{"cells": [{"cell_type": "markdown", "metadata": {}, "source": ["# 2A.ml - Machine Learning et Marketting - correction\n", "\n", "Classification binaire, correction."]}, {"cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [{"name": "stdout", "output_type": "stream", "text": ["Populating the interactive namespace from numpy and matplotlib\n"]}], "source": ["%matplotlib inline"]}, {"cell_type": "code", "execution_count": 2, "metadata": {"collapsed": true}, "outputs": [], "source": ["import matplotlib.pyplot as plt"]}, {"cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [{"data": {"text/html": ["<b>Plan</b>\n", "<div id=\"my_menu_id\">run previous cell, wait for 2 seconds</div>\n", "<script>\n", "function repeat_indent_string(n){\n", "    var a = \"\" ;\n", "    for ( ; n > 0 ; --n) {\n", "        a += \"    \";\n", "    }\n", "    return a;\n", "}\n", "var update_menu_string = function(begin, lfirst, llast, sformat, send) {\n", "    var anchors = document.getElementsByClassName(\"section\");\n", "    if (anchors.length == 0) {\n", "        anchors = document.getElementsByClassName(\"text_cell_render rendered_html\");\n", "    }\n", "    var i,t;\n", "    var text_menu = begin;\n", "    var text_memo = \"<pre>\\nlength:\" + anchors.length + \"\\n\";\n", "    var ind = \"\";\n", "    var memo_level = 1;\n", "    var href;\n", "    var tags = [];\n", "    for (i = 0; i <= llast; i++) {\n", "        tags.push(\"h\" + i);\n", "    }\n", "\n", "    for (i = 0; i < anchors.length; i++) {\n", "        text_memo += \"**\" + anchors[i].id + \"--\\n\";\n", "\n", "        var child = null;\n", "        for(t = 0; t < tags.length; t++) {\n", "            var r = anchors[i].getElementsByTagName(tags[t]);\n", "            if (r.length > 0) {\n", "child = r[0];\n", "break;\n", "            }\n", "        }\n", "        if (child == null){\n", "            text_memo += \"null\\n\";\n", "            continue;\n", "        }\n", "\n", "        if (anchors[i].hasAttribute(\"id\")) {\n", "            // when converted in RST\n", "            href = anchors[i].id;\n", "            text_memo += \"#1-\" + href;\n", "            // passer \u00e0 child suivant (le chercher)\n", "        }\n", "        else if (child.hasAttribute(\"id\")) {\n", "            // in a notebook\n", "            href = child.id;\n", "            text_memo += \"#2-\" + href;\n", "        }\n", "        else {\n", "            text_memo += \"#3-\" + \"*\" + \"\\n\";\n", "            continue;\n", "        }\n", "        var title = child.textContent;\n", "        var level = parseInt(child.tagName.substring(1,2));\n", "\n", "        text_memo += \"--\" + level + \"?\" + lfirst + \"--\" + title + \"\\n\";\n", "\n", "        if ((level < lfirst) || (level > llast)) {\n", "            continue ;\n", "        }\n", "        if (title.endsWith('\u00b6')) {\n", "            title = title.substring(0,title.length-1).replace(\"<\", \"&lt;\").replace(\">\", \"&gt;\").replace(\"&\", \"&amp;\")\n", "        }\n", "\n", "        if (title.length == 0) {\n", "            continue;\n", "        }\n", "        while (level > memo_level) {\n", "            text_menu += \"<ul>\\n\";\n", "            memo_level += 1;\n", "        }\n", "        while (level < memo_level) {\n", "            text_menu += \"</ul>\\n\";\n", "            memo_level -= 1;\n", "        }\n", "        text_menu += repeat_indent_string(level-2) + sformat.replace(\"__HREF__\", href).replace(\"__TITLE__\", title);\n", "    }\n", "    while (1 < memo_level) {\n", "        text_menu += \"</ul>\\n\";\n", "        memo_level -= 1;\n", "    }\n", "    text_menu += send;\n", "    //text_menu += \"\\n\" + text_memo;\n", "    return text_menu;\n", "};\n", "var update_menu = function() {\n", "    var sbegin = \"\";\n", "    var sformat = '<li><a href=\"#__HREF__\">__TITLE__</a></li>';\n", "    var send = \"\";\n", "    var text_menu = update_menu_string(sbegin, 2, 4, sformat, send);\n", "    var menu = document.getElementById(\"my_menu_id\");\n", "    menu.innerHTML=text_menu;\n", "};\n", "window.setTimeout(update_menu,2000);\n", "            </script>"], "text/plain": ["<IPython.core.display.HTML object>"]}, "execution_count": 4, "metadata": {}, "output_type": "execute_result"}], "source": ["from jyquickhelper import add_notebook_menu\n", "add_notebook_menu()"]}, {"cell_type": "markdown", "metadata": {}, "source": ["### Donn\u00e9es"]}, {"cell_type": "markdown", "metadata": {}, "source": ["Tout d'abord, on r\u00e9cup\u00e8re la base de donn\u00e9es : [Bank Marketing Data Set](https://archive.ics.uci.edu/ml/datasets/Bank+Marketing)."]}, {"cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": ["url = \"https://archive.ics.uci.edu/ml/machine-learning-databases/00222/\"\n", "file = \"bank.zip\"\n", "import pyensae.datasource\n", "data = pyensae.datasource.download_data(file, website=url)"]}, {"cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [{"data": {"text/html": ["<div>\n", "<table border=\"1\" class=\"dataframe\">\n", "  <thead>\n", "    <tr style=\"text-align: right;\">\n", "      <th></th>\n", "      <th>age</th>\n", "      <th>job</th>\n", "      <th>marital</th>\n", "      <th>education</th>\n", "      <th>default</th>\n", "      <th>balance</th>\n", "      <th>housing</th>\n", "      <th>loan</th>\n", "      <th>contact</th>\n", "      <th>day</th>\n", "      <th>month</th>\n", "      <th>duration</th>\n", "      <th>campaign</th>\n", "      <th>pdays</th>\n", "      <th>previous</th>\n", "      <th>poutcome</th>\n", "      <th>y</th>\n", "    </tr>\n", "  </thead>\n", "  <tbody>\n", "    <tr>\n", "      <th>4516</th>\n", "      <td>33</td>\n", "      <td>services</td>\n", "      <td>married</td>\n", "      <td>secondary</td>\n", "      <td>no</td>\n", "      <td>-333</td>\n", "      <td>yes</td>\n", "      <td>no</td>\n", "      <td>cellular</td>\n", "      <td>30</td>\n", "      <td>jul</td>\n", "      <td>329</td>\n", "      <td>5</td>\n", "      <td>-1</td>\n", "      <td>0</td>\n", "      <td>unknown</td>\n", "      <td>no</td>\n", "    </tr>\n", "    <tr>\n", "      <th>4517</th>\n", "      <td>57</td>\n", "      <td>self-employed</td>\n", "      <td>married</td>\n", "      <td>tertiary</td>\n", "      <td>yes</td>\n", "      <td>-3313</td>\n", "      <td>yes</td>\n", "      <td>yes</td>\n", "      <td>unknown</td>\n", "      <td>9</td>\n", "      <td>may</td>\n", "      <td>153</td>\n", "      <td>1</td>\n", "      <td>-1</td>\n", "      <td>0</td>\n", "      <td>unknown</td>\n", "      <td>no</td>\n", "    </tr>\n", "    <tr>\n", "      <th>4518</th>\n", "      <td>57</td>\n", "      <td>technician</td>\n", "      <td>married</td>\n", "      <td>secondary</td>\n", "      <td>no</td>\n", "      <td>295</td>\n", "      <td>no</td>\n", "      <td>no</td>\n", "      <td>cellular</td>\n", "      <td>19</td>\n", "      <td>aug</td>\n", "      <td>151</td>\n", "      <td>11</td>\n", "      <td>-1</td>\n", "      <td>0</td>\n", "      <td>unknown</td>\n", "      <td>no</td>\n", "    </tr>\n", "    <tr>\n", "      <th>4519</th>\n", "      <td>28</td>\n", "      <td>blue-collar</td>\n", "      <td>married</td>\n", "      <td>secondary</td>\n", "      <td>no</td>\n", "      <td>1137</td>\n", "      <td>no</td>\n", "      <td>no</td>\n", "      <td>cellular</td>\n", "      <td>6</td>\n", "      <td>feb</td>\n", "      <td>129</td>\n", "      <td>4</td>\n", "      <td>211</td>\n", "      <td>3</td>\n", "      <td>other</td>\n", "      <td>no</td>\n", "    </tr>\n", "    <tr>\n", "      <th>4520</th>\n", "      <td>44</td>\n", "      <td>entrepreneur</td>\n", "      <td>single</td>\n", "      <td>tertiary</td>\n", "      <td>no</td>\n", "      <td>1136</td>\n", "      <td>yes</td>\n", "      <td>yes</td>\n", "      <td>cellular</td>\n", "      <td>3</td>\n", "      <td>apr</td>\n", "      <td>345</td>\n", "      <td>2</td>\n", "      <td>249</td>\n", "      <td>7</td>\n", "      <td>other</td>\n", "      <td>no</td>\n", "    </tr>\n", "  </tbody>\n", "</table>\n", "</div>"], "text/plain": ["      age            job  marital  education default  balance housing loan  \\\n", "4516   33       services  married  secondary      no     -333     yes   no   \n", "4517   57  self-employed  married   tertiary     yes    -3313     yes  yes   \n", "4518   57     technician  married  secondary      no      295      no   no   \n", "4519   28    blue-collar  married  secondary      no     1137      no   no   \n", "4520   44   entrepreneur   single   tertiary      no     1136     yes  yes   \n", "\n", "       contact  day month  duration  campaign  pdays  previous poutcome   y  \n", "4516  cellular   30   jul       329         5     -1         0  unknown  no  \n", "4517   unknown    9   may       153         1     -1         0  unknown  no  \n", "4518  cellular   19   aug       151        11     -1         0  unknown  no  \n", "4519  cellular    6   feb       129         4    211         3    other  no  \n", "4520  cellular    3   apr       345         2    249         7    other  no  "]}, "execution_count": 6, "metadata": {}, "output_type": "execute_result"}], "source": ["import pandas\n", "df = pandas.read_csv(\"bank.csv\",sep=\";\")\n", "df.tail()"]}, {"cell_type": "markdown", "metadata": {}, "source": ["### Exercice 1 : pr\u00e9dire y en fonction des attributs\n", "\n", "Les donn\u00e9es ne sont pas toutes au format num\u00e9rique, il faut convertir les variables cat\u00e9gorielles. Pour cela, on utilise la fonction [DictVectorizer](http://scikit-learn.org/stable/modules/generated/sklearn.feature_extraction.DictVectorizer.html)."]}, {"cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [{"name": "stdout", "output_type": "stream", "text": ["['age', 'balance', 'day', 'duration', 'campaign', 'pdays', 'previous']\n", "['job', 'marital', 'education', 'default', 'housing', 'loan', 'contact', 'month', 'poutcome']\n", "y\n"]}], "source": ["import numpy\n", "import numpy as np\n", "numerique = [ c for c,d in zip(df.columns,df.dtypes) if d == numpy.int64 ]\n", "categories = [ c for c in df.columns if c not in numerique and c not in [\"y\"] ]\n", "target = \"y\"\n", "print(numerique)\n", "print(categories)\n", "print(target)\n", "num = df[ numerique ]\n", "cat = df[ categories ]\n", "tar = df[ target ]"]}, {"cell_type": "markdown", "metadata": {}, "source": ["On traite les variables cat\u00e9gorielles :"]}, {"cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [{"data": {"text/plain": ["['contact=cellular',\n", " 'contact=telephone',\n", " 'contact=unknown',\n", " 'default=no',\n", " 'default=yes',\n", " 'education=primary',\n", " 'education=secondary',\n", " 'education=tertiary',\n", " 'education=unknown',\n", " 'housing=no',\n", " 'housing=yes',\n", " 'job=admin.',\n", " 'job=blue-collar',\n", " 'job=entrepreneur',\n", " 'job=housemaid',\n", " 'job=management',\n", " 'job=retired',\n", " 'job=self-employed',\n", " 'job=services',\n", " 'job=student',\n", " 'job=technician',\n", " 'job=unemployed',\n", " 'job=unknown',\n", " 'loan=no',\n", " 'loan=yes',\n", " 'marital=divorced',\n", " 'marital=married',\n", " 'marital=single',\n", " 'month=apr',\n", " 'month=aug',\n", " 'month=dec',\n", " 'month=feb',\n", " 'month=jan',\n", " 'month=jul',\n", " 'month=jun',\n", " 'month=mar',\n", " 'month=may',\n", " 'month=nov',\n", " 'month=oct',\n", " 'month=sep',\n", " 'poutcome=failure',\n", " 'poutcome=other',\n", " 'poutcome=success',\n", " 'poutcome=unknown']"]}, "execution_count": 8, "metadata": {}, "output_type": "execute_result"}], "source": ["from sklearn.feature_extraction import DictVectorizer\n", "prep = DictVectorizer()\n", "cat_as_dicts = [dict(r.iteritems()) for _, r in cat.iterrows()]\n", "temp = prep.fit_transform(cat_as_dicts)\n", "cat_exp = temp.toarray()\n", "prep.feature_names_"]}, {"cell_type": "markdown", "metadata": {}, "source": ["On construit les deux matrices $(X,Y)$ = (features, classe).\n", "\n", "**Remarque :** certains mod\u00e8les d'apprentissage n'acceptent pas les corr\u00e9lations. Lorsqu'on cr\u00e9e des variables cat\u00e9gorielles \u00e0 choix unique, les sommes des colonnes associ\u00e9es \u00e0 une cat\u00e9gories fait n\u00e9cessairement un. Avec deux variables cat\u00e9gorielles, on introduit n\u00e9cessairement des corr\u00e9lations. On pense \u00e0 enlever les derni\u00e8res cat\u00e9gories : ``'contact=unknown', 'default=yes', 'education=unknown',`` ``'housing=yes',`` ``'job=unknown', 'loan=yes', 'marital=single', 'month=sep',`` ``'poutcome=unknown'``."]}, {"cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [{"data": {"text/plain": ["((4521, 42), (4521,))"]}, "execution_count": 9, "metadata": {}, "output_type": "execute_result"}], "source": ["cat_exp_df = pandas.DataFrame( cat_exp, columns = prep.feature_names_ )\n", "reject = ['contact=unknown', 'default=yes', 'education=unknown', 'housing=yes','job=unknown', \n", "          'loan=yes', 'marital=single', 'month=sep', 'poutcome=unknown']\n", "keep = [ c for c in cat_exp_df.columns if c not in reject ]\n", "cat_exp_df_nocor = cat_exp_df [ keep ]\n", "X = pandas.concat ( [ num, cat_exp_df_nocor ], axis= 1)\n", "Y = tar.apply( lambda r : (1.0 if r == \"yes\" else 0.0))\n", "X.shape, Y.shape"]}, {"cell_type": "markdown", "metadata": {}, "source": ["Quelques corr\u00e9lations sont tr\u00e8s grandes malgr\u00e9 tout :"]}, {"cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [{"data": {"text/plain": ["array([[ 1.        ,  0.99733687,  0.96756321, ...,  0.89646012,\n", "         0.9809934 ,  0.94772372],\n", "       [ 0.99733687,  1.        ,  0.98202501, ...,  0.8917544 ,\n", "         0.99153146,  0.96013301],\n", "       [ 0.96756321,  0.98202501,  1.        , ...,  0.90132068,\n", "         0.998155  ,  0.98697606],\n", "       ..., \n", "       [ 0.89646012,  0.8917544 ,  0.90132068, ...,  1.        ,\n", "         0.90491984,  0.94963638],\n", "       [ 0.9809934 ,  0.99153146,  0.998155  , ...,  0.90491984,\n", "         1.        ,  0.98331872],\n", "       [ 0.94772372,  0.96013301,  0.98697606, ...,  0.94963638,\n", "         0.98331872,  1.        ]])"]}, "execution_count": 10, "metadata": {}, "output_type": "execute_result"}], "source": ["import numpy\n", "numpy.corrcoef(X)"]}, {"cell_type": "markdown", "metadata": {}, "source": ["On divise en base d'apprentissage et de test :"]}, {"cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [], "source": ["from sklearn.model_selection import train_test_split\n", "X_train, X_test, Y_train, Y_test = train_test_split(X, Y, test_size=0.33)"]}, {"cell_type": "markdown", "metadata": {}, "source": ["Puis on cale un mod\u00e8le d'apprentissage :"]}, {"cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [], "source": ["from sklearn.ensemble import GradientBoostingClassifier, RandomForestClassifier\n", "type_classifier = GradientBoostingClassifier\n", "clf = type_classifier()\n", "clf = clf.fit(X_train, Y_train.ravel()) "]}, {"cell_type": "markdown", "metadata": {}, "source": ["La m\u00e9thode [ravel](http://pandas.pydata.org/pandas-docs/stable/generated/pandas.Series.ravel.html#pandas.Series.ravel) \u00e9vite de prendre en compte l'index de *Y_train*. La m\u00e9thode [train_test_split](http://scikit-learn.org/stable/modules/generated/sklearn.model_selection.train_test_split.html) conserve dans l'index les positions initiales des \u00e9l\u00e8ments. Mais l'index fait que ``Y_train[0]`` ne d\u00e9signe pas le premier \u00e9l\u00e9ment de ``Y_train`` mais le premier \u00e9l\u00e9ment du tableau initial. ``Y_train.ravel()[0]`` d\u00e9signe bien le premier \u00e9l\u00e9ment du tableau. On calcule ensuite la matrice de confusion ([Confusion matrix](http://scikit-learn.org/stable/auto_examples/plot_confusion_matrix.html)) :"]}, {"cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [{"name": "stdout", "output_type": "stream", "text": ["[[2685   14]\n", " [ 161  169]]\n", "[[1261   40]\n", " [ 120   71]]\n"]}, {"data": {"text/plain": ["<matplotlib.text.Text at 0x294ed68>"]}, "execution_count": 13, "metadata": {}, "output_type": "execute_result"}, {"data": {"image/png": 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RoRAiIvQUNiFEUCI6M0V0KISISCdtB6A5lGQI0UXUXSKECEpEZ6aIDoUQERHRmSmiQyFE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\naGhowODBg/HOO++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"text/plain": ["<matplotlib.figure.Figure at 0x5a37898>"]}, "metadata": {}, "output_type": "display_data"}], "source": ["from sklearn.metrics import confusion_matrix\n", "for x,y in [ (X_train, Y_train), (X_test, Y_test) ]:\n", "    yp  = clf.predict(x)\n", "    cm = confusion_matrix(y.ravel(), yp.ravel())\n", "    print(cm)\n", "    \n", "import matplotlib.pyplot as plt\n", "plt.matshow(cm)\n", "plt.title('Confusion matrix')\n", "plt.colorbar()\n", "plt.ylabel('True label')\n", "plt.xlabel('Predicted label') "]}, {"cell_type": "markdown", "metadata": {}, "source": ["Si le model choisi est un [GradientBoostingClassifier](http://scikit-learn.org/stable/modules/generated/sklearn.ensemble.GradientBoostingClassifier.html), on peut regarder l'importance des variables dans la construction du r\u00e9sultat. Le graphe suivant est inspir\u00e9 de la page [Gradient Boosting regression](http://scikit-learn.org/stable/auto_examples/ensemble/plot_gradient_boosting_regression.html) m\u00eame si ce n'est pas une r\u00e9gression qui a \u00e9t\u00e9 utilis\u00e9e ici."]}, {"cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [{"data": {"text/plain": ["<matplotlib.text.Text at 0x149d5a90>"]}, "execution_count": 14, "metadata": {}, "output_type": "execute_result"}, {"data": {"image/png": 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Vi3BKOkZBGYuzszOHDh3i999/Jzc3Fzs7OyZMmCC/kfv6669RKpU8efKEqVOnyp8FguqK\neHp1iPwylmnTpsmxT15eXsyfP5+FCxdib2/P4cOHMTY2xt3dnQsXLgB5qXy8vLyEQxJUe8RMSYco\nSsYCcPfuXTZv3kxaWhqZmZm0bdsWgJdffpndu3fj6elJWFgYH330UZHt1lSZiYGBARYWFqUqq1Kp\nSl32eVJV/VZ130JmUoORJIng4GD8/f1xdHQkLCyMiIgIIC9/WmJiIhEREUiSRKNGjYpso6bKTHJz\nc0v9dkm8favcfoXMpIZQlIwFICMjA0tLS3Jycjh+/LhWna5du7J8+XJeeumlqjBZIHjuiJmSDpFf\nxmJpaYmzszMKhYIhQ4bw6aefUqdOHVxcXLR0cj4+PmzevBlvb+8qtFwgeH4Ip6RjDBw4kIEDBxb6\nvmfPnkWWv3btGl5eXvLxKAJBdUc4pWrM+vXr+euvv5g+fXqZ69YEmUk9M/H41kTET7UaM3LkyGeu\nq28yE0H1QTglPaU6ykyErEQ/EE5JT6mOMhMhK9EPhFPSMRYtWkRycjJZWVn06dOHHj16cPjwYXbt\n2oW5uTmOjo4YGhoycuRIHj9+zJo1a/jnn38AeO+992jevHkVj0AgKB/CKekYvr6+mJmZkZWVxfTp\n03nhhRfYtm0bixYtwtjYmNmzZ9O4cWMAvvvuO/r160fz5s1JSkpi7ty5LFu2rIpHIBCUD+GUdIxf\nfvmFs2fPApCcnMzRo0dxd3eXX/m/+OKLPHjwAIDw8HBiY2PlpAUZGRlkZmZqJSsQCKobwinpEBER\nEVy5coV58+ZhaGjI7NmzadSoEbGxsUWWlySJuXPnFnlmd35qivatLFq3ggjtW+UitG81hPT0dMzM\nzDA0NCQ2NpbIyEh69OjB1atXSU9Px8jIiDNnzuDo6Ajk5ZT79ddfGTBgAADR0dE0adKkULs1RftW\nFq1bQYT2rXL7Lc8fPuGUdAgPDw8OHjzI5MmTsbe3x9XVFSsrKwYOHMj06dMxNzenYcOG8lLugw8+\nYN26dUydOhW1Wk2LFi0YPXp0FY9CICgfwinpELVq1SoyOtvJyYkePXqgVqtZtGgRHTp0APL+In3y\nySeVbaZAUKEIp1QNCA0NJTw8nOzsbNq2bSs7pfJQHWUmQlaiH4ifcjVg+PDhz71NITMR6CrCKT0j\niYmJLFiwgCVLlpSqfHBwMO3bt8fLy6uCLSsduiQzEfIRQX6EUyoH1TlVti7JTIR8RJAf4ZTKQW5u\nLl9//TW3b9/GwcGBCRMmsHv3bi5cuEBWVhaurq6MGTOmUL2tW7cWWWb27Nm4uLhw5coV0tPT+eij\nj3Bzc0OtVvPjjz9y6dIllEolPXr04LXXXiMqKorvv/+ezMxMLCws8PX1xdLSsrJvg0DwXBFOqRzc\nv3+fcePG4erqyurVqzlw4AC9e/fmrbfeAmDlypVcuHCBdu3aadUrqYxarWbevHlcvHiR0NBQZsyY\nwe+//05iYiKLFy9GoVCQlpZGbm4uGzZswN/fHwsLC06ePMlPP/3EuHHjKvcmCATPGeGUykG9evVw\ndXUFoEuXLuzbt4/69euze/duMjMzSUtLw8HBoZBTCg8PZ8+ePUWW0ew5OTk5kZSUJJd/9dVX5eWi\nmZkZ9+7d4+7duwQGBiJJEpIkUbdu3coaukBQYQin9BxRKBSsW7eOBQsWYGVlRWhoKNnZ2VplsrOz\nWbduHUFBQUWW0UhGlEplia/PJUnC0dGROXPmPNUuXZeZlEc+UlqEzKRyETKTKiIpKYkbN27QrFkz\njh8/jpubG5GRkVhYWJCRkcHp06fp1KmTVp3s7GwUCkWJZTRohLZt2rTh4MGDuLu7o1QqSU1Nxd7e\nnsePHxMZGYmrqyu5ubk8ePCgyDRLui4zKY98pLQImUnl9itkJlWEvb09+/fvJzg4GAcHB1599VVS\nU1OZPHkydevWxcXFpVAdU1NTXn755RLLaNAs13r06MGDBw+YMmUKtWrVokePHvTq1YvJkyezfv16\n0tPTUavV9O3bt9jcbwJBdUEhaf4cC/SKDosOV7UJMkGvOVV4MKeYKVUe9vb25aovZkp6ii7JTIR8\nRJAf8TToKUJmItBVhFPSASIiIti9ezfTpk2rtD6rWmYipCWC4hBOSUeobMlKVctMhLREUBzCKVUw\niYmJzJs3j6ZNm2rJUSIiIggJCcHIyEgrA8nNmzf57rvvyM7ORqVS4evrS4MGDZg5cyYjR46UkwZ8\n8cUXjB49mtTUVL777jvZqc2ePRtjY+MqGatA8DwQTqkSyC9H+e9//8vevXs5ePAgs2bNwtbWVisD\nSaNGjfjyyy9RKpWEh4ezadMm/Pz86NGjB3/88Qfvv/8+9+/fJzs7G0dHR4KCghg9ejSurq5kZmZi\naGhYhSMVCMqPWNRXAvnlKD4+Pty6dQtbW1tsbW2BPImKhrS0NJYuXYqfnx8hISHExMQAeVlMLl68\niFqtJiwsjO7duwPQvHlzQkJC2LdvH2lpaSiV4kcqqN6ImVIVkJ6eXuy1zZs306pVK6ZMmUJiYiKz\nZ88G8iQDrVu35s8//+TUqVMEBQUB8MYbb9C+fXsuXLjAjBkz+OyzzwrFieiizKQypCX5ETKTykXI\nTHScgnKUNm3a8Pvvv5OQkICNjQ0nTpyQy6anp2NlZQXAH3/8odXOyy+/TFBQEC1btpSTB8THx+Pg\n4ICDgwO3bt3i/v37hZySLspMKkNakh8RPFm5/QqZiY5TUI7St29fmjZtyvz58zEyMsLNzY2MjAwA\nBgwYwKpVq9i2bVuh0wWcnJwwNTWVl26Ql7zyypUrKJVKHBwc8PDwqMyhCQTPHeGUKgGlUsmECRO0\nvvPw8CjSgbi6urJ8+XL585AhQ+T/JycnI0kSbdu2lb8bOXJkBVgsEFQdwilVAs8jBuno0aP8/PPP\nvPfee8/BoqqXmQhpiaA4hCBXT7l//36l96mv+yv6NubyCnLF+2OBQKBTiDm0DrBlyxZatmxJq1at\nKq3P56F9E/o1QUUgnNJzRq1WlzmAsSrihp6H9k3o1wQVgXBKZaA4HdukSZPw9vYmPDycAQMG4Ozs\nzLp160hJSUGlUjF27FgsLS2ZOnUqq1atAiAzM5NPPvmEVatW8d///ldOVBkeHs4PP/yAWq3G2dmZ\n0aNHU6tWLcaPH09QUBDm5uZERUWxceNGZs6cSUREhNC+CWoUwimVkYI6tv3798tnbi9YsACAOXPm\n8OGHH2JnZ8fNmzdZu3YtX3zxBU2aNCEiIoKWLVty/vx5PDw8tGZV2dnZBAcHM3PmTOzs7Fi5ciUH\nDhygT58+xb7B27Nnj9C+CWoUwimVkYI6tn379gHg7e0NQEZGBtevX2fZsmXywf+a1+CdOnXi5MmT\ntGzZkpMnT9KrVy+ttu/fv4+trS12dnYAdO/enf3799OnTx+Ke0mq0b75+Pjg5eUlR4Pnp6JkJmWV\niuij5EIfxwxCZlKlaGYwmiWTJEmYmZnJ2rT8eHp68vPPP5Oamsrt27eL3NguzvkYGBigVqsByMr6\n3yZ1abRvFSUzKatURB9fj+vrmMvzh0+8OikjGh0bIKdVyo+JiQk2NjacPn1a/u7OnTtAnuNycnLi\nu+++o127doWWZPb29iQlJREfHw/kBUxqnImNjQ1RUXmb02fOnJHraLRvr7/+Os7OzlUSfyQQPE/E\nTKmMFJVW6bffftMqM3HiRNasWcO2bdtQq9V4e3vLh7N5e3uzbNkyWf2fH0NDQ8aNG8fSpUvlje5X\nXnkFgLfeeovVq1djamqqNesR2jdBTUNEdJeBxMREFixYwJIlS6ralHJzODy63G2UNU5JX5cy+jZm\nkWKpkqnss7QriqrIZiIQlAaxp1QG6tevz+LFi6vaDIGgRiNmSjrIuXPniI2N5fXXX6+wPkqSmQj5\niKAqEU5JB/H09MTT07NC+yhJZiLkI4KqRDilIjhy5Ah79+5FoVDg6OhIp06d2L59Ozk5OVhYWDBx\n4kRq165NaGgoCQkJJCQkkJSUxHvvvUdkZCSXLl3C2tqagIAAlEol48ePp1OnTly6dAkjIyMmTpyI\nra0t58+fL7LdsLAwoqKiGDlyJPHx8Xz99ddkZWXRvn17fv31V77//nsiIiIIDQ3FwsKCe/fu4eTk\nxMcff1zVt04gKDdijl6AmJgYduzYwcyZM1m4cCEffPABLVq0YO7cuQQFBeHt7c2uXbvk8gkJCcyc\nORN/f39WrFhB69atWbx4MYaGhly4cEEuZ25uzuLFi+nVqxcbNmwAKNTuzp07C9mzYcMG+vbty6JF\ni7C2ttbaaI+OjuaDDz5g6dKlxMfHc/369Qq8MwJB5SBmSgW4fPkyL774Iubm5gCYmZlx9+5dNm7c\nyMOHD8nNzcXGxkYur9GvOTo6olar5aNqHR0dSUhIkMtpZCidO3cmJCQEyAvELK5dDTdu3MDf3x/I\nk7X88MMP8jUXFxfq1q0LQJMmTUhMTNRKbKmhrDKTiso0oo+SC30cMwiZSYWzYcMG+vfvT7t27eRl\nkwaNAFahUFCr1v9up0KhkGUhms8F/19Su0VRMKQsf39KpVLW2BWkrA9FRWUa0ceYHX0ds5CZPEda\ntWrF6dOnSU1NBSA1NZX09HR5RhIWFlZs3ZLiUE+ePAnAiRMnZEFvadpt1qyZLFnRtCEQ1GTETKkA\njRo1YtCgQcycORMDAwOaNGnC4MGDWbp0Kebm5ri7u5OYmFhk3ZICK9PS0pg6dSqGhob83//9H0Cp\n2n3//fdZsWIFO3bsoG3btnK+N4GgpiJkJpVA/gPaykpWVhYqVd7r+ZMnT3LixAmmTp1abps6LDpc\n7LWg15wqJOJbX5cy+jZmITOpBpRHmhIVFcW6deuAvE33cePGPRebSkqxJNIfCaoSMVPSU0SKpZrd\nb1X2LVIsFSAxMZHjx48/c/2wsDAePXr0HC3SZvbs2fK5SOPHj5c31IsjODhY6/yk58W1f7K0/iVl\nqJ9eSSCoBGrcPD0hIYHjx4/j4+PzTPWPHDmCo6MjlpaWz9mywlTEiQOlzaZSUGYipCUCXUHnnFJB\niceQIUNYvXo1KSkp1K5dG19fX6ytrQkODsbExISoqCgePXrEsGHD8PLyYtOmTdy/f5+AgAC6detG\nhw4dWLlyJZmZmQCMHDlSfiW/c+dOjh8/jlKpxMPDAycnJ27dusWKFStQqVQEBgY+9SD+jIwM1q9f\nT1RUFAqFgsGDB9OxY0f+/vtvtmzZQk5ODra2tvj6+mJkZKRVV7NyLnhO0549e8jMzOStt97SKr91\n61YuXLhAVlYWrq6ujBkzBsibfTVu3Jjr16/TuXNn+vXrV/4fhEBQReiUU9JIPAIDAzE3Nyc1NZVV\nq1bRvXt3unbtyh9//MH69evlt0+PHj1izpw5xMTEsHDhQry8vHj33XfZs2cPAQEBQN7bqxkzZlCr\nVi3i4uJYvnw58+fP5+LFi5w/f5758+djaGhIWloaZmZm7N+/nxEjRtC0aVMAQkJCiIiIKGSrt7c3\nr7/+Otu2bcPMzEw+0iQ9PZ2UlBS2bdvGF198gUqlYteuXezdu5c333yz2LGXZtbUu3dv2VGtXLmS\nCxcu0K5dOyAv4HH+/PlluNsCgW6iU06poMTD3NycyMhI2Ql17dqVH3/8US7foUMHIC+26N9//y2y\nzZycHNavX090dDRKpZIHDx4AEB4ezksvvSTPhMzMzOQ6+ff+33vvvRJtDg8P55NPPpE/m5qacuHC\nBWJiYpgxYwaSJJGbmyvPzspDeHi4PItKS0vDwcFBdkoaGUtRlEZmUlHSkvzoo+RCH8cMNVxmUtIM\nojQ5zn755RcsLS1ZvHgxarWad999t0z9h4SEaP1Ca2zSzJSKQpIk2rZty8SJE0vVR/5MJZCX/60g\n2dnZrFu3jqCgIKysrAgNDdUqV3BpmJ/SPBQVJS3Jjz6+idLXMZdHZqJTTqlVq1YsXryYfv36ycs3\nV1dXjh8/TteuXTl27Fih7CEaNLMbY2NjMjIy5O/T09OxtrYG8varNL/8bdq0Ydu2bfj4+KBSqUhN\nTcXc3BwTExOePHki13/aTKlNmzbs379fLpeWlkazZs1Yv349cXFx2NnZkZmZSXJyMg0aNCiyjTp1\n6vD48WOABu2UAAAgAElEQVRSU1MxMjLi/PnzvPDCC1plsrOz5aSXGRkZnD59mk6dOpVom0BQHdEp\np1SUxGPkyJEEBwezZ88eeaO7KDQzqsaNG6NQKPD396d79+706tWLJUuWcPToUTw8POT8bB4eHty5\nc4dp06ZhaGjICy+8wNChQ+nWrRtr1qzByMioVBvdgwYNYt26dfj5+WFgYMBbb71Fx44d8fX1Zfny\n5eTk5AAwdOjQQk5JY7Om3vTp07G2tqZhw4aF+jE1NeXll19m8uTJ1K1bFxcXl7LdXIGgmiCCJ/WU\ngjKTipKW5EdflzL6NmYhMxE8EwVlJkJaItAVxJOop4gUSwJdRTglIDQ0FBMTk2KDDh8/fkxQUBA5\nOTl88MEHxW62F0f+M7fPnj2Lvb19kftGlUnBbCYig4lAVxBOqRSEh4fj6OjI2LFjy93W2bNnadeu\nXZU7JSEzEegqeuuUtm/fzpEjR7C0tMTKygpnZ2fi4+NZt24dKSkpqFQqxo4dS1ZWFj/++CNZWVlE\nRUURGBhISEgIt27dIisrixdffJHBgwcD2ucmRUVFsXHjRmbOnCn3GRkZyblz57h69So7duzAz8+v\nyHO58xMWFsa5c+fIysoiPj6eDh06MGzYMACOHz8uJxto164d//nPfyrobgkElYdeOqWoqChOnTrF\n4sWLycnJISAgAGdnZ7799ls+/PBD7OzsuHnzJmvXruWLL77g7bfflpdfAO+88w5mZmao1WrmzJnD\n3bt3cXR0fKpUxNXVFU9PT9q3b4+XlxcAu3fv5sSJE4XKtmjRgvfffx+AO3fusGjRIgwMDPjkk0/o\n06cPCoWCTZs2sXDhQkxNTQkMDOTcuXMVni9OIKho9NIpXbt2jQ4dOmBoaIihoSGenp5kZWVx/fp1\nli1bJgdiFncQ/4kTJzh06BBqtZpHjx4RExODo6NjiWd0F8eAAQMYMGBAiWVat24tx1c1atSIxMRE\nUlJScHd3lyU5Pj4+REREFOmUhMxEyEwqmxotM6ks1Go1ZmZmBAUFlVguISGBvXv3smDBAkxNTQkO\nDpblHvnlIllZxafFzs/u3buLPP+pZcuW8kypYJYUjbMsrRMUMhMRp1TZ/dYYmUll0aJFC4KDgxk4\ncCA5OTmcP3+enj17YmNjw+nTp3nxxReBvGVT48aNteo+efIEY2NjTExMePToERcvXpR/4W1sbIiK\nisLDw6PYg9mMjY21ZCylmSkVhYuLCxs2bCA1NRVTU1NOnDhB7969y9yOQKBr6KVTatq0Kd7e3kyZ\nMgVLS0ucnZ0BmDhxImvWrGHbtm2o1Wq8vb0LOaXGjRvTpEkTJk2ahLW1tVZ4wFtvvcXq1asxNTUt\ndmbSuXNnvvnmG/bt21eqje6CaPatLC0teffdd5k1axaQt9Et9pMENQEhM9FThMykZvdblX0LmYng\nmRAyE4GuIp5EPUXITAS6il7oChITE/Hz86uw9mfMmFFhbVcUIpOJQFfRm5lSRWQO0TBnzpwKa7ui\nyC8zERITgS6hN04pNzeXb775hsjISKysrPD39yc2NpY1a9aQlZUlZxwxNTVl9uzZDB8+HCcnJ1JS\nUpg2bRqrVq0iJiaG4OBgcnNzUavV+Pn5YWdnx4gRI/j++++JiIggNDQUCwsL7t27h5OTEx9//DEA\nFy5cYOPGjRgbG+Pq6kp8fDzTpk17qt2JiYnMmzcPNzc3LdsNDQ2Jjo4u0n6BoDqjN04pLi6OSZMm\nMXbsWL766itOnz7N7t27GTVqFG5ubmzZsoXQ0NAij7/VzLIOHDhAnz598PHxkR1T/usA0dHRLF26\nFEtLS2bMmMH169dxcnJizZo1zJkzh3r16rF8+XK5zpUrVwgJCSk0k1OpVPIMLL/ty5Yt48yZM/j4\n+LBq1Sot+7ds2SIHXAoE1RW9cUo2NjY4OjoCeXFK8fHxpKeny3FG3bp1Y9myZSW24erqyo4dO0hO\nTqZjx47Y2dkVKuPi4kLdunUBaNKkCYmJiRgZGWFnZ0e9evWAvFilQ4cOAXnR1gsXLiy17U5OTiQk\nJJCenl5m+wWC6oDeOKX8Z20rlUrS0tKKLatUKmUJR/6MIT4+Pri6usr54saMGVMoSDK/JESpVD5V\nEqKZKRXEyMhInikVtF1jU2lDzJ6mfasM3Rvopw5MH8cMQvtWKgr+ApuammJmZsa1a9dwc3Pj6NGj\ntGzZEoD69etz69YtnJ2dOXXqlFwnISEBGxsbevfuTVJSEnfu3MHd3f2pzsHe3p6EhASSkpKoV68e\nJ0+elK+VZqZUVPumpqaYm5sXaX9BnvZQVIbuDfQzkFBfxyy0b6Wg4J6NQqFg/PjxfPvtt1obxZCn\nR1u2bBmHDh2Skz0CnDx5kmPHjmFgYEDdunUZNGhQkW0XRKVSMXr0aObOnYuxsTHOzs5lehtYXFlf\nX99CG90CQXVHyEwqiYyMDPn4kbVr12Jvb0+fPn2qzJ78MpPKkJiA/s4a9G3MQmZSTTh06BBHjhwh\nJyeHpk2b8sorr1SpPfllJkJiItAlxExJT7l//36l96mPswZ9HHN5Z0o6LTNJTEws8gC00hIWFsaj\nR49KXT4iIoLIyMhStbt+/fpnsikiIoIFCxY8U93niZCYCHQVnXZKCQkJ5XJKR44cITk5udTlr1y5\nwvXr15+5v9JSkZKX0hLwWxQBv0WRlJZT1aYIBFpU6GbCkSNH2Lt3LwqFAkdHR4YMGcLq1atJSUmh\ndu3a+Pr6Ym1tTXBwMCYmJkRFRfHo0SOGDRuGl5cXmzZt4v79+wQEBNCtWzc6dOjAypUryczMBGDk\nyJG4uroCsHPnTo4fP45SqcTDwwMnJydu3brFihUrUKlUBAYGasX7FCQxMZGDBw9iYGDA8ePH+eCD\nD7C3t2fNmjX8888/ALz//vtyfxoeP35cZJnQ0FDi4+OJi4sjJSWFAQMG0KNHDyBv03vp0qWFpCjh\n4eH88MMPqNVqnJ2dGT16NLVq1WL8+PF069aN8+fPo1armTRpEvb29mRmZrJ+/XpiYmLIyclh8ODB\n4qA3QbWnwpxSTEwMO3bsIDAwEHNzc1JTU1m1ahXdu3ena9eu/PHHH6xfv56pU6cC8OjRI+bMmUNM\nTAwLFy7Ey8uLd999lz179hAQEADknXs9Y8YMatWqRVxcHMuXL2f+/PlcvHhRDmg0NDQkLS0NMzMz\n9u/fz4gRI2jatCkAISEhREREFLLV29ub119/nZ49e2olpfz666/p168fzZs3Jykpiblz5xaKmv7u\nu++KLXP37l3mzZvHkydP8Pf3p3379kDxUpTg4GBmzpyJnZ0dK1eulGUtAHXq1CEoKIgDBw6wZ88e\nxo4dy/bt22ndujXjxo0jPT2d6dOn06ZNG1QqIa4VVF8qzCldvnyZF198Uc62YW5uTmRkpOyEunbt\nyo8//iiX79ChA5CXrePff/8tss2cnBzWr19PdHQ0SqWSBw8eAHkzjJdeekmeCZmZmcl18u/jF6Vr\nK4nw8HBiY2PlNjIyMuRZWmnKeHp6UqtWLSwsLGjVqhU3b97E1NS0SCmKsbExtra2snSle/fu7N+/\nX3ZKHTt2BPJkJn/++ScAf//9N+fPn2f37t3y/UlKSir3RqNAUJVU6rvgkvZSSlpaafjll1+wtLRk\n8eLFqNVq3n333TL1HxISoiW30NikmSkVRJIk5s6dqyUdKUuZ/OPN7xzLKkWB/92fguX9/Pxo0KBB\nsfWgZJlJZUlMQD8lF/o4ZtBRmUmrVq1YvHgx/fr1k5dvrq6uHD9+nK5du3Ls2DGtQ/fzo/nlNDY2\nJiMjQ/4+PT0da2trIG+/SqPSb9OmDdu2bcPHxweVSkVqairm5uaYmJhoZQ552kzJxMSE9PR0+XOb\nNm349ddf5Wwj0dHRNGnSRKtOSWXOnTvHwIEDefLkCVevXmXYsGHFvoq3t7cnKSmJ+Ph4bG1tOXr0\n6FN/kG3btmXfvn1yksyi7IOSH4rKkpiAfr4e19cx66TMpFGjRgwaNIiZM2diYGBAkyZNGDlyJMHB\nwezZs0fe6C4KzQyjcePGKBQK/P396d69O7169WLJkiUcPXoUDw8POULaw8ODO3fuMG3aNAwNDXnh\nhRcYOnQo3bp1Y82aNRgZGT11oxugffv2LF26lPPnz/PBBx8wcuRI1q5dy9SpU1Gr1bRo0YLRo0dr\n1fnggw9Yt25dkWUcHR2ZNWsWKSkpvPnmm1haWhbrlAwNDRk3bhxLly6VN7o1AZbFzTDffPNNvvvu\nO6ZMmYIkSdjY2Mj7bwJBdUUET1YQoaGhWpvmuoZGZlJZEhPQ31mDvo1ZyEwEz4RGZiIkJgJdQzyR\nFcTgwYOr2oQSEdlMBLqKcEp6yrV/soC8mVI9Y50O7BfoGVXyNJZHO1YcZ8+eJTY2Vv68ZcsWLl++\n/Fz7eBZ0xY6CCJmJQFepMTOls2fP0q5dOxo2bAgUPvK1KlCr1RVmhyRJOqGhEwieNxXilI4dO8a+\nffvIzc3FxcWF0aNHExYWxs6dOzE3N8fR0VF+PR8cHEz79u3x8vICkNMVQWE923/+8x8OHTrE77//\nTm5uLnZ2dkyYMIHo6GjOnTvH1atX2bFjB35+fmzdulVut6yasqehSXvUtGlTbt++jYODAxMmTECl\nUjF+/Hi8vb0JDw9nwIABXLp0SbZj/PjxdO7cmUuXLmFgYMCYMWPYtGkT8fHx9O/fn549e5KRkcGi\nRYtIS0sjNzeXIUOG4OnpSWJiInPnzsXFxYXbt2/TqVMnUlNT5ewlhw4dIjY2lhEjRlTEj1QgqDSe\nu1OKjY3l5MmTBAYGolQqWbt2LUePHmXr1q0EBQVhYmLCrFmzZD1aQTR//YvSswF4eXnJwtaff/6Z\nw4cP89prr+Hp6anl3DRkZ2eXWVNWmrRH9+/fZ9y4cbi6urJ69WoOHDggv/63sLCQjye5dOmSVhs2\nNjYsXLiQkJAQgoODCQwMJDMzEz8/P3r27IlKpWLq1KkYGxuTkpLCZ599Jots4+LimDBhAi4uLmRk\nZODv78+IESNQKpWEhYUxZsyYZ/uhCQQ6xHN3SuHh4dy+fZvp06cjSRLZ2dncuHGDli1byjo4b29v\nWbdWUjtF6dnu3r3L5s2bSUtLIzMzk7Zt25bYzv3798usKSvNYf716tWTTwzo0qULv/32m+yUvL29\ni62nEeU6OjqSmZmJkZERRkZGqFQq0tPTMTIyYtOmTVy9ehWFQsHDhw9lLWD9+vVxcXEB8qLdW7Vq\nxfnz52nYsCG5ubk4ODgU2aeQmQiZSWWjczKTbt268c4778ifz507x+nTp4ssmz+dkSRJ5OSUvPEa\nHByMv78/jo6OhIWFFan6L0hZNWWlSXtUEppI85L6UygUWho4hUKBWq3m2LFjPH78mKCgIJRKJePH\nj5dTKhkZGWm19fLLL7N9+3YaNmxI9+7di+1TyExE8GRl96tTMpNWrVqxaNEi+vbtS+3atUlNTaVJ\nkyZs2LCB1NRUjI2NOX36NI0bNwbyljO3bt3ixRdf5OzZs7JTKk7PlpGRgaWlJTk5ORw/fhwrKysg\nzxHk17lpeBZNWWlmSklJSdy4cYNmzZpx/PhxWrRo8Sy3S0bjONPT06lTpw5KpZLLly+TlJRUqIwG\nFxcX/vnnH6Kjo1m8eHG5+hcIdIXn7pQaNWrE0KFDCQwMRJIkatWqxahRoxg8eDCfffYZ5ubmskMC\n6NGjBwsXLsTf35+2bds+Vc/29ttv8+mnn1KnTh1cXFxkR9S5c2e++eYb9u3bh5+fn9z+s2jKSoO9\nvT379+8nODgYBwcHevbs+dQ2S3OtS5cuBAUFMXXqVJycnOS3icXV79SpE3fu3MHU1PRZhyIQ6BRC\n+/YMJCYmsmDBApYsWVLVprBgwQL69etHq1atylTvcHg0ULnBk/q6lNG3MdfoxAG6TFXHCKWnp/N/\n//d/8oZ3WXGzVuFmrRLR3AKdQ8yU9BSRYqlm91uVfdf4mdKMGTOKvVaedEXBwcGcOXPmWc2qMoqT\nrZT1Xoj0SgJdReed0tNewVf1Mqqyefvtt4tdrpXlXgjdm0BX0Xntm0Z2snHjRi5duoRSqWTgwIFy\ngGJ6ejoLFiwgLi6OVq1aFToZsiQiIiLYu3evVlonoMi+IiIi2L17N9OmTQNg/fr1ODs7061bN378\n8UcuXLiAUqmkbdu2DBs2rMTUSwkJCSQkJJCUlMR7771HZGQkly5dwtramoCAAJRKJVu3buXChQtk\nZWXh6uoqR2vnl+VcunSJkJAQjIyMaN68+fO87QJBlaHzTkmhUHDmzBnu3r3LkiVL+Pfff5k+fTot\nW7YE4NatWyxbtox69eoxd+5czpw5g5eXF1999VWRUeN9+/ala9euQNFpnU6fPl1sX0XNRFJTUzl7\n9ixfffUVgHzGd0mplxISEpg5cyb37t3j888/Z8qUKQwbNozFixdz4cIFPD096d27N2+99RYAK1eu\n5MKFC7Rr107uNzs7m2+++YZZs2Zha2tbKPWTQFBd0XmnJEkS169fp3PnzkCeVq1ly5bcunULExMT\nXFxcqF+/PpAXq3Tt2jW8vLz45JNPntp2UWmdSuqrKExNTVGpVPz3v/+lXbt2suMoKfWSh4cHSqUS\nR0dH1Gq1LJVxdHQkISFBrr9nzx4yMzNJS0vDwcFByynFxsZia2uLra0tkBffdOjQoSJtLE5mUpkS\nE9BPyYU+jhl0UGZSlWhmM1999VWhN0wKhUJrplSatE4alEqlnD0F8hJjar6fN28ely9f5tSpU/z2\n22988cUXJaZeeprUJDs7m3Xr1hEUFISVlRWhoaGy1CQ/pX1xWtxDUZkSE9DPN1H6OmadkplUBG5u\nbhw8eJCuXbuSmprK1atXGT58OLGxsdy8eZPExESsra05efKkHFldmplSfjS/4C1atOD3338v1FdO\nTg6xsbHk5OSQmZnJ5cuXadGiBZmZmWRmZuLh4YGrq6ucgrs06Zny95uf7OxsFAoFFhYWZGRkcPr0\naTp16qRVpmHDhiQlJZGQkICNjQ0nTpwo03gFAl1F552SQqGgY8eOcnZdpVLJ8OHDqVOnDrGxsbi4\nuLBu3Tri4+Nxd3eXVf/P0g9QbF+QJ+nw8/PDxsZGPnrlyZMnLFy4UJ7JaHLLlZR6qah+82NqasrL\nL7/M5MmTqVu3rnwyQH4MDQ358MMPmT9/PkZGRri5uWnlyBMIqis6HTyZkpLCtGnTWLVqVVWbUuPo\nsOhwpaZXAv1dyujbmGts8OTDhw/5/PPP5eWP4PkS9JqTSK8k0El09qmsW7cuy5cvr2ozaiwixZJA\nV6nSmVJ1z2qSnp7OgQMHnqnujh07tD6XJKepCITMRKCr6Ozy7Vk5e/Ys9+7dkz+XJMsoL6mpqezf\nv7/M9dRqdSGnVJoTLfNT3q1AITMR6CoVunyr6VlNNm3aREJCAgEBAbRu3Zphw4axe/duTp06RU5O\nDh07dmTw4MGFMpE4OzuTlZVFQEAAjRo14uOPP5bHK7KZCPSdCnNK+pDV5N133yUmJoagoCAA/v77\nb+Li4pg/fz6SJBEUFMS1a9ewtrbWykQCcObMGble/vGKbCYCfafCnJK+ZDXJz19//cXff/9NQEAA\nkiSRmZnJgwcPsLa21spEUhKSJFVaNhMhM6m5/VZ13zorM9G3rCaSJPHGG2/IZ4BrSExMLJSJpDhb\nKjObiZCZ1Nx+q7JvnZWZ6ENWExMTE62+PDw82Lx5Mz4+PhgbG5OcnCxr2wo6oVq1apGbm4uBgYHW\ndZHNRKDvVJhT0oesJubm5jRv3pwpU6bg4eHBsGHDiImJ4fPPPwfynNbHH3+MQqEo1Mcrr7zClClT\ncHJyksuAyGYiEOi0zETwdJ41m4mQmdTsfquy7xorMxGUTHmzmQiZiUBXEU9lNcXU1LRcMhwhMxHo\nKno7U6qoLCmlJTo6mosXL8qfz507x65du8rV5uzZs4mKiipVWSExEegqeuuUKiNLSv6TKgtS0Cl5\nenry+uuvl6mN8iAkJgJdRW+XbxWVJSU4OBhDQ0Oio6Np3rw5Q4YMYf369cTExJCTk8PgwYPx8PBg\ny5YtZGdnc/36dd544w0yMzOJiopi5MiRpWrD09OTrKwsgoODuXv3Lvb29vIRvQJBdUZvnVJFZklJ\nTk5m7ty5APz000+0bt2acePGkZ6ezvTp02nTpg1vv/227IQg78SE/JSmjQMHDmBsbMzSpUu5e/cu\nAQEBFXW7BIJKQ2+dUkVmScl/nvbff//N+fPn2b17NwA5OTlaAZHlaePq1auyTMbR0VEr7is/RclM\nKltiAvopudDHMYMOy0xqEmXJklJQDuLn50eDBg20vouMjCyxv9K0UZDiQs6KeigqW2IC+hmzo69j\n1kmZSXWgMrKktG3bln379snLNE1Wk4ISlWdpo0WLFhw7dgx3d3fu3r3L3bt3y2SbQKCL6O3bN02W\nlMaNGzN16lTmzJmjlblEkyXFz88PW1vbZ86SMmjQIHJycpgyZQp+fn5s3rwZyJu9xMTEEBAQwKlT\np56pjVdffZWMjAwmT55MaGgoTk5Oz2SjQKBL6KXMRGRJgcPh0ZUeQKmvSxl9G7OQmZQRkSUlDyEx\nEegqevdkiiwpedQz1ru/R4Jqgl4+mVUtMRk/fjypqamlLv88JCgFETITga6idzMlqByJyfNs39PT\nUz6n+3mRlJZDPWMhyhXoHnrplCpKYnL+/Hm2b99OTk4OFhYWTJw4UT51c/ny5SQnJ9OsWTM5nigx\nMZF58+bRrFkzrl+/jrOzMy+99BJbtmzh8ePHTJw4EWdnZ8LCwrQkKCYmJkRFRfHo0SOGDRtWKEmC\nQFCd0UunVFESkxYtWsjSkMOHD7Nr1y6GDx9OaGgobm5uvPnmm1y4cIE//vhDrhsXF4efnx+NGjVi\n2rRpnDhxgjlz5nDu3Dm2b9/O1KlTC/X36NEj5syZQ0xMDAsXLhROSVCj0EunVFESk6SkJDZu3MjD\nhw/Jzc3FxsYGgKtXrzJlyhQA2rVrJ2dzgbyzyRs1agTkHSGsObDN0dGxWDlKhw4d5PKaTCcCQU1B\nL51SWSmtxGTDhg3079+fdu3aERERQWhoaJHt5Q8N02RRgbxMKprPCoVCzqpSkPx1SoPQvgntW2Uj\ntG/PQEVITNLT06lbty6grfpv0aIFx48fZ9CgQVy8eFFOqAnlT79dmvpC+yaCJyu7X6F9KyMaiUlk\nZCRTp05FqVTKEpPY2FhZYhIfH4+7u3upJSaDBw9m6dKlmJub4+7uTmJiovz98uXL8fPzo3nz5tSr\nV0/LlvKORUNAQIBW1l2BoDqidzITITHJQ8hMana/Vdm3kJmUASEx+R9CZiLQVfTqyRQSk/8hZCYC\nXaVaPZkVJQ8JDg7mzJkzz7XN8pI/M0lZZSkCQXWmWjmlqpCHVLTkpCJsqKgMKAJBZVCtlm8VJQ+B\nvHOwd+7cyZMnTxgxYgTt2rXTuh4aGoqJiQn9+vUD8o6nnT59OvXq1ePYsWPs27eP3NxcXFxcGD16\ndCFHolar+fHHH2W7e/TowWuvvUZ4eDg//PADarUaZ2dnRo8eTa1a2j+W/O8iFi1aRHJyMllZWfTp\n04cePXrI9+aVV17h8uXLjBo1iubNm5f+xgoEOkS1ckoVmYEkKSmJ+fPnExcXx+zZs1mxYsVTbQGI\njY3l5MmTBAYGolQqWbt2LceOHZPb1fD777+TmJjI4sWLUSgUpKWlkZ2dTXBwMDNnzsTOzo6VK1dy\n4MABORlAUfj6+mJmZkZWVhbTp0/Hy8sLc3NzMjMzcXV1ZcSIEWW6pwKBrlGtnFJlZCCxs7PD1taW\n2NjYp9oCEB4ezu3bt5k+fTqSJJGdnY2lpWWh8uHh4bz66quyMzMzM+POnTvY2tpiZ2cHQPfu3dm/\nf3+JTumXX37h7NmzQF4apri4OFxcXFAqlUIDJ6gRVCunVFbKkoEkP5IkFVp+GRgYaO3VZGdny//v\n1q0b77zzjlb5P//8k61bt6JQKBg7dmyxNpYlTCwiIoIrV64wb948DA0NmT17tpyAUqVSFbv3VJTM\nREguana/Vd23XslMKioDyenTp+nWrRvx8fEkJCRgb2+vlQapfv36XLhwAYCoqCgSEhIAaNWqFYsW\nLaJv377yMSUZGRl07NhRKxK8TZs2HDx4EHd3d5RKJampqdjb25OUlER8fDy2trYcPXq0xB9eeno6\nZmZmGBoaEhsbq2VfSc6tqIdCBBLW7H6rsm+9kplUlDwEoF69enz66ac8efKEMWPGFNps9vLy4ujR\no/j5+dGsWTM5arVRo0YMHTqUwMBAJEmiVq1ajBo1SktKAtCjRw8ePHjAlClTqFWrFj169KBXr16M\nGzeOpUuXyhvdr7zySpHjBvDw8ODgwYNMnjwZe3t7XF1dC5URCKo71UZmIuQhz5eCy9nKQF9nDfo2\nZr2QmQh5iECgP1SL5ZuQhwgE+kO1mCkJBAL9oUqcUlWnOKqJhIWF8ejRo6o2QyAoN1XilKo6xVFN\n5MiRIyQnJ1e1GQJBuamSPaWK0rAFBwejUqm4ffs2jx8/Zty4cRw5coTIyEiaNWuGr68vAGvXruXW\nrVtkZWXx4osvMnjwYCBPjd+tWzfOnz+PWq1m0qRJ2Nvbc/PmTb777juys7NRqVT4+vrSoEEDsrKy\nWLVqFTExMTRo0ICHDx8yatQonJyc+Pvvv9myZQs5OTnY2tri6+uLkZER48ePp3Pnzly6dAkDAwPG\njBnDpk2biI+Pp3///nJs1e7duzl16hQ5OTl07NiRwYMHyymZ3NzciIyMxMrKCn9/f86fP8+tW7dY\nsWIFKpWKwMDAMp/jLRDoClXilCpSw5aWlsbcuXM5d+4cQUFBzJ07V05fdOfOHRo3bsw777yDmZkZ\narWaOXPmcPfuXRwdHYE86UpQUBAHDhxg9+7dfPTRRzRq1Igvv/wSpVJJeHg4mzZtws/Pj/3792Nu\nbkYdhL0AABgsSURBVM6SJUu4d+8e/v7+QF74wrZt2/jiiy9QqVTs2rWLvXv38uabbwJ5GUwWLlxI\nSEgIwcHBBAYGkpmZiZ+fHz179uTvv/8mLi6O+fPnI0kSQUFBXLt2DWtra+Li4pg0aRJjx45l2bJl\nnDlzBh8fH/bv38+IESNo2rRpZfwIBYIKo0qcUkVq2Nq3bw/kpSiytLTUSl+UmJhI48aNOXHiBIcO\nHUKtVvPo0SNiYmJkp6QJuHRycuLPP/8E8hzdypUrefDggVaWkWvXrtG3b18AHBwcaNy4MQA3btwg\nJiaGGTNmIEkSubm5WoGO+W3MzMzEyMgIIyMjVCoV6enp/PXXX/z9998EBAQgSRKZmZk8ePAAa2tr\nbGxsZFudnJzkyHLNfS0KITMRMpPKpsbLTMqiYcufoqhg+qLc3FwSEhLYu3cvCxYswNTUlODgYC0d\nm6aOpjzA5s2badWqFVOmTCExMZHZs2cXaafGKUiSRNu2bZk4cWKR5fLbmD9yXKFQoFarkSSJN954\no1B0d2JiYqEx5be9OITMRARPVna/1VJmUlEatvwUNXN48uQJxsbGmJiY8OjRIy5evPhUL56eno6V\nlRWAVnbb5s2bc/LkSVq2bElMTAz37t0DoFmzZqxfv564uDjs7OzIzMwkOTmZBg0alMpeDw8PNm/e\njI+PD8bGxiQnJ8vOq7jZkLGxMU+ePCmxfYGgOlBle0oVpWEr2E9BGjduTJMmTZg0aRLW1ta4ubmV\nWB5gwIABrFq1im3btmkd/tarVy9WrVqFn58f9vb2ODg4YGpqSu3atfH19WX58uXk5OQAMHToUBo0\naFDim0XNtTZt2hAbG8vnn38OgImJCR9//DEKhaLY+t27d2fNmjUYGRmJjW5BtabStW81ScOmVqvJ\nzc3F0NCQ+Ph4AgMD+eqrrzAwMKhq056K0L7V7H6rsu/yat8qdab08OFDZs2aVWM0bFlZWcyePVue\nDY0ePbpaOCSBQJepNqcECJ4vYqZUs/utyr514pSAsLAw1q9f/zyakjl79qzWkbRbtmzh8uXLz7UP\nXULIawSCPHRWkHv27Fn5bRbkxda0atWqCi2qeMoirxFplAQ1lVLtKRWVQigsLIydO3dibm6Oo6Oj\n/LYnODiY9u3by4fYayQlADt37uT48eMolUo8PDz4z3/+w6FDh/j999/Jzc3Fzs6OCRMmEB0dzblz\n57h69So7duzAz8+PrVu3yu0Wl5aoOJnI08jMzGTZsmUkJyejVqt588036dSpE1FRUXz//fdkZmZi\nYWGBr68vlpaWxMXFsWbNGh4/foyBgQGTJ0/GxsamSNlMREQEoaGhWFhYcO/ePZycnPj4448BuHTp\nEiEhIRgZGWmlRCpO1hIWFsaff/5JRkYGkiRRr149OnbsSIcOHQD4+uuv8fb2xtPTswyPgECgWzzV\nKRWVQujo0aNs3bqVoKAgTExMmDVrVrHyBs1f/4sXL3L+/Hnmz5+PoaEhaWlpQN4xs5rcZT///DOH\nDx/mtddew9PTU8u5aXhaWqL8MpE9e/YwduxYrly5QkhISKGZiEqlYs6cOVy6dAkrKyumTZsG5MUy\n5ebmsmHDBvz9/bGwsODkyZP89NNPjBs3jhUrVjBw4EA8PT3JyclBrVaXKJuJjo5m6dKlWFpaMmPG\nDK5fv46TkxPffPMNs2bNwtbWlmXLlsl2FSdrAbh9+zZLlizB1NSUiIgIfvnlFzp06EB6ejo3btxg\nwoQJT/uRCgQ6zVOdUlEphG7cuEHLli0xNzcHwNvbu0hNWsF2XnrpJXlGZWZmBsDdu3fZvHkzaWlp\nZGZm0rZt2xLbuX//folpiYqSibi7u7Nw4cJi23R0dGTjxo1s2rSJdu3a4ebmxr1797h796589rYk\nSdStW5eMjAySk5Pl2YgmqPHatWslymbq1q0LQJMmTUhMTMTIyAhbW1tsbW0B6NKlC4cOHQKKl7VA\nXgyTqakpAC1btmTdunWkpKRw+vRpvLy8UCoLr8iFzETITCqbCpeZFEwhdO7cOU6fPl1kWaVSqSW3\n0LwuL47g4GD8/f1xdHQkLCyMiIiIp9pT0gvDomQimplSQYyMjJgzZw4NGjQgKCiIixcvypKSDh06\n4OjoWOiYlYyMjKfaV5D8UpL8dhU3jpJkLf/f3vkHRV3nf/yxuyCcQovLyqUwHUN7gg2iYjEmxE7Z\n1IU049z0w06DjUYnQTsxSUvv1JtxPLrLtDPMrMAyr8IO57jr5pxTKISsRFImwfQG1NUMdkF+CAvs\nft73x375fEEBUVlY5f2YcWQ/u/t+vj+7+3nt+/3e9/P18vPz6/VYs9nMl19+SVlZmZoF4UqkzUT+\n+jbcujdjM7nmQnd0dDSHDx+mubkZgNbWVsLDw6mqqqK1tRWn09krQIWEhPDf//4XcC9WdwelmJgY\nioqK1Dplra2tgPsiDwoKwul0cujQIbWd/mwTPcsSAdcsSwT/P1K68l93wGlsbGTMmDEkJCTw+OOP\nU1NTw6RJk2hublbLGLlcLqxWK/7+/gQHB6sFIZ1OJ52dnUyZMoWysjIURaG5uZmqqipMJlO/fQoN\nDcVms6mG2tLSUvW+/mwtfWE2m/n888/VNiWSW51rjpT6KyH05JNPsmbNGgICAlR3PLhLCb322mu8\n/PLLTJs2DX9/f8Dt5zpz5gyrV6/G19eXGTNmMH/+fJ566ileffVV9Ho9JpNJDUTx8fHs2LGDf/3r\nX+p6CrhHQv2VJbrR5HBnz55l9+7dqkG2e+F8xYoVvP/++7S1taEoCnPnziUsLIylS5fyzjvv8Omn\nn+Lj40NmZuaAtpm+8PX1ZdGiRWzatAk/Pz+ioqLUUVh/tpa+0Ov1hIaG3rAVRyLxNuTmyVucjo4O\nsrKy1B8dBovcPHl7646k9i1lM5EMLZWVlbz99tskJydfV0CSSLwZGZRuYaZOnXpbGJslkp6M6mom\nbW1t7N+/f1i0JBLJ4BjV1UxaW1v597//3ed9Q2HjGAkriLSfSG51bqtqJs3NzezcuRO73Q6AxWJh\n8uTJ5Ofnqz+/22w25s6dy69+9Sv27NlDXV0dq1atYurUqcTGxvLJJ58wbtw4Lly4wJYtW/q02Gg0\nGlJSUpgzZw7Hjx8nKCiI5cuXExgYyIYNG/jFL36h5iBPTEwcVJ+SkpJ47LHHgL5tPd2a3Zadw4cP\nc/ToUdLT08nJycHX15fa2loiIyNJSUkZ6rdMIhk2bqtqJnl5eSQnJxMZGYnNZmPjxo2qfePChQus\nX7+etrY2li9fziOPPMKCBQuwWq1kZ2cD7qljTU0Nmzdvxmg09mmxKSkpITExkY6ODkwmE6mpqezd\nu5f8/HzS0tIA956mTZs2AW4/2mD79Oijj/Ljjz/2qznQCLKhoYGNGzcO3ZskkYwQt1U1k8rKSs6f\nP6/ulHY4HHR0dAAQGxuLTqcjMDAQvV7fbzVZk8mE0WhU27vSYhMUFAS4A+v9998PQGJiIq+//rra\nRveI70b6NJDmQLs3uvvSF9JmIm0mw42sZvJ/IyUhBBs3buxl6+imZ87q7qohfdGXjaOnxebKPl2r\njcH2SavVqn0ajOaVVUyu7HdPpM1E7lMabl2P2kw8RVRUFKWlpX3aMrqrmSiKQllZmZrcf/ny5VdZ\nRbKzs9XySjExMarlAtzu/IH42c9+NmAFkL4sNjabDXAvKHfba0pKSnoVIOjJYPvUPQoaSDMoKIgL\nFy6gKIpqNpZIbjduq2omzz33HO+99x5ZWVkoisKUKVP6XCTvHnEEBAQQGRnJypUrmT59+lWWjv4s\nNkajET8/P06fPs1nn32mLnQPRZ8G0nzmmWfYtGkTer2eiIiIGzIHSyTejqxmcoP0/CXsVkTaTG5v\n3ZHU9ooc3YOlsbGRtWvX3hbVTIZrL5VEMtqQhlyJROJVeG3hAInn6Plz7WjQHUltec7XjwxKEonE\nq5BBSSKReBUyKI1Crmd37e2gO5La8pyvH7nQLZFIvAo5UpJIJF6FDEoSicSruCUMuZKh4bvvviMv\nLw8hBA8++CDz5s3zmJbdbmfbtm00NTWh0WiYM2cOSUlJtLa2smXLFurr6wkJCSEzM1MtrjmUKIrC\nK6+8gsFgYNWqVcOm29bWxttvv825c+fQaDQsWbKEiRMnelz7H//4B0VFRWg0Gu666y7S09NxOBwe\n0d2+fTtHjx5Fr9fz5z//GWDA17egoICioiJ0Oh0Wi+WaBWcRklGBy+USS5cuFXV1daKrq0usXLlS\nWK1Wj+k1NjaKmpoaIYQQ7e3t4sUXXxRWq1V8+OGHYt++fUIIIQoKCsTu3bs9ol9YWCi2bt0q/vjH\nPwohxLDpbtu2TRw8eFAIIYTT6RSXL1/2uLbdbhcZGRmiq6tLCCHE5s2bRVFRkcd0q6qqRE1NjXjp\npZfUY/1pnTt3TmRlZQmn0yl++uknsXTpUqEoyoDty+nbKOH06dNMnDiRCRMm4OPjQ3x8vFpQ0xME\nBQURHh4OuAuLhoaGYrfbOXLkCGazGXCXXPdEH+x2OxUVFcyZM0c9Nhy6bW1tVFdX8+CDDwKg0+kY\nO3bssGgrioLD4cDlctHZ2YnBYPCYblRUFOPGjet1rD+tI0eOMHv2bHQ6HSEhIUycOJHTp08P2L6c\nvo0SGhoaCA4OVm8bDIZrfjiGirq6Os6cOcPkyZNpampSk9YFBQXR1NQ05Hq7du3i2Wefpa2tTT02\nHLp1dXUEBgaSk5PDmTNniIiIwGKxeFzbYDCQnJxMeno6fn5+xMTEEBMTMyzn3E1/Wg0NDUyePLlX\nXxsaGgZsS46UJB7F4XCwefNmLBaLWi25J0NtbO5e6wgPDx8wU6cnDNWKolBTU8Ojjz5KdnY2fn5+\n7Nu3z+Paly9f5siRI+Tk5LBjxw46OjooKSnxuO5A3IyWHCmNEgwGg5osDtzfYAaDwaOaLpeL119/\nncTERO677z7A/S166dIl9X+9Xj+kmtXV1Rw5coSKigo6Oztpb2/nL3/5i8d1wf0aBwcHc/fddwMw\na9Ys9u3b53HtyspKQkJCCAgIACAuLo6TJ08Oyzl305/WlZ87u91+zc+dHCmNEkwmExcvXqS+vh6n\n00lpaSn33nuvRzW3b99OWFgYSUlJ6rGZM2dSXFwMQHFx8ZD34Te/+Q3bt29n27ZtLF++nOjoaJYt\nW+ZxXXBfmMHBwWquqsrKSsLCwjyubTQaOXXqFJ2dnQghhkVXCNFrJNqf1r333ktZWRlOp5O6ujou\nXryoZpjtD7mjexTx3XffkZubixCChx56yKNbAqqrq1m3bh133XUXGo0GjUbDM888g8lk4o033sBm\nszFhwgQyMzOvWjQdKk6cOEFhYaG6JWA4dGtra9mxYwdOp5Of//znpKenoyiKx7Xz8/MpKytDp9MR\nHh7OCy+8gMPh8Iju1q1bOXHiBC0tLej1ep566inuu+++frUKCgo4ePAgPj4+g9oSIIOSRCLxKuT0\nTSKReBUyKEkkEq9CBiWJROJVyKAkkUi8ChmUJBKJVyGDkkQi8SpkUJIMKydOnGDJkiU3/PydO3fy\nt7/9bQh7JPE2pM1Ect1kZGTQ1NSETqfD39+fadOm8fzzz+Pn5zekOsXFxRw8eJA//OEP6rFFixYN\nqUY3GRkZLFmyhOjoaI+0fz1s2LCBBx54gIceemikuzIiyJGS5IZYvXo1u3bt4rXXXqOmpoaCggKP\n6Iy2SsSKoox0F0YcOVKS3BR6vZ5p06ZRW1urHnM6nezZs4fDhw/jdDqJi4sjNTUVX1/fq56/b98+\nDhw4QHNzM0ajkaeffpq4uDjOnz/Pzp07URSFlJQUdDodubm55OTkEBwczNNPP01mZibPPvsssbGx\ngPuCXrx4MWvXriU8PJwffviBDz/8EKvVyoQJE7BYLNxzzz3XPKfi4mIOHDiAyWSiuLiYgIAAli1b\nxoULF/jkk09wOp0sXLhQzR+Uk5ODr68vP/30E6dOnSIiIoKMjAyMRiMAJ0+eJC8vj4sXLzJx4kQs\nFouazmPDhg1ERkby/fffU1tbS1xcHFVVVZw6dYpdu3ZhNptJS0sjLy+Pr7/+mra2NiZNmkRqaipR\nUVGA22JitVrx9fXl22+/xWg0kpGRQUREBOA2webm5lJdXY0Qgvj4eNLS0gA4ePAghYWFNDU1YTKZ\nWLx4sdrvEWNIUtFJRhXp6emisrJSCCGEzWYTL730ksjLy1Pvz83NFdnZ2eLy5cuivb1dZGdniz17\n9gghhPj+++/FCy+8oD72q6++Eo2NjUIIIcrKysTChQvV20VFReL3v/99L+233npLfPzxx0IIIfLz\n88XWrVvV+8rLy0VmZqYQwp2NMS0tTVRUVAghhDh+/LhIS0sTzc3N1zynoqIiMX/+fFFcXCwURRF/\n/etfxZIlS8R7770nurq6xLFjx0RKSopwOBxqn1JSUkRVVZXo6uoSubm54ne/+50QQoiWlhZhsVhE\nSUmJcLlc4tChQ8JisYiWlhYhhBDr168X6enpwmq1CpfLJZxOp1i/fr04cOBAr/6VlJSI1tZW4XK5\nRGFhoVi0aJGaafLTTz8VCxYsEBUVFUJRFPHRRx+JV199VQjhzji6cuVKsWvXLtHR0SG6urpEdXW1\nEEKIb775Rrz44ovi/PnzwuVyic8++0ysXbu2/zd+mJDTN8kN8ac//YnU1FTS09PR6/U8+eST6n0H\nDhzAYrEwduxY/P39mTdvHqWlpX22M2vWLDU52P333z+ozITdJCQkUF5eTmdnJwCHDh0iPj4egJKS\nEmbMmMH06dMBmDp1KhEREVRUVAyq7ZCQEMxmMxqNhtmzZ2O323niiSfw8fEhJiYGHx8fLl68qD4+\nNjaWqKgofHx8mD9/PqdOnaKhoYGjR48yadIkEhIS0Gq1xMfHExoaSnl5ufpcs9lMaGgoWq0WnU7X\n77mOGzcOrVZLcnIyXV1dajYCcGeDnD59OhqNhsTERM6ePQu4M45eunSJhQsXMmbMGHx8fIiMjATg\nP//5D/PmzWPSpElotVrmzZtHbW1tr1QjI4GcvkluiKysLKKjo6mqquLNN9+kpaWFsWPH0tzcTGdn\nJ6tWrVIfK65Ic9GTL774gn/+85/U19cD7qRwLS0tg+rDnXfeSVhYGOXl5cycOZPy8nLmz58PQH19\nPV999VWvi9/lcg16Ibs7UAKMGTMGgDvuuKPXMYfDod7umdXT39+fcePG0dDQQGNj41XTIaPR2Cv7\n4mCmS3//+98pKiri0qVLALS3t9Pc3Nxnf/38/Ojs7ERRFOx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"text/plain": ["<matplotlib.figure.Figure at 0x149491d0>"]}, "metadata": {}, "output_type": "display_data"}], "source": ["import numpy as np\n", "feature_name = X.columns\n", "\n", "limit = 20\n", "feature_importance = clf.feature_importances_[:20]\n", "feature_importance = 100.0 * (feature_importance / feature_importance.max())\n", "sorted_idx = np.argsort(feature_importance)\n", "pos = np.arange(sorted_idx.shape[0]) + .5\n", "plt.subplot(1, 2, 2)\n", "plt.barh(pos, feature_importance[sorted_idx], align='center')\n", "plt.yticks(pos, feature_name[sorted_idx])\n", "plt.xlabel('Relative Importance')\n", "plt.title('Variable Importance')"]}, {"cell_type": "markdown", "metadata": {}, "source": ["Il faut tout de m\u00eame rester prudent quant \u00e0 l'interpr\u00e9tation du graphe pr\u00e9c\u00e9dent. La documentation au sujet de l[importance des features](http://scikit-learn.org/stable/modules/ensemble.html#feature-importance-evaluation) pr\u00e9cise plus ou moins comment sont calcul\u00e9s ces chiffres. Toutefois, lorsque des variables sont tr\u00e8s corr\u00e9l\u00e9es, elles sont plus ou moins interchangeables. Tout d\u00e9pend alors comment l'algorithme d'apprentissage choisit telle ou telle variables, toujours dans le m\u00eame ordre ou dans un ordre al\u00e9atoire."]}, {"cell_type": "markdown", "metadata": {}, "source": ["#### variables\n", "\n", "On utilise le code de la s\u00e9ance 3 [Analyse en Composantes Principales](http://www.xavierdupre.fr/app/ensae_teaching_cs/helpsphinx/notebooks/td2a_cenonce_session_3A.html?highlight=acp#PCA) pour observer les variables."]}, {"cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [{"data": {"text/plain": ["PCA(copy=True, n_components=4, whiten=False)"]}, "execution_count": 15, "metadata": {}, "output_type": "execute_result"}], "source": ["from sklearn.decomposition import PCA\n", "pca = PCA(n_components=4)\n", "x_transpose = X.T\n", "pca.fit(x_transpose)"]}, {"cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [{"data": {"text/plain": ["<matplotlib.text.Text at 0x161b9630>"]}, "execution_count": 16, "metadata": {}, "output_type": "execute_result"}, {"data": {"image/png": 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6UCIicpxTbuQaDAZERkbiww8/xPr165GRkYHq6mpnTE1ERE5k85q+VqtFWVmZsm0ymaDV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\nIomw9ImIJMLSJyKSCEufiEgi/wcHLKKupdAc3QAAAABJRU5ErkJggg==\n", "text/plain": ["<matplotlib.figure.Figure at 0xa81cdd8>"]}, "metadata": {}, "output_type": "display_data"}], "source": ["plt.bar(numpy.arange(len(pca.explained_variance_ratio_))+0.5, pca.explained_variance_ratio_)\n", "plt.title(\"Variance expliqu\u00e9e\")"]}, {"cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [{"data": {"image/png": 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"text/plain": ["<matplotlib.figure.Figure at 0x161f2a90>"]}, "metadata": {}, "output_type": "display_data"}], "source": ["import warnings\n", "warnings.filterwarnings('ignore')\n", "X_reduced = pca.transform(x_transpose)\n", "plt.figure(figsize=(18,6))\n", "plt.scatter(X_reduced[:, 0], X_reduced[:, 1])\n", "for label, x, y in zip(x_transpose.index, X_reduced[:, 0], X_reduced[:, 1]):\n", "    plt.annotate(\n", "        label,\n", "        xy = (x, y), xytext = (-10, 10),\n", "        textcoords = 'offset points', ha = 'right', va = 'bottom',\n", "        bbox = dict(boxstyle = 'round,pad=0.5', fc = 'yellow', alpha = 0.5),\n", "        arrowprops = dict(arrowstyle = '->', connectionstyle = 'arc3,rad=0'))"]}, {"cell_type": "markdown", "metadata": {}, "source": ["Les variables les plus dissemblables sont celles qui contribuent le plus. Toutefois, \u00e0 la vue de ce graphique, il appara\u00eet qu'il faut normaliser les donn\u00e9es avant d'interpr\u00e9ter l'ACP :"]}, {"cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [{"data": {"text/plain": ["<matplotlib.text.Text at 0x1628bd68>"]}, "execution_count": 18, "metadata": {}, "output_type": "execute_result"}, {"data": {"image/png": 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TSx2TyYTk5GQAQGxsLBoaGlBfXw/gaog0NjbCbrfj8uXLCA0N9cI0iIioPdxel7HZbAgL\nC3OW9Xo9ysvL3dax2WyIiYnB5MmTMWfOHAQFBSE+Ph7x8fEdOHwiIroZXl0YvnjxIgoLC7F27Vq8\n+eabaGxsxMGDB73ZJRERtYHbMwG9Xo+6ujpn2WazQa/Xt6hjtVqdZavVCr1ej5KSEkRERCA4OBgA\nMGLECBw9ehSjRo1q0Y/FYoHFYnGW09LSoNPp2jwh9f8uQ3U0tVrdrvG0JjAwsMP21Rlxfv6N8/Nv\nW7dudf4cFxeHuLi4G9Z3GwIDBw5EdXU1amtrERoaCqPRiPnz57vUSUhIwO7duzFy5EgcO3YMWq0W\nISEh6NWrF8rKynDlyhV069YNJSUlGDBgQKv9tDbY8+fPuxteC3a7vc1tPN1ve8bTGp1O12H76ow4\nP//G+fkvnU6HtLS0NrVxGwIqlQoZGRlYtmwZhBAYM2YMoqOjUVBQAEVRMG7cOAwbNgzFxcWYN28e\nNBoNZs+eDeBqgNx7773IysqCWq2GwWDAuHHj2jc7IiLqcIoQQvh6ENdz+vTpNrcptV5B1icnOnws\nKx6IwV1hgR2yr658JAJwfv6O8/Nfffr0aXMbfmOYiEhiDAEiIokxBIiIJMYQICKSGEOAiEhiDAEi\nIokxBIiIJMYQICKSGEOAiEhiDAEiIokxBIiIJMYQICKSGEOAiEhiDAEiIokxBIiIJMYQICKSGEOA\niEhiDAEiIokxBIiIJMYQICKSGEOAiEhiDAEiIokxBIiIJMYQICKSGEOAiEhiDAEiIokxBIiIJMYQ\nICKSGEOAiEhiDAEiIokxBIiIJMYQICKSGEOAiEhiDAEiIokxBIiIJMYQICKSWIAnlcxmM/Lz8yGE\nQEpKClJTU1vUycvLg9lsRlBQEDIzM2EwGAAADQ0NeOONN3Dq1CkoioLZs2cjNja2QydBRETt4zYE\nHA4HcnNzsXTpUoSGhmLRokVITExEVFSUs05xcTFqamqwevVqlJWVIScnB8uXLwcAbNiwAUOHDsWz\nzz4Lu92Oy5cve282RETUJm4vB5WXlyMyMhLh4eEICAhAUlISTCaTSx2TyYTk5GQAQGxsLBoaGlBf\nX4+GhgaUlpYiJSUFAKBWq9GjRw8vTIOIiNrD7ZmAzWZDWFiYs6zX61FeXu62js1mg0qlgk6nw9q1\na1FZWYmYmBjMmDEDgYGBHTgFIiJqL4/WBNrL4XCgoqICGRkZGDBgAPLz87Fjxw6kpaV5s9tbpq7R\ngbqLzW1up66vh91uv2GdXtoA9NJw3Z6IvMttCOj1etTV1TnLNpsNer2+RR2r1eosW61WZ52wsDAM\nGDAAAHDvvfdix44drfZjsVhgsVic5bS0NOh0ujZM5Sp1fX2b23i0X7W6xXjK6uuR9ckJr/T36kOx\n6B/e9vl3BoGBge363fkLzs+/dfX5bd261flzXFwc4uLibljfbQgMHDgQ1dXVqK2tRWhoKIxGI+bP\nn+9SJyEhAbt378bIkSNx7NgxaLVahISEALgaAqdPn0afPn1QUlKC6OjoVvtpbbDnz593N7wW3B1h\nt5fdbm8xHm/1db3+/IVOp/PbsXuC8/NvXXl+Op2uzVda3IaASqVCRkYGli1bBiEExowZg+joaBQU\nFEBRFIwbNw7Dhg1DcXEx5s2bB41Gg9mzZzvbz5gxA6+//jqam5tx++23Y86cOW2fGREReYVHawJD\nhgxBdna2y7bx48e7lDMyMlptazAY8NJLL7VzeERE5E1ceSQikhhDgIhIYgwBIiKJMQSIiCTGECAi\nkhhDgIhIYgwBIiKJMQSIiCTGECAikphXnyJKHau9Ty31BJ9aSiQnhoAfqbvY7LWnlq54IAa9NPw7\nD0Sy4aEfEZHEGAJERBJjCBARSYwhQEQkMYYAEZHEGAJERBJjCBARSYwhQEQkMYYAEZHEGAJERBJj\nCBARSYwhQEQkMYYAEZHEGAJERBJjCBARSYwhQEQkMYYAEZHEGAJERBJjCBARSYwhQEQkMYYAEZHE\nGAJERBJjCBARSYwhQEQkMYYAEZHEAjypZDabkZ+fDyEEUlJSkJqa2qJOXl4ezGYzgoKCkJmZCYPB\n4HzN4XBg0aJF0Ov1yMrK6rDBk3fVNTpQd7G5ze3U9fWw2+03rNNLG4BeGh6DEPma2xBwOBzIzc3F\n0qVLERoaikWLFiExMRFRUVHOOsXFxaipqcHq1atRVlaGnJwcLF++3Pn6xx9/jKioKFy6dMk7syCv\nqLvYjKxPTnhl3yseiEEvTaBX9k1EnnN7KFZeXo7IyEiEh4cjICAASUlJMJlMLnVMJhOSk5MBALGx\nsWhoaEB9fT0AwGq1ori4GGPHjvXC8ImI6Ga4DQGbzYawsDBnWa/Xw2azeVxn48aNmD59OhRF6agx\nExFRB/HqRdmioiL07NkTBoMBQggIIbzZHRERtZHbNQG9Xo+6ujpn2WazQa/Xt6hjtVqdZavVCr1e\njy+//BKFhYUoLi7GlStXcOnSJaxZswZz585t0Y/FYoHFYnGW09LSoNPp2jwh9f8uQ3U0tVrdYjze\n6kvW/vxFYGCg347dE5yff9u6davz57i4OMTFxd2wvtsQGDhwIKqrq1FbW4vQ0FAYjUbMnz/fpU5C\nQgJ2796NkSNH4tixY9BqtQgJCcG0adMwbdo0AMDhw4fx4YcfthoA1xvs+fPn3Q2vBXd3pbSX3W5v\nMR5v9SVrf/5Cp9P57dg9wfn5L51Oh7S0tDa1cRsCKpUKGRkZWLZsGYQQGDNmDKKjo1FQUABFUTBu\n3DgMGzYMxcXFmDdvHjQaDWbPnt3uSRAR0a3j0fcEhgwZguzsbJdt48ePdylnZGTccB+DBw/G4MGD\n2zg8IiLyJn5bh4hIYgwBIiKJMQSIiCTm0ZoA0a3Q3mcVucPnFBFdH0OAOg1vPauIzykiuj4eHhER\nSYwhQEQkMV4OIml56+8lcA2C/AlDgKTFNQgiXg4iIpIazwSIbhHeAkudEUOA6Bbh5SfqjHj4QEQk\nMZ4JEHVRvPuJPMEQIOqibvXlJ655+CeGABF1CH8JHZ7puGIIEJFf4kJ7x5An7oiIqAWGABGRxBgC\nREQSYwgQEUmMIUBEJDGGABGRxBgCREQSYwgQEUmMIUBEJDGGABGRxBgCREQSYwgQEUmMIUBEJDGG\nABGRxBgCREQSYwgQEUmMIUBEJDGGABGRxDz685Jmsxn5+fkQQiAlJQWpqakt6uTl5cFsNiMoKAiZ\nmZkwGAywWq1Ys2YNzp07B0VRMHbsWEyaNKnDJ0FERO3jNgQcDgdyc3OxdOlShIaGYtGiRUhMTERU\nVJSzTnFxMWpqarB69WqUlZUhJycHy5cvh1qtxuOPPw6DwYDGxkZkZWXhnnvucWlLRES+4/ZyUHl5\nOSIjIxEeHo6AgAAkJSXBZDK51DGZTEhOTgYAxMbGoqGhAfX19QgJCYHBYAAAaDQaREVFwWazdfws\niIioXdyGgM1mQ1hYmLOs1+tbfJB7Uufs2bOorKxEbGzszY6ZiIg6yC1ZGG5sbMSqVauQnp4OjUZz\nK7okIiIPuF0T0Ov1qKurc5ZtNhv0en2LOlar1Vm2Wq3OOna7HStXrsTo0aORmJh43X4sFgssFouz\nnJaWBp1O5/lM/kddX9/mNh7tV61uMR5v9cX+vN8X+2N/be3PX2zdutX5c1xcHOLi4m5Y320IDBw4\nENXV1aitrUVoaCiMRiPmz5/vUichIQG7d+/GyJEjcezYMWi1WoSEhAAA1q1bh+joaLd3BbU22PPn\nz7sbXgt2u73NbTzd70/H462+2J/3+2J/7K+t/fkDnU6HtLS0NrVxGwIqlQoZGRlYtmwZhBAYM2YM\noqOjUVBQAEVRMG7cOAwbNgzFxcWYN28eNBoN5syZAwAoLS3FgQMH0K9fPyxcuBCKomDq1KkYMmRI\n+2ZIREQdyqPvCQwZMgTZ2dku28aPH+9SzsjIaNHurrvuwrvvvnsTwyMiIm/iN4aJiCTGECAikhhD\ngIhIYgwBIiKJMQSIiCTGECAikhhDgIhIYgwBIiKJMQSIiCTGECAikhhDgIhIYgwBIiKJMQSIiCTG\nECAikhhDgIhIYgwBIiKJMQSIiCTGECAikhhDgIhIYgwBIiKJMQSIiCTGECAikhhDgIhIYgwBIiKJ\nMQSIiCTGECAikhhDgIhIYgwBIiKJMQSIiCTGECAikhhDgIhIYgwBIiKJMQSIiCTGECAikhhDgIhI\nYgwBIiKJBXhSyWw2Iz8/H0IIpKSkIDU1tUWdvLw8mM1mBAUFITMzEwaDweO2RETkG27PBBwOB3Jz\nc7F48WKsXLkSRqMRVVVVLnWKi4tRU1OD1atXY+bMmcjJyfG4LRER+Y7bECgvL0dkZCTCw8MREBCA\npKQkmEwmlzomkwnJyckAgNjYWDQ0NKC+vt6jtkRE5DtuQ8BmsyEsLMxZ1uv1sNlsHtXxpC0REfkO\nF4aJiCTmdmFYr9ejrq7OWbbZbNDr9S3qWK1WZ9lqtUKv16O5udlt22ssFgssFouznJaWhj59+ng+\nk//p0wcw3W1oc7v2uJV9sT/2x/5825+/2Lp1q/PnuLg4xMXF3bC+2zOBgQMHorq6GrW1tWhubobR\naERCQoJLnYSEBOzfvx8AcOzYMWi1WoSEhHjU9seDTUtLc/778US6mq48N4Dz83ecn//aunWry+eo\nuwAAPDgTUKlUyMjIwLJlyyCEwJgxYxAdHY2CggIoioJx48Zh2LBhKC4uxrx586DRaDB79uwbtiUi\nos7Bo+8JDBkyBNnZ2S7bxo8f71LOyMjwuC0REXUOnXZh2JPTGH/VlecGcH7+jvPzX+2ZmyKEEF4Y\nCxER+YFOeyZARETexxAgIpKYRwvDt1JXfuCc1WrFmjVrcO7cOSiKgrFjx2LSpEm+HlaHcjgcWLRo\nEfR6PbKysnw9nA7X0NCAN954A6dOnYKiKJg9ezZiY2N9PawOsWvXLuzbtw+KoqBfv36YM2cOAgI6\n3UeEx9atW4eioiL07NkTr776KgDgwoUL+Pvf/47a2lpERETgmWeeQY8ePXw80vZpbX6bN2/GN998\ng4CAANx+++2YM2eO+/mJTsRut4u5c+eKs2fPiqamJrFgwQLxww8/+HpYHeY///mPqKioEEIIcenS\nJfH00093qfkJIcSHH34osrOzxcsvv+zroXjFmjVrxN69e4UQQjQ3N4uLFy/6eEQdw2q1iszMTNHU\n1CSEEGLVqlXi888/9/Gobs6RI0dERUWF+MMf/uDctmnTJrFjxw4hhBAffPCB2Lx5s6+Gd9Nam9+3\n334r7Ha7EEKIzZs3iy1btrjdT6e6HNTVHzgXEhLifMS2RqNBVFRUl3qWktVqRXFxMcaOHevroXhF\nQ0MDSktLkZKSAgBQq9V+exTZGofDgcbGRtjtdly+fBmhoaG+HtJNueuuu6DVal22FRYWOh92ef/9\n9/v150tr84uPj4dKdfVjPTY21uVJDtfTqc71WnvgXHl5uQ9H5D1nz55FZWVll7mUAAAbN27E9OnT\n0dDQ4OuheMXZs2eh0+mwdu1aVFZWIiYmBjNmzEBgYKCvh3bT9Ho9Jk+ejDlz5iAoKAjx8fGIj4/3\n9bA63Llz5xASEgLg6kHZuXPnfDwi79m3bx+SkpLc1utUZwKyaGxsxKpVq5Ceng6NRuPr4XSIa9cm\nDQYDhBAQXfDOY4fDgYqKCkycOBErVqxAUFAQduzY4ethdYiLFy+isLAQa9euxZtvvonGxkYcPHjQ\n18PyOkVRfD0Er3j//fehVqsxatQot3U7VQh48rA6f2e327Fy5UqMHj0aiYmJvh5OhyktLUVhYSHm\nzp2L7OxsWCwWrFmzxtfD6lB6vR5hYWEYMGAAAODee+/FiRMnfDyqjlFSUoKIiAgEBwdDpVJhxIgR\nOHr0qK+H1eFCQkJQX18PAKivr0fPnj19PKKO9/nnn6O4uBjz58/3qH6nCoG2PHDOX61btw7R0dFd\n7q6gadOmYd26dVizZg1+//vf4+c//znmzp3r62F1qJCQEISFheH06dMArn5wdpVnYfXq1QtlZWW4\ncuUKhBAoKSlBVFSUr4d10356Vjp8+HB8/vnnAK5+WPr758tP52c2m7Fz504sXLgQ3bp182gfne4b\nw2azGRspp8yMAAAA0UlEQVQ2bHA+cK4r3SJaWlqKF154Af369YOiKFAUBVOnTsWQIUN8PbQOdfjw\nYXz44Ydd8hbRkydP4s0330Rzc7Pnt+D5iW3btuFf//oX1Go1DAYDZs2a5de3iGZnZ+Pw4cM4f/48\nevbsibS0NCQmJuK1115DXV0dwsPD8cwzz7RYXPUXrc3vgw8+QHNzM3Q6HYCri8NPPvnkDffT6UKA\niIhunU51OYiIiG4thgARkcQYAkREEmMIEBFJjCFARCQxhgARkcQYAkREEmMIEBFJ7P8B6jF527wc\nAPkAAAAASUVORK5CYII=\n", "text/plain": ["<matplotlib.figure.Figure at 0x161fd5f8>"]}, "metadata": {}, "output_type": "display_data"}], "source": ["from sklearn.preprocessing import normalize\n", "xnorm = normalize(x_transpose)\n", "pca = PCA(n_components=10)\n", "pca.fit(xnorm)\n", "plt.bar(numpy.arange(len(pca.explained_variance_ratio_))+0.5, pca.explained_variance_ratio_)\n", "plt.title(\"Variance expliqu\u00e9e\")"]}, {"cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [{"data": {"image/png": 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XrwGWdWqgc3a2l0ceWVrgoAtgwoQNvPXWtXTqFENmZm6g/4iIFDc924iIiIgEUcWKkRw9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kjq1XMgJdjtoKoO8vJUl6ECYPVqN8aN027LQyIjw8ycOftcxghnH+78fMrCxx/vuIExQkdH536h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\ngg==\n", "text/plain": ["<matplotlib.figure.Figure at 0x1644f9e8>"]}, "metadata": {}, "output_type": "display_data"}], "source": ["X_reduced = pca.transform(xnorm)\n", "plt.figure(figsize=(18,6))\n", "plt.scatter(X_reduced[:, 0], X_reduced[:, 1])\n", "for label, x, y in zip(x_transpose.index, X_reduced[:, 0], X_reduced[:, 1]):\n", "    plt.annotate(\n", "        label,\n", "        xy = (x, y), xytext = (-10, 10),\n", "        textcoords = 'offset points', ha = 'right', va = 'bottom',\n", "        bbox = dict(boxstyle = 'round,pad=0.5', fc = 'yellow', alpha = 0.5),\n", "        arrowprops = dict(arrowstyle = '->', connectionstyle = 'arc3,rad=0'))"]}, {"cell_type": "markdown", "metadata": {}, "source": ["Nettement mieux. En r\u00e8gle g\u00e9n\u00e9rale, il est pr\u00e9f\u00e9rable de normaliser ses donn\u00e9es avant d'apprendre un mod\u00e8le. Cela n'est pas toujours n\u00e9cessaire (comme pour les arbres de d\u00e9cision). Toutefois, num\u00e9riquement, avoir des donn\u00e9es d'ordre de grandeur tr\u00e8s diff\u00e9rent introduit toujours plus d'approximations."]}, {"cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [], "source": ["from sklearn.pipeline import Pipeline\n", "from sklearn.preprocessing import Normalizer\n", "from sklearn.ensemble import GradientBoostingClassifier\n", "\n", "clf = Pipeline([\n", "      ('normalize', Normalizer()),\n", "      ('classification', GradientBoostingClassifier())\n", "    ])\n", "clf = clf.fit(X_train, Y_train.ravel()) "]}, {"cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [{"name": "stdout", "output_type": "stream", "text": ["non normalis\u00e9\n", " [[1261   40]\n", " [ 120   71]]\n", "normalis\u00e9\n", " [[1270   31]\n", " [ 127   64]]\n"]}], "source": ["from sklearn.metrics import confusion_matrix\n", "x,y = X_test, Y_test\n", "yp  = clf.predict(x)\n", "cm2 = confusion_matrix(y, yp)\n", "print(\"non normalis\u00e9\\n\",cm)\n", "print(\"normalis\u00e9\\n\",cm2)"]}, {"cell_type": "markdown", "metadata": {}, "source": ["C'est plus ou moins \u00e9quivalent lorsque les variables sont normalis\u00e9es dans ce cas. Il faudrait v\u00e9rifier sur la courbe ROC."]}, {"cell_type": "markdown", "metadata": {}, "source": ["### Exercice 2 : tracer la courbe ROC\n", "\n", "On utilise l'exemple [Receiver Operating Characteristic (ROC)](http://scikit-learn.org/stable/auto_examples/plot_roc.html) qu'il faut modifi\u00e9 car la r\u00e9ponse juste dans notre cas est le fait de pr\u00e9dire la bonne classe. Cela veut dire qu'il y a deux cas pour lesquels le mod\u00e8le pr\u00e9dit le bon r\u00e9sultat : on choisit la classe qui la probabilit\u00e9 la plus forte."]}, {"cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [{"data": {"text/plain": ["array([[ 0.9792842 ,  0.0207158 ],\n", "       [ 0.98228488,  0.01771512],\n", "       [ 0.83708208,  0.16291792],\n", "       [ 0.98675536,  0.01324464],\n", "       [ 0.98818146,  0.01181854]])"]}, "execution_count": 22, "metadata": {}, "output_type": "execute_result"}], "source": ["from sklearn.metrics import roc_curve, auc\n", "probas = clf.predict_proba(X_test)\n", "probas[:5]"]}, {"cell_type": "markdown", "metadata": {}, "source": ["On construit le vecteur des bonnes r\u00e9ponses :"]}, {"cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [{"data": {"text/plain": ["array([[ 1.        ,  0.9792842 ],\n", "       [ 1.        ,  0.98228488],\n", "       [ 1.        ,  0.83708208],\n", "       [ 1.        ,  0.98675536],\n", "       [ 1.        ,  0.98818146]])"]}, "execution_count": 23, "metadata": {}, "output_type": "execute_result"}], "source": ["rep = [ ]\n", "yt = Y_test.ravel()\n", "for i in range(probas.shape[0]):\n", "    p0,p1 = probas[i,:]\n", "    exp = yt[i]\n", "    if p0 > p1 :\n", "        if exp == 0 :\n", "            # bonne r\u00e9ponse\n", "            rep.append ( (1, p0) )\n", "        else :\n", "            # mauvaise r\u00e9ponse\n", "            rep.append( (0,p0) )\n", "    else :\n", "        if exp == 0 :\n", "            # mauvaise r\u00e9ponse\n", "            rep.append ( (0, p1) )\n", "        else :\n", "            # bonne r\u00e9ponse\n", "            rep.append( (1,p1) )\n", "mat_rep = numpy.array(rep)\n", "mat_rep[:5]"]}, {"cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [{"data": {"text/plain": ["('taux de bonne r\u00e9ponse', 0.89410187667560337)"]}, "execution_count": 24, "metadata": {}, "output_type": "execute_result"}], "source": ["\"taux de bonne r\u00e9ponse\",sum(mat_rep[:,0]/len(mat_rep)) # voir matrice de confusion"]}, {"cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [{"data": {"text/plain": ["<matplotlib.legend.Legend at 0x17e0df60>"]}, "execution_count": 25, "metadata": {}, "output_type": "execute_result"}, {"data": {"image/png": 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2bdpEgwYNbB2OEJVWbvJ49dVXjT+//vrrVglGCHt340iqhQsXSuIQtZZZPd8z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\nxcfX6qfW6XRMnjyZ1NRUq59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A8vPzcXd3x8HBwRbhWlRQUBANGjQo9/mqfm7WmuRRXtHE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\nRK5CYII=\n", "text/plain": ["<matplotlib.figure.Figure at 0x1648f630>"]}, "metadata": {}, "output_type": "display_data"}], "source": ["fpr, tpr, thresholds = roc_curve(mat_rep[:,0], mat_rep[:, 1])\n", "roc_auc = auc(fpr, tpr)\n", "plt.plot(fpr, tpr, label='ROC curve (area = %0.2f)' % roc_auc)\n", "plt.plot([0, 1], [0, 1], 'k--')\n", "plt.xlim([0.0, 1.0])\n", "plt.ylim([0.0, 1.0])\n", "plt.xlabel('False Positive Rate')\n", "plt.ylabel('True Positive Rate')\n", "plt.title('ROC')\n", "plt.legend(loc=\"lower right\")"]}, {"cell_type": "markdown", "metadata": {}, "source": ["Ce score n'est pas si mal pour un premier essai. On n'a pas tenu compte du fait que la classe 1 est sous-repr\u00e9sent\u00e9e (voir [Quelques astuces pour faire du machine learning](http://www.xavierdupre.fr/blog/2014-03-28_nojs.html). A priori, ce ne devrait pas \u00eatre le cas du [GradientBoostingClassifier](http://scikit-learn.org/stable/modules/generated/sklearn.ensemble.GradientBoostingClassifier.html). C'est une famille de mod\u00e8les qui, lors de l'apprentissage, pond\u00e8re davantage les exemples o\u00f9 ils font des erreurs. L'algorithme de  [boosting](http://fr.wikipedia.org/wiki/Boosting) le plus connu est [AdaBoost](http://fr.wikipedia.org/wiki/AdaBoost).\n", "\n", "On tire maintenant deux \u00e9chantillons al\u00e9atoires qu'on ajoute au graphique pr\u00e9c\u00e9dent :"]}, {"cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [{"name": "stdout", "output_type": "stream", "text": ["(697,) (697,) (699,) (699,)\n"]}, {"data": {"text/plain": ["<matplotlib.legend.Legend at 0x17e82940>"]}, "execution_count": 26, "metadata": {}, "output_type": "execute_result"}, {"data": {"image/png": 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k1dGjR/nxxx/x9JSRgfWJS59OWVlZxMbaSoMrioKqqnTt2pUtW7ZUaXD1hapq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\nYII=\n", "text/plain": ["<matplotlib.figure.Figure at 0x17e30dd8>"]}, "metadata": {}, "output_type": "display_data"}], "source": ["import random\n", "Y1 = numpy.array([ random.randint(0,1) == 0 for i in range(0,mat_rep.shape[0]) ])\n", "Y2 = numpy.array([ random.randint(0,1) == 0 for i in range(0,mat_rep.shape[0]) ])\n", "\n", "fpr1, tpr1, thresholds1 = roc_curve(mat_rep[Y1,0], mat_rep[Y1, 1])\n", "roc_auc1 = auc(fpr1, tpr1)\n", "fpr2, tpr2, thresholds2 = roc_curve(mat_rep[Y2,0], mat_rep[Y2, 1])\n", "roc_auc2 = auc(fpr2, tpr2)\n", "print(fpr1.shape,tpr1.shape,fpr2.shape,tpr2.shape)\n", "\n", "import matplotlib.pyplot as plt\n", "fig = plt.figure()\n", "ax = fig.add_subplot(1,1,1)\n", "\n", "ax.plot(fpr, tpr, label='ROC curve (area = %0.2f)' % roc_auc)\n", "ax.plot([0, 1,2], [0, 1,2], 'k--')\n", "ax.set_xlim([0.0, 1.0])\n", "ax.set_ylim([0.0, 1.0])\n", "ax.set_xlabel('False Positive Rate')\n", "ax.set_ylabel('True Positive Rate')\n", "ax.set_title('ROC')\n", "ax.plot(fpr1, tpr1, label='ech 1, area=%0.2f' % roc_auc1)\n", "ax.plot(fpr2, tpr2, label='ech 2, area=%0.2f' % roc_auc2)\n", "ax.legend(loc=\"lower right\")"]}, {"cell_type": "code", "execution_count": 26, "metadata": {}, "outputs": [], "source": []}], "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": "3.6.4"}}, "nbformat": 4, "nbformat_minor": 2}