TME1-4/bagging_boosting.ipynb

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    "# Fouille de données et medias sociaux\n",
    "# TP4 : Bagging et Boosting\n",
    "\n",
    "## Exercice 1 Bagging\n",
    "### Question 1\n",
    "Écrivez une fonction (ou une classe) implémentant la méthode Bagging."
   ]
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   "source": [
    "import numpy as np\n",
    "from sklearn.base import ClassifierMixin\n",
    "from sklearn.tree import DecisionTreeClassifier\n",
    "from collections import Counter\n",
    "from sklearn.metrics import accuracy_score\n",
    "from sklearn.utils import shuffle\n",
    "from sklearn.base import clone\n",
    "\n",
    "class BaggingClassifier(ClassifierMixin):\n",
    "    def __init__(self, base_estimator=None, n_estimators=5, \n",
    "                 max_samples=1.0, bootstrap=True, verbose=0,\n",
    "                oob_score=False):\n",
    "        if base_estimator is None:\n",
    "            self.base_estimator = DecisionTreeClassifier()\n",
    "        else:\n",
    "            self.base_estimator = base_estimator\n",
    "            \n",
    "        self.n_estimators = n_estimators\n",
    "        self.max_samples = max_samples\n",
    "        self.bootstrap = bootstrap\n",
    "        self.verbose = verbose\n",
    "        self.oob_score = oob_score\n",
    "        self.estimators = None\n",
    "        self.oob_score_ = None\n",
    "        \n",
    "    def fit(self, X, y):\n",
    "        self.estimators = []\n",
    "        if self.oob_score:\n",
    "            self.oob_counters = [Counter() for elt in X]\n",
    "            # self.oob_counters[i] = predictions for sample i\n",
    "        if self.verbose >= 1:\n",
    "            print(\"##### Fitting the classifiers #####\")\n",
    "        for i in range(self.n_estimators):\n",
    "            if self.verbose >= 1:\n",
    "                print(\"Fitting classifier n°%d...\" % i)\n",
    "            clf = clone(self.base_estimator)\n",
    "            sample_idx = np.random.choice(X.shape[0], \n",
    "                                          int(X.shape[0]*self.max_samples), \n",
    "                                          replace=self.bootstrap)\n",
    "            if self.verbose >= 2:\n",
    "                print(\"Random indexes:\", sample_idx)\n",
    "            clf.fit(X[sample_idx], y[sample_idx])\n",
    "            if self.verbose >= 1:\n",
    "                print(\"Done.\")\n",
    "            \n",
    "            if self.oob_score:\n",
    "                oob_samples = np.setdiff1d(np.arange(X.shape[0]), sample_idx)\n",
    "                preds = clf.predict(X)\n",
    "                for i in oob_samples:\n",
    "                    self.oob_counters[i].update([preds[i]])\n",
    "                    \n",
    "            self.estimators.append(clf)\n",
    "          \n",
    "        if self.oob_score:\n",
    "            if Counter() in self.oob_counters:\n",
    "                print(\"Warning, some samples don't have OOB estimations, \\\n",
    "                        the number of estimators seems to be too low.\")\n",
    "            else:\n",
    "                self.oob_predictions = [c.most_common(1)[0][0] for c in self.oob_counters]\n",
    "                errors = np.count_nonzero(self.oob_predictions != y)\n",
    "                self.oob_score_ = errors / X.shape[0]\n",
    "        \n",
    "        if self.verbose >= 1:\n",
    "            print(\"##### Fitting is over #####\")\n",
    "        \n",
    "    def predict(self, X):\n",
    "        predictions = np.empty((X.shape[0], len(self.estimators)))\n",
    "        for j, clf in enumerate(self.estimators):\n",
    "            predictions[:, j] = clf.predict(X)\n",
    "        \n",
    "        most_common = [Counter(line).most_common(1)[0][0] for line in predictions]\n",
    "        return most_common\n",
    "        \n",
    "    def score(self, X, y):\n",
    "        return accuracy_score(self.predict(X), y)\n",
    "    \n",
    "    \n",
    "    "
   ]
  },
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   "cell_type": "markdown",
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   "source": [
    "### Question 2\n",
    "Appliquez cette méthode sur des arbres de décisions."
   ]
  },
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   "cell_type": "code",
   "execution_count": 2,
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     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Shape of X: (150, 4)\n",
      "Shape of y: (150,)\n",
      "Classes in y: (array([0, 1, 2]), array([50, 50, 50]))\n",
      "Scores with bag_clf: 0.933333333333\n"
     ]
    }
   ],
   "source": [
    "from sklearn import datasets\n",
    "from sklearn.model_selection import train_test_split, GridSearchCV\n",
    "\n",
    "iris = datasets.load_iris()\n",
    "X, y = iris.data, iris.target\n",
    "\n",
    "print(\"Shape of X:\", X.shape)\n",
    "print(\"Shape of y:\", y.shape)\n",
    "print(\"Classes in y:\", np.unique(y, return_counts=True))\n",
    "\n",
    "X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.3)\n",
    "\n",
    "bag_clf = BaggingClassifier(base_estimator=DecisionTreeClassifier(), oob_score=True,\n",
    "                            n_estimators=100, verbose=0)\n",
    "bag_clf.fit(X_train, y_train)\n",
    "print(\"Scores with bag_clf:\", bag_clf.score(X_test, y_test))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "### Question 3\n",
    "Évaluez et commentez l’erreur en généralisation par rapport à un arbre unique."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
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    "deletable": true,
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   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "For the BaggingClassifier, OOB error: 0.02857142857142857\n",
      "For the DecisionTreeClassifier, OOB error: 0.0444444444444\n",
      "Best parameters found for the DecisionTreeClassifier: {'min_samples_split': 0.25074999999999997, 'splitter': 'random', 'criterion': 'gini', 'max_depth': 35}\n"
     ]
    }
   ],
   "source": [
    "print(\"For the BaggingClassifier, OOB error:\", bag_clf.oob_score_)\n",
    "\n",
    "# Evaluating the OOB error on a decision tree:\n",
    "\n",
    "# Parameters for the Grid Search:\n",
    "params = {\"criterion\":(\"gini\", \"entropy\"),\n",
    "          \"splitter\":(\"best\", \"random\"),\n",
    "          \"max_depth\":np.arange(5, 51, 5),\n",
    "          \"min_samples_split\":np.linspace(1e-3, 1., 5)\n",
    "            }\n",
    "\n",
    "gridsearch = GridSearchCV(DecisionTreeClassifier(), params)\n",
    "gridsearch.fit(X_train, y_train)\n",
    "\n",
    "print(\"For the DecisionTreeClassifier, OOB error:\", 1 - gridsearch.score(X_test, y_test))\n",
    "print(\"Best parameters found for the DecisionTreeClassifier:\", gridsearch.best_params_)"
   ]
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    "## Exercice 2 Boosting\n",
    "### Question 1\n",
    "**Montrer que le coefficient de pondération des hypothèses vaut bien ce qu’il vaut.**\n",
    "\n",
    "Soit un problème d'apprentissage avec $((x_i, y_i)_{i \\in \\{1..n\\}}$, $x_i \\in X$, $y_i \\in \\{-1, +1\\}$\n",
    "\n",
    "Après l'itération n° $m-1$, notre classifieur Boost est une combinaison linéaire de classifieurs faibles $h_i:X \\rightarrow \\{-1, +1\\}$ pondéré par les coefficients $a_i$:\n",
    "\n",
    "$C_{m-1}(x) = \\sum_{i=1}^{m-1}{a_i ⋅ h_i(x)}$.\n",
    "\n",
    "On veut trouver un nouvel estimateur faible $h_m$ pour avoir l'estimateur Boost à l'itération $m$.\n",
    "\n",
    "Soit l'erreur totale de $C_m$ : $E = \\sum_{i=1}^n{e^{-y_i ⋅ C_m(x_i)}}$, \n",
    "\n",
    "posons $w_i^1 = 1$ et $w_i^m = e^{-y_i ⋅ C_{m-1}(x_i)}$ pour $1 < m$, \n",
    "on a alors :\n",
    "\n",
    "$E = \\sum_{i=1}^n{e^{-y_i ⋅ C_m(x_i)}} \\\\\n",
    "E = \\sum_{y_i = h_m(x_i)}{w_i^m⋅e^{-a_m}} + \\sum_{y_i \\neq h_m(x_i)}{w_i^m⋅e^{a_m}} \\\\\n",
    "E = \\sum_{i=1}^n{w_i^m ⋅ e^{-a_m}} + \\sum_{y_i \\neq h_m(x_i)}{w_i^m⋅(e^{a_m} - e^{-a_m})} $\n",
    "\n",
    "Ainsi l'estimateur faible $h_m$ qui minimise $E$ est celui qui minimise $\\sum_{y_i \\neq h_m(x_i)}{w_i^m}$, c'est-à-dire le classifieur qui fait le moins d'erreurs de classification, avec la pondération $w_i^m$.\n",
    "\n",
    "Après avoir trouvé ce classifieur $h_m$, il faut trouver le coefficient $a_m$, c'est le coefficient qui minimise $E$ :\n",
    "\n",
    "$\\frac {dE}{da_m} = \\sum_{y_i \\neq h_m(x_i)}{w_i^m⋅e^{a_m}} - \\sum_{y_i = h_m(x_i)}{w_i^m⋅e^{-a_m}}$\n",
    "\n",
    "$\\frac {dE}{da_m} = 0 \\Leftrightarrow \\sum_{y_i \\neq h_m(x_i)}{w_i^m⋅e^{a_m}} - \\sum_{y_i = h_m(x_i)}{w_i^m⋅e^{-a_m}} = 0 \\\\\n",
    "\\Leftrightarrow \\sum_{y_i \\neq h_m(x_i)}{w_i^m⋅e^{a_m}}  = \\sum_{y_i = h_m(x_i)}{w_i^m⋅e^{-a_m}}\\\\\n",
    "\\Leftrightarrow e^{2⋅a_m}⋅\\sum_{y_i \\neq h_m(x_i)}{w_i^m}  = \\sum_{y_i = h_m(x_i)}{w_i^m}\\\\\n",
    "\\Leftrightarrow 2⋅a_m = ln(\\frac {\\sum_{y_i = h_m(x_i)}{w_i^m}}{\\sum_{y_i \\neq h_m(x_i)}{w_i^m} })\\\\\n",
    "\\Leftrightarrow a_m = \\frac 1 2 ln(\\frac {\\sum_{y_i = h_m(x_i)}{w_i^m}}{\\sum_{y_i \\neq h_m(x_i)}{w_i^m} })$\n",
    "\n",
    "Ainsi on peut écrire l'erreur pondérée : \n",
    "\n",
    "$\\epsilon_m = \\frac {\\sum_{y_i \\neq h_m(x_i)}{w_i^m}} {\\sum_{i=1}^n{w_i^m}}$\n",
    "\n",
    "Et donc $a_m = \\frac 1 2 ln(\\frac {1-\\epsilon_m} {\\epsilon_m})$\n",
    "\n",
    "### Question 2\n",
    "Écrivez une fonction (ou une classe) implémentant la méthode AdaBoost."
   ]
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   "source": [
    "class AdaBoostClassifier(ClassifierMixin):\n",
    "    \n",
    "    def __init__(self, base_estimator=None, n_estimators=50, verbose=False):\n",
    "        \"\"\" Create an AdaBoostClassifier.\n",
    "        :param base_estimator: The estimator used to fit the data. \n",
    "            Support for sample weighting is required\n",
    "        :param n_estimators: Number of used estimators\"\"\"\n",
    "        if base_estimator is None:\n",
    "            self.base_estimator = DecisionTreeClassifier()\n",
    "        else:\n",
    "            self.base_estimator = base_estimator\n",
    "        self.n_estimators = n_estimators\n",
    "        self.verbose = verbose\n",
    "\n",
    "    def fit(self, X, y):\n",
    "        self.sample_weight = np.array([1/y.shape[0]] * y.shape[0])\n",
    "        self.estimators = []\n",
    "        self.alphas = []\n",
    "        for it in range(self.n_estimators):\n",
    "            clf = clone(self.base_estimator)\n",
    "            clf.fit(X, y, sample_weight=self.sample_weight)\n",
    "            prediction = clf.predict(X)\n",
    "            misclass = np.arange(y.shape[0])[prediction != y]\n",
    "            error = sum(self.sample_weight[misclass])\n",
    "            \n",
    "            if error == 0:\n",
    "                error = 1/y.shape[0]\n",
    "            alpha = 1/2 * np.log((1-error)/error)\n",
    "            if self.verbose:\n",
    "                print(20*'-')\n",
    "                print(\"Weights:\", self.sample_weight[:20])\n",
    "                print(\"Misclassified:\", misclass[:10])\n",
    "                print(\"Summed error: %f, score: %f (%d misclassified)\" %(error, 1-error, len(misclass)))\n",
    "                print(\"Alpha:\", alpha)\n",
    "                print(20*'-')\n",
    "            self.sample_weight = self.sample_weight * np.exp(-y * prediction * alpha)\n",
    "            self.sample_weight /= sum(self.sample_weight)\n",
    "            self.estimators.append(clf)\n",
    "            self.alphas.append(alpha)\n",
    "            \n",
    "    def predict(self, X):\n",
    "        predictions = np.zeros(X.shape[0])\n",
    "        for clf, alpha in zip(self.estimators, self.alphas):\n",
    "            if self.verbose:\n",
    "                print(clf.predict(X)[:10])\n",
    "            predictions += alpha * clf.predict(X)\n",
    "            \n",
    "        return (np.sign(predictions))\n",
    "    \n",
    "    def get_sample_weight(self):\n",
    "        return self.sample_weight\n"
   ]
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   "source": [
    "### Question 3\n",
    "**Comment adapter un classifieur qui ne gère pas naturellement des pondérations pour qu’il puisse en tenir\n",
    "compte ?**\n",
    "\n",
    "Si un classifieur ne gère pas les pondérations, on peut dupliquer certains exemples afin que la proportion de ces exemples reflète leur poids.\n",
    "Par exemple si les poids sont les suivants :\n",
    "* Exemple 1 : 1/3\n",
    "* Exemple 2 : 1/3\n",
    "* Exemple 3 : 1/2\n",
    "\n",
    "Alors on peut créer un nouveau ensemble de données d'entraînement qui contiendra : {ex1, ex1, ex2, ex2, ex3, ex3, ex3}, et les proportions seront respectées.\n",
    "\n",
    "Plus formellement, il faudrait approcher les poids par des fractions rationnelles, puis tout mettre au même dénominateur, et le numérateur de chaque fraction donne le nombre d'échantillons à avoir pour cet exemple.\n",
    "\n",
    "\n",
    "\n",
    "### Question 4\n",
    "**Appliquez cette méthode sur des stumps (arbres de décision à un nœud).**"
   ]
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   "cell_type": "code",
   "execution_count": 5,
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   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "##### Extracting the data #####\n",
      "Shape of X: (569, 30)\n",
      "Shape of y: (569,)\n",
      "Classes in y: (array([-1,  1]), array([212, 357]))\n",
      "##### Testing AdaBoost with stumps: #####\n",
      "Score on the test set: 0.964912280702\n",
      "Score on the train set: 0.994974874372\n"
     ]
    }
   ],
   "source": [
    "# Testing with stumps:\n",
    "print(\"##### Extracting the data #####\")\n",
    "breast_cancer = datasets.load_breast_cancer()\n",
    "X, y = breast_cancer.data, breast_cancer.target\n",
    "\n",
    "y = (y*2) - 1 # To bring y into {-1, +1}\n",
    "print(\"Shape of X:\", X.shape)\n",
    "print(\"Shape of y:\", y.shape)\n",
    "print(\"Classes in y:\", np.unique(y, return_counts=True))\n",
    "\n",
    "X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.3)\n",
    "\n",
    "        \n",
    "print(\"##### Testing AdaBoost with stumps: #####\")\n",
    "np.set_printoptions(precision=4)\n",
    "adaboost = AdaBoostClassifier(base_estimator=DecisionTreeClassifier(max_depth=1), \n",
    "                              n_estimators=20, verbose=False)\n",
    "adaboost.fit(X_train, y_train)\n",
    "print(\"Score on the test set:\", accuracy_score(adaboost.predict(X_test), y_test))\n",
    "print(\"Score on the train set:\", accuracy_score(adaboost.predict(X_train), y_train))\n"
   ]
  },
  {
   "cell_type": "markdown",
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    "editable": true
   },
   "source": [
    "### Question 5\n",
    "Tracez les courbes de l’erreur d’apprentissage et de l’erreur de test en fonction du nombre de classifieurs."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
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   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "##### Finding the error of one stump #####\n",
      "Stump test error: 0.0994152046784\n",
      "##### Finding the error of a tree #####\n",
      "Tree test error: 0.0818713450292\n",
      "##### Computing the errors for AdaBoost #####\n"
     ]
    },
    {
     "data": {
      "image/png": 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tqVl8AjgTeA8gIl4FdixmUKXkPgszs821Jlmsi4gAAkBS9+KGVFquWZiZba41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\nH31j9Om9kdYAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fe004667438>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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ri9mzZ3P++edz0UUXhfU9CiaifRaq+rKqjlLVEap6p7vsFlVd5D5frqpDVTVdVbNVdZzX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\nAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fdfd036eb00>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "print(\"##### Finding the error of one stump #####\")\n",
    "stump = DecisionTreeClassifier(max_depth=1)\n",
    "stump.fit(X_train, y_train)\n",
    "stump_test_error  = 1 - stump.score(X_test, y_test)\n",
    "stump_train_error = 1 - stump.score(X_train, y_train)\n",
    "print(\"Stump test error:\", stump_test_error)\n",
    "\n",
    "print(\"##### Finding the error of a tree #####\")\n",
    "gridsearch = GridSearchCV(DecisionTreeClassifier(), \n",
    "                          param_grid={'max_depth':np.logspace(0.1, 2, 10, dtype=int),\n",
    "                                     'splitter':(\"best\", \"random\")})\n",
    "gridsearch.fit(X_train, y_train)\n",
    "tree_test_error  = 1 - gridsearch.score(X_test, y_test)\n",
    "tree_train_error = 1 - gridsearch.score(X_train, y_train)\n",
    "print(\"Tree test error:\", tree_test_error)\n",
    "\n",
    "\n",
    "print(\"##### Computing the errors for AdaBoost #####\")\n",
    "max_estimators = 500\n",
    "n_estimators_list = range(1, max_estimators, 10)\n",
    "errors_test = []\n",
    "errors_train = []\n",
    "for n_estimators in n_estimators_list:\n",
    "    adaboost = AdaBoostClassifier(base_estimator=DecisionTreeClassifier(max_depth=1),\n",
    "                                  n_estimators=n_estimators)\n",
    "    adaboost.fit(X_train, y_train)\n",
    "    errors_test.append( 1 - accuracy_score(adaboost.predict(X_test), y_test))\n",
    "    errors_train.append(1 - accuracy_score(adaboost.predict(X_train), y_train))\n",
    "\n",
    "min_gen_error = min(errors_test)\n",
    "\n",
    "plt.hlines(stump_train_error, xmin=0, xmax=max_estimators, label=\"Stump\", colors=\"r\")\n",
    "plt.hlines(tree_train_error, xmin=0, xmax=max_estimators, label=\"Single tree\", colors=\"black\")\n",
    "plt.plot(n_estimators_list, errors_train, label=\"AdaBoost\")\n",
    "plt.title(\"Performance of AdaBoost on the training set\")\n",
    "plt.xlabel(\"Number of stumps\")\n",
    "plt.ylabel(\"Error rate\")\n",
    "plt.legend()\n",
    "plt.show()\n",
    "\n",
    "plt.hlines(stump_test_error, xmin=0, xmax=max_estimators, label=\"Stump\", colors=\"r\")\n",
    "plt.hlines(tree_test_error, xmin=0, xmax=max_estimators, label=\"Single tree\", colors=\"black\")\n",
    "plt.plot(n_estimators_list, errors_test, label=\"AdaBoost\")\n",
    "plt.title(\"Performance of AdaBoost on the testing set\")\n",
    "plt.xlabel(\"Number of stumps\")\n",
    "plt.ylabel(\"Error rate\")\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Question 6\n",
    "Affichez les points associés aux poids les plus élevés (donc les plus difficiles à classer). Sont-ils bien classés\n",
    "désormais ? Étaient-ils bien classé avec un seul arbre de décision ? Avec le Bagging ?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Comparing accuracy on hard examples:\n",
      "- Accuracy of AdaBoost on hard examples: 59/59 right guesses\n",
      "- Accuracy of a stump on hard examples:  38/59 right guesses\n",
      "- Accuracy of a tree on hard examples:   38/59 right guesses\n",
      "- Accuracy of Bagging on hard examples:  29/59 right guesses\n"
     ]
    }
   ],
   "source": [
    "from collections import Counter\n",
    "\n",
    "print(\"Comparing accuracy on hard examples:\")\n",
    "sample_weight = adaboost.get_sample_weight()\n",
    "# Indexes of hard examples (weight above the mean)\n",
    "idx_hard = np.arange(sample_weight.shape[0])[sample_weight > sample_weight.mean()]\n",
    "adaboost_predict = adaboost.predict(X_train[idx_hard])\n",
    "trues = Counter(adaboost_predict * y_train[idx_hard])[1]\n",
    "print(\"- Accuracy of AdaBoost on hard examples: %d/%d right guesses\" % (trues, len(y[idx_hard])))\n",
    "\n",
    "stump_predict = stump.predict(X_train[idx_hard])\n",
    "print(\"- Accuracy of a stump on hard examples:  %d/%d right guesses\" % (Counter(stump_predict * y[idx_hard])[1],\n",
    "                                                                      len(y[idx_hard])))\n",
    "\n",
    "tree_predict = gridsearch.predict(X_train[idx_hard])\n",
    "print(\"- Accuracy of a tree on hard examples:   %d/%d right guesses\" % (Counter(tree_predict * y[idx_hard])[1],\n",
    "                                                                      len(y[idx_hard])))\n",
    "\n",
    "\n",
    "bagging_clf = BaggingClassifier()\n",
    "bagging_clf.fit(X_train, y_train)\n",
    "bagging_predict = bagging_clf.predict(X_train[idx_hard])\n",
    "print(\"- Accuracy of Bagging on hard examples:  %d/%d right guesses\" % (Counter(bagging_predict * y[idx_hard])[1],\n",
    "                                                                      len(y[idx_hard])))\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Question 7\n",
    "**Appliquez AdaBoost à des arbres de décision de profondeur plus grande.**\n",
    "\n",
    "**Comment se comporte la généralisation quand la profondeur des arbres augmente ?**\n",
    "\n",
    "On obtient un comportement de sur-apprentissage, l'erreur sur le *train set* tend vers 0, tandis que celle sur le *test set* n'est pas minimale"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "##### Computing the errors for AdaBoost #####\n"
     ]
    },
    {
     "data": {
      "image/png": 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uBM4CPl2vzExgLPAoMAqYne6dcVRdAUkTgXVOFGZmLaeUIcpvzyvTwPM2ShoP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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fdfd0300a90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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0ifj4eD744AMmTZrEzp07qVq1aqG3XxC9g1splYc3NQFfOnfuHMuWLWPnzp2I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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fdfd02b2898>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "print(\"##### Computing the errors for AdaBoost #####\")\n",
    "max_estimators = 500\n",
    "n_estimators_list = range(1, max_estimators, 10)\n",
    "errors_test = []\n",
    "errors_train = []\n",
    "for n_estimators in n_estimators_list:\n",
    "    adaboost = AdaBoostClassifier(base_estimator=DecisionTreeClassifier(),\n",
    "                                  n_estimators=n_estimators)\n",
    "    adaboost.fit(X_train, y_train)\n",
    "    errors_test.append( 1 - accuracy_score(adaboost.predict(X_test), y_test))\n",
    "    errors_train.append(1 - accuracy_score(adaboost.predict(X_train), y_train))\n",
    "\n",
    "# print(n_estimators_list)\n",
    "# print(errors_list)\n",
    "plt.hlines(stump_train_error, xmin=0, xmax=max_estimators, label=\"Stump\", colors=\"r\")\n",
    "plt.hlines(tree_train_error, xmin=0, xmax=max_estimators, label=\"Single tree\", colors=\"black\")\n",
    "plt.plot(n_estimators_list, errors_train, label=\"AdaBoost\")\n",
    "plt.title(\"Performance of AdaBoost on the training set\")\n",
    "plt.xlabel(\"Number of estimators\")\n",
    "plt.ylabel(\"Error rate\")\n",
    "plt.legend()\n",
    "plt.show()\n",
    "\n",
    "plt.hlines(stump_test_error, xmin=0, xmax=max_estimators, label=\"Stump\", colors=\"r\")\n",
    "plt.hlines(tree_test_error, xmin=0, xmax=max_estimators, label=\"Single tree\", colors=\"black\")\n",
    "plt.hlines(min_gen_error, xmin=0, xmax=max_estimators, label=\"AdaBoost stumps\", colors=\"purple\")\n",
    "plt.plot(n_estimators_list, errors_test, label=\"AdaBoost trees\")\n",
    "plt.title(\"Performance of AdaBoost on the testing set\")\n",
    "plt.xlabel(\"Number of estimators\")\n",
    "plt.ylabel(\"Error rate\")\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  }
 ],
 "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": "3.5.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}