/gYY/7SZ48XXw03/h1U9eyAtfXIrfAyE7RMgOEbbDyOQmNjS2csWT6SARQhGnvX1+yA5hMAjOa2dFhI7/oq+ibS+3/+f8H2f/6Ge7mP17tPXVv337LnF1TpYLSyzc4sYSC5fV2d7exxILtxWdLz3mWy6K04u5ctaVg/su46RJQyk1eIUnQUHFgJNGU7CJtw69xWtVr7EifTqF1bn89tIUbn6ylhU/epmHbijFpKfgFjcel4cJGakcPBbGDmVRXpCN23LjsTzdPtv/kjYYjDEYnJPr7eX29q594ulvMERnHd/etX+X5Xrr3z6vvc02NhETIWgHiUQiROwItrEJmzC27cyLGKe9vWwbm7Ad7li267wFhQvGd9IQkQuAOwEX8EtjzB095qcADwFLgDrgE8aYfSMdp1KqFyIw52J44y7w1UNaXsxuwUiQLXVbWFO9hterXmdD7QYiJkK2N5vZ06ewcONEvvuFlwivfBPrn/6JH/wpm9J7f44rMwNw/mI+979fIbspg59ctXwkRzhmdE1kiZS0pCEiLuCnwPlAFfCeiDxljOl6NuxGoN4YM1NErgG+D3xi5KNVSvXqpIvgrz+GXath/lUANPgb2Hh0I+tr1rOueh0fHP2AoO3coDcnfw5/O+9vObPkTOZPmI/lNxz64B1CmxvIvfgixGVx8Ktf4+CXbqX03nsRrxcR4fy5RTzw5j6a/SGyUj3JHPGo1POQWKIkc09jObDLGLMHQER+D1wKdE0alwLfiJYfA/5HRMToK72UGjXCkxawM7uQjZsfZGPjejbWbmRf0z4A3OJmbsFcrpl9DadMPIVFExdRkFbQfQXpkFqRi29jLTkXlJN94YXYPj+H/+VfOPT1f2Hyf/0AsSzOn1vML17fy+qtNVy2eMrID1QBIMn6+1dErgIuMMZ8Nlr/NHCqMeaWLn0+iPapitZ3R/v0+gSzpUuXmjVr1iQ2eKUSJNAW4rVHdxDyR0Z0u76mShqPrCcUbIox1xCxI4TtMGE7TMTYHXOc4+rhjvMDFuAWwYPgjk7x/Nt3Sup0FmWvpCZwEJtI+8oxEeMcAmtfSfR0QeL/PT02+exmzvrp5we1rIisNcYs7a/fuDgRLiI3AzcDlJWVJTkapQZv9/padrxTTf7kjI6rchLN17SdY5WPIWLh8uRiAGNs7K4ncKNJoevVQuCcjHSLhQVYdvdEF4lO8dgf3MFk7zS8Vmpnoys6jcBx+vEiEuz9AZDDJZlJ4yBQ2qVeEm2L1adKRNxADs4J8W6MMfcB94Gzp5GQaJUaAfs/qCMzL4Vr/m15wpJGW6iNQy2HqGqpYudfX6fxyXfwFbh55dQ6asyujn6Znkxm5s5kbsHJzC2Yy9yCuUzLmYbbGhf/1lSDlMxv/z2gQkSm4SSHa4DrevR5CrgeeAu4CnhJz2eo8SoStqnceoyKZUWDShjGGBoDjdT6aqn11VLnq3PKbbUc9R3lUOshDjYfpM5fBwYW78xh4a5caieEOPzhHM4sXMT0nOnMzJ3J9NzpFKUPLg41viUtaRhjwiJyC/A8zk7or4wxm0Xkm8AaY8xTwP3Ab0RkF3AMJ7EoNa4YY/CFfRzYcZSQP4J3apBNtZvwhX3OFPHhC/loCjY5U8D5bAw20hxo7tYeNscfnkh3p1OYXkhxRjHnlJ7DZG8RPLeN5l27qTjrbL5885dxe7xJGLkai+JKGiIyA6gyxgRE5BxgAfCQMaZhKBs3xjwLPNuj7d+7lP3Ax4eyjXiF7BBb67Z2j68CZzfOAAAaq0lEQVTHsdT+dnLi6d9fn/6us45rnYPZhulZHYZ19txEP8vEs87j2uKI2zY2xpiOG6O6TdjYdvSzx7yY/WP0ab9zORQJdZa73Kncs71rvT0xACw4dA4ruJy/3/Z3+HfHfly4JRZZ3iyyvdnkeHPITslmcuZksr3ZZKdkU5BawIT0CRSmFTIhzflM96R3LH/sUBVP/+T71B7Yx9mfvpElF12mexNqQOLd0/gjsFREZuKcO3gSeAT4aKICG2nNwWY++ewnkx2GGsUEwRKr2+QSFx7L40wuT7e7lNvrqe5Usqysbm3tU5o7jVR3KmnuNOxjxYQzbb616j9Id6eT5k7rmFLdqWR7s8nwZGDJwB8ZZ4xh8ysvsvrX9+L2pnD5P/870xcvS8Cfkhrv4k0advRw0uXA3caYu0VkfSIDG2mZnkzuOe+e49p7/ius5wWEx11QeFz1+H/FDXSd8fxLsL9l4llnfxdHDvjPIo5l+vvzGtQ6e2j/y11Eun32TAAWFpYV/eySFLoul0iP/PFtcqanc0H5gmFdb1tjA6t//XN2vPU6pScv4MJbvkJW/oRh3YY6ccSbNEIici3OSelLom3j6pZMr8vLmSVnJjsMdYIK+sPUV7dRsaxo2NZpjOGDV17gtd/8ilDAz8pr/oZll16JZbmGbRvqxBNv0vgM8DngO8aYvdErnn6TuLCUOrEcrWoBA4VlWcOyviO7d/Lqb+6nausHTJl9MuffdAsFJaX9L6hUP+JNGucbY77UXokmDn2NllLDpHZ/MzD0pNFYU81ff/8Q2954lbSsbM6/+Rbmn/thxNJX56jhEW/SuB7nabRd3RCjTSk1CLUHmknP8ZKRkzKo5esPH+TdJx9jy2svYVkuTr38apZ97CpS0tP7X1ipAegzaUTPY1wHTBORp7rMysK5b2LcCPp9vPHowx317uc8u1S6zIh5Mll66du9U4zlpefsWJUYzb3E0614fEy9ntQd5vGJZUU/XR11y7Kc9o55FiJOO5Z0zpfOPlbXuuUs43J7cLndWG43Lrcbl9vTpezGcrnHzOWktZXNA97LMMZwcOtm1v/lGXa+/QaW28WCVRew/NKPk1WgJ7pVYvS3p/EmcBiYAPywS3szsDFRQSVDOBjkg5dfiNY6r/XvdutAl0rH/QD9ze/Zbjp7dLZ17du1GHsdKn6Wq0sS6ZJg3B4vntRUPN4UPKmpuL0peFJScaek4OmYnHpKWjopGRmkZGSSGp1SMjJwe1OGJSmFAhHqD7cyfXFhXP0Dba1see0lNrzwHHVVB0hJz2DpJZez5KLLyMiN/T4LpYZLn0nDGLMf2A+cPjLhJE96dg63PvCHZIcxIN2TTW8JK1b/ASTFru1xJLTuITk31Rnb7pza68a5qc7YnfVu8+32+d3n2bYNdvTmunCESDiMHQ4RCYc7ps56qEtbl3ooRCQUIhTwEwoEaKk/RjgQIBQIEAr4CQcChEPBvv7oAXC53Z2JJCubjNxcMnLzyMjJIz03zynn5pGRl0dmbn6v5xWOVrVgDEzsY08jFPCzd/0atr/5OnvWryEcDFA0vYIP/92XmL3iLDypqb0uq9RwiveO8CtwXoA0EedIhADGGJOdwNhUP+I6VKQGxbYjhINBQn4/QV8bgdZW/K0tBNpa8be0dJQDLS3421rxNTVy7GAVlZs34W9pPm59Lreb7MKJZBcWkVNYRHbhRHImFpFbPJmD251HjU+c2v3Xqa2pkX0b1rFn3XvsWfsuoYCf9JxcTj5nFfPOWUXxjIoR+bNQqqt4T4T/ALjEGLO1355KjQOW5cKbmoY3NW3Ah3zCoRBtjfW0NtTT2tBAS91Rmo7W0FhbQ1PNEXbu24OvqbHbMmKl8eR/PUNu8STSsnM4uG0L1Xt3gTGkZecwe+XZnHT6mZTOnY/l0vssVPLEmzSqNWEoFR+3x0P2hIlkT5jYa5+Q309jzRHqqw+z+tdv4U1txZPqp2rbZlrr6ymeOYszrv4U0xYtYWL5dL1kVo0a/V09dUW0uEZEHgWeAALt840xjycwNqXGLU9qKhPKyknPnUzE9rH4wpksPt95gZgxZsxc9aVOPP3taVzSpdwGfLhL3QCaNJQaguq9zmGq4mmd5zM0YajRrL+rpz4zUoEodSKq3tuEZcmwPT5EqUSL9+qpu2I0N+K8LOnJ4Q1JqRPHkb1NFJRk4vbqyW01NsR7di0VWATsjE4LcN7pfaOI/CRBsSk1rtm2oWZ/E0XT9Mp1NXbEe/XUAuAMY0wEQER+BrwOrAQ2JSg2pca1+sOthPyRbuczlBrt4t3TyAMyu9QzgPxoEgnEXkQp1Zcje5yT4EXTcpIciVLxG8jNfe+LyCs4NxyfBXxXRDKAFxMUm1Lj2uFdjaRleciZmJbsUJSKW1xJwxhzv4g8CyyPNv2LMeZQtPy1hESm1Dh3aFcDk2fm6iW2akzp8/CUiMyOfp4CTAIqo1NxtE0pNQgt9X6a6/xMmpmb7FCUGpD+9jS+AtxM98eitzPAh4Y9IqVOAId2NQAwuUKThhpb+ru57+bo57kjE45SJ4bDOxvxpLooKMnsv7NSo0hcV0+JSLqI/KuI3BetV4jIxYkNTanx6/DuBiZNz8Gy9HyGGlviveT210AQWBGtHwS+nZCIlBrn/K0h6g61MmmmXmqrxp54k8YMY8wPgBCAMaYNfdePUoNyZHcjGPQkuBqT4k0aQRFJI/rCTxGZgd7Up9SgVG2vx+Wx9PEhakyKN2n8B/BnoFREfgusBv5psBsVkXwReUFEdkY/j3s1mogsEpG3RGSziGwUkU8MdntKjSZV2+qZNCMHt0cfUqjGnniTxvXAM8A3gUeApcaYV4aw3duA1caYCpwEdFuMPm3A3xhjTgYuAH4iIro/r8a0tqYgdQdbmHLSwF4hq9RoEW/SuB/nSbcfA+4Gfi4iXx7Cdi8FHoyWHwQu69nBGLPDGLMzWj4E1ACFQ9imUkl3cEc9ACWzNWmosSnex4i8LCKvAcuAc4HPAScDdw5yu0XGmMPR8hGgqK/OIrIc8AK7B7k9pUaFqu31eFNdTNSXLqkxKt6XMK3GebLtWziPRF9mjKnpZ5kXgeIYs27vWjHGGBExfaxnEvAb4HpjjN1Ln5tx7lynrKysr7CUSqqqbfVMnpWH5Yp3J1+p0SXep9xuBJYA83De2NcgIm8ZY3y9LWCMWdXbPBGpFpFJxpjD0aQQMwGJSDbOuZTbjTFv97Gt+4D7AJYuXdprAlIqmZrqfDTV+lhwTkmyQ1Fq0OL6544x5h+MMWcBVwB1ODf7NQxhu0/hnFwn+nncK2NFxAv8H/CQMeaxIWxLqVGhapuez1BjX7yPEblFRB4F1uOcxP4VcOEQtnsHcL6I7ARWReuIyFIR+WW0z9U47+24QUTej06LhrBNpZLqwOY6MnJTyJ+ckexQlBq0eA9PpQI/AtYaY8JD3agxpg44L0b7GuCz0fLDwMND3ZZSo0EkYlO5tZ4ZpxTq+zPUmBbv1VP/nehAlBrPqvc0EvSFmXpyQbJDUWpI9BIOpUbA/g+OYVlCyZz8ZIei1JBo0lBqBOzfXEfxjBxS0uI9IqzU6KRJQ6kEa6kPUFfVwtR5emhKjX2aNJRKsANb6gAo0/MZahzQpKFUgu19v5as/FQKpuiltmrs06ShVAIF/WEqt9YzbdEEvdRWjQuaNJRKoMotx4iEbaYv1Ac0q/FBk4ZSCbTn/VpSMzz6PnA1bmjSUCpBIhGbfZvqKF9QoE+1VeOG/iQrlSCHtjcQ9IWZpoem1DiiSUOpBNm1vga316J0rt4FrsYPTRpKJUAkYrN7XQ3TFhbi8bqSHY5Sw0aThlIJULW1nkBrmIqlE5MdilLDSpOGUgmwc001KeluyubqXeBqfNGkodQwC4ci7Hm/lumLCnF59FdMjS/6E63UMDvwwTFC/ggVS4uSHYpSw06ThlLDbPs7R0jL8jDlpNxkh6LUsNOkodQw8jUH2bfxKCedWqw39KlxSX+qlRpGO96txrYNs0+flOxQlEoITRpKDaOtbx1m4tQsCqZkJjsUpRJCk4ZSw6T2QDN1VS26l6HGNU0aSg2TrW8cwnILFcv0qik1fmnSUGoYBP1htr1zhJlLJpKa4Ul2OEoljCYNpYbBjnerCfkjzD+7JNmhKJVQmjSUGiJjDB+8epAJpZkUTctOdjhKJZQmDaWG6MjuRuoOtjD/7BJ9D7ga9zRpKDVEG1+uwpvm1hPg6oSQlKQhIvki8oKI7Ix+5vXRN1tEqkTkf0YyRqXi0XTUx+51NZx85mQ8KfreDDX+JWtP4zZgtTGmAlgdrffmW8BrIxKVUgP0/upKxBIWnFua7FCUGhHJShqXAg9Gyw8Cl8XqJCJLgCLgLyMUl1Jx87eG2PrGIWYtKyIzLyXZ4Sg1IpKVNIqMMYej5SM4iaEbEbGAHwJf7W9lInKziKwRkTW1tbXDG6lSvfjg1YOEgzaLzi9LdihKjRh3olYsIi8CxTFm3d61YowxImJi9PsC8Kwxpqq/K1KMMfcB9wEsXbo01rqUGlZBf5gNqyuZOq9AnzOlTigJSxrGmFW9zRORahGZZIw5LCKTgJoY3U4HzhSRLwCZgFdEWowxfZ3/UGpEbHqlCn9riGUXTUt2KEqNqIQljX48BVwP3BH9fLJnB2PMJ9vLInIDsFQThhoNgv4w779QSdnJBXoznzrhJOucxh3A+SKyE1gVrSMiS0Xkl0mKSam4dOxlXFye7FCUGnFJ2dMwxtQB58VoXwN8Nkb7A8ADCQ9MqX74W0Os/8sByk4uoHhaTrLDUWrE6R3hSg3A2uf2EfCFWXHFjGSHolRSaNJQKk5NR31sfKWK2adP0ium1AlLk4ZScXr7id2ICKdeoldMqROXJg2l4nBwez0719Sw+MNlZOalJjscpZJGk4ZS/YhEbF57dAdZBaks+cjUZIejVFJp0lCqH5teruLYoVZWfrwCt1efZKtObJo0lOpDY62Pd57aw9T5BUxbOCHZ4SiVdJo0lOqFMYaXH96KWMLZ156kb+VTCk0aSvVq8+uHOLi9gTOunElWvp78Vgo0aSgVU0N1G2/8cRcls/OYu3JyssNRatTQpKFUD5GwzV/u34zLLZx3/Vw9LKVUF5o0lOrh7Sd2U3ugmQ99eo6+kU+pHjRpKNXFrrU1vP9iJfPOnsL0RYXJDkepUUeThlJRdYdaWP3QVoqmZbPy4xXJDkepUUmThlJAW1OQZ3+2CU+Kiwv/bj4ut/5qKBWL/maoE14oEOGZn26grSHARz83n4xcPY+hVG80aagTmh2xef6XH1B7oJkPf/Zkiqfri5WU6osmDXXCMrbhlUe2s39THWddexLTFuqJb6X6o0lDnZCMbXjlt9vY+sZhln60nHlnTUl2SEqNCUl5R7hSyWTbhpcf2sq2t4+w9KPlLNeXKikVN00a6oQSCdusfnArO9+rZvkl01h2kSYMpQZCk4Y6YfhbQzx37yYO7WzgtMums+SC8mSHpNSYo0lDnRAaatp45qcbaarzseozcznp1OJkh6TUmKRJQ417ezceZfWDWxCES7+8mMkVuckOSakxS5OGGrciYZu3/m83G1ZXMqE0kwtunkdOYXqyw1JqTNOkocaluoMtrH5wK7UHmpl/bglnXDETl0evMFdqqDRpqHElErJZ8+d9rPvzfrxpbi74u3nMWDwx2WEpNW4kJWmISD7wKFAO7AOuNsbUx+hXBvwSKAUM8FFjzL4RC1SNKQe21PHXP+yk/kgbs5YXsfLqCtIyvckOS6lxJVl7GrcBq40xd4jIbdH6P8fo9xDwHWPMCyKSCdgjGaQaG44dauWNP+7iwOY6sgvTuOiLCyifPyHZYSk1LiUraVwKnBMtPwi8Qo+kISJzAbcx5gUAY0zLCManxoBjh1pZ89w+dq2pxpPq5oyrZjL/7BI9d6FUAiUraRQZYw5Hy0eAohh9ZgENIvI4MA14EbjNGBMZoRjVKGSM4cieJjasPsDu9bW4vS4WrSpj8UfK9FCUUiMgYUlDRF4EYt1BdXvXijHGiIiJ0c8NnAksBg7gnAO5Abg/xrZuBm4GKCsrG1LcanQKBSLsXlfDxperqD3QjDfNzZILprLwvFJNFkqNoIQlDWPMqt7miUi1iEwyxhwWkUlATYxuVcD7xpg90WWeAE4jRtIwxtwH3AewdOnSWAlIjUG2bTi4vZ7t7xxhz/paQoEIeZMyOPu6k5i1vAhvql78p9RIS9Zv3VPA9cAd0c8nY/R5D8gVkUJjTC3wIWDNyIWokiEcinBwewP7Nh5l74ZaWhuDeNPcVCydyEmnFTNpZi4ikuwwlTphJStp3AH8QURuBPYDVwOIyFLgc8aYzxpjIiLyVWC1OH9LrAV+kaR4VYIYY6g/0sahHfUc2HKMym31hAMR3F6L0jn5zFpeTPmCAtweV7JDVUqRpKRhjKkDzovRvgb4bJf6C8CCEQxNJVgoEKG2spna/c0c2dPIwR31+JpDAGTmpXDSqcWUzy+gZHaeJgqlRiE9KKwSwtiG5mN+jh1upaG6jbqqFmoONFN/uBUTPeuUmZdC6dx8pszKY8qsXLInpOmhJ6VGOU0aatBCwQgtx/w01/lpPuZMjbU+6o+00VDdRiTUeS9mWpaHieXZzFhcyMSp2RROzSIjJyWJ0SulBkOThupg24agL0zQF8bfGqKtKYivOYSvOUhbcxBfs1NvawrS2hDA3xLqtrxYQlZ+CnnFGZTOziOvOIO84nRyi9P1slilxglNGqOcMQY70j7ZHeVIezlsCIcihEM2kaDtlLt+tpej80OhCCFfmIAv4iQIv5MkAr4wIX/v9026PRZp2V7Ss71k5adSNC2brPxUZypwPjNyvFguvRtbqfFMk0ZU0Bfm1d9vx0SPqBhjnLIxGBOtm+Prxo624/Q3xkDX+T2Xsbuvy7ZjJ4X2uhmmu04sl+D2WLi8LrypLlLS3HjT3KTnpONNc5OS6sab5sIbbU/L9JCW5SSJtCwvnhQ9Ka2U0qTRwY4YjuxuBBFEQNo/LecTBLE62zv7OW1EPy2XxOjTe92ywHJZWC5nWcuS7nVXz3pn2RWtu70Wbo8Ll9fC43Xh8li4PRZurys6z9I9AKXUsNCkEZWa6eHT316R7DCUUmpU039+KqWUipsmDaWUUnHTpKGUUipumjSUUkrFTZOGUkqpuGnSUEopFTdNGkoppeKmSUMppVTcxAzXcypGCRFpBHZ2acoBGnupt5e7tk0Ajg5y8z23NZA+sdr7ir1rPdaYhjKOvuKMp89Ax9JfOVnfSW/zxuJYhvLz1bU8Fn9XEvmd9BVnPH1G01gqjDE5/fZynoM0fibgvnjr7eUebWuGa9sD6ROrPd6x9DKmQY9jpMfSXzlZ38l4GstQfr76+FkbE2NJ5HcynsYSzziMMePy8NSfBlD/Uy99hmvbA+kTqz3escQa01CN5FjiKQ/WUMbR27yxOJah/Hx1LevPV3zxxNtnNI0lrnWMu8NTQyUia4wxS5Mdx1CNl3GAjmW0Gi9jGS/jgJEZy3jc0xiq+5IdwDAZL+MAHctoNV7GMl7GASMwFt3TUEopFTfd01BKKRU3TRpKKaXipklDKaVU3DRpxElEzhGR10XkXhE5J9nxDJWIZIjIGhG5ONmxDIWIzIl+J4+JyOeTHc9QiMhlIvILEXlURD6c7HgGS0Smi8j9IvJYsmMZjOjvxoPR7+KTyY5nKBLxXZwQSUNEfiUiNSLyQY/2C0Rku4jsEpHb+lmNAVqAVKAqUbH2Z5jGAvDPwB8SE2V8hmMsxpitxpjPAVcDZyQy3r4M01ieMMbcBHwO+EQi4+3NMI1jjzHmxsRGOjADHNcVwGPR7+JjIx5sPwYyloR8F0O5E3KsTMBZwCnAB13aXMBuYDrgBTYAc4H5wNM9pomAFV2uCPjtGB/L+cA1wA3AxWN5LNFlPgY8B1w31scSXe6HwCnjYByPJev7GOK4vg4sivZ5JNmxD2Usifgu3JwAjDGviUh5j+blwC5jzB4AEfk9cKkx5ntAX4ds6oGURMQZj+EYS/TwWgbOL4hPRJ41xtiJjDuW4fpejDFPAU+JyDPAI4mLuHfD9L0IcAfwnDFmXWIjjm2Yf1dGjYGMC+dIQgnwPqPwaMwAx7JluLc/6v5ARtAUoLJLvSraFpOIXCEiPwd+A/xPgmMbqAGNxRhzuzHm73H+gv1FMhJGHwb6vZwjIndFv5tnEx3cAA1oLMCtwCrgKhH5XCIDG6CBficFInIvsFhEvp7o4Iagt3E9DlwpIj9j+B41kmgxx5KI7+KE2NMYDsaYx3F+mMYNY8wDyY5hqIwxrwCvJDmMYWGMuQu4K9lxDJUxpg7nvMyYZIxpBT6T7DiGQyK+ixN5T+MgUNqlXhJtG4t0LKPTeBnLeBlHT+NpXCM2lhM5abwHVIjINBHx4pwYfirJMQ2WjmV0Gi9jGS/j6Gk8jWvkxpLsKwFG6GqD3wGHgRDOsb4bo+0fBXbgXHVwe7Lj1LHoWJI9jZdxjOdxJXss+sBCpZRScTuRD08ppZQaIE0aSiml4qZJQymlVNw0aSillIqbJg2llFJx06ShlFIqbpo0lBpmIrJPRCYMtY9So5EmDaWUUnHTpKHUEIjIEyKyVkQ2i8jNPeaVi8g2EfmtiGwV5+2C6V263Coi60Rkk4jMji6zXETeEpH1IvKmiJw0ogNSqh+aNJQamr81xiwBlgJfEpGCHvNPAu4xxswBmoAvdJl31BhzCvAz4KvRtm3AmcaYxcC/A99NaPRKDZAmDaWG5ksisgF4G+cpoxU95lcaY96Ilh8GVnaZ1/6o/bVAebScA/xv9FWePwZOTkTQSg2WJg2lBin6BsRVwOnGmIXAepx3yHfV8+FuXeuB6GeEznfbfAt42RgzD7gkxvqUSipNGkoNXg5Qb4xpi56TOC1GnzIROT1avg74axzrbH8Pwg3DEqVSw0iThlKD92fALSJbcd7t/XaMPtuBL0b75OGcv+jLD4Dvich69M2aahTSR6MrlSAiUg48HT3UpNS4oHsaSiml4qZ7GkoppeKmexpKKaXipklDKaVU3DRpKKWUipsmDaWUUnHTpKGUUipumjSUUkrF7f8Bi/RlGqtnykUAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ax = plt.gca()\n",
    "\n",
    "ax.plot(alphas, coefs)\n",
    "ax.set_xscale('log')\n",
    "plt.xlabel('alpha')\n",
    "plt.ylabel('weights')\n",
    "plt.axis('tight')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Comme on peut le voir, le lasso permet de supprimer des variables en mettant leur poids à zéro. C'est le cas si deux variables sont corrélées. L'une sera sélectionnée par le Lasso, l'autre supprimée. C'est aussi son avantage par rapport à une régression ridge qui ne fera pas de sélection de variables.\n",
    "\n",
    "On peut observer maintenant le comportement de l'erreur."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "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": [
    "ax = plt.gca()\n",
    "\n",
    "ax.plot(alphas, errors)\n",
    "ax.set_xscale('log')\n",
    "plt.xlabel('alpha')\n",
    "plt.ylabel('error')\n",
    "plt.axis('tight')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[2.864149965701444, 1.853156120172837]"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "min(errors)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "On fait encore mieux qu'avec la régression ridge! En effet, le lasso a pour avantage de pouvoir sélectionner un sous-ensemble des variables explicatives afin de permettre une meilleur généralisation."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "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": "3.7.2"
  },
  "toc": {
   "base_numbering": 1,
   "nav_menu": {},
   "number_sections": true,
   "sideBar": true,
   "skip_h1_title": false,
   "title_cell": "Table of Contents",
   "title_sidebar": "Contents",
   "toc_cell": false,
   "toc_position": {},
   "toc_section_display": true,
   "toc_window_display": false
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}