Wine-quality2.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Nous allons utiliser la version régression du K-nn afin de prédire la qualité du vin, sur le dataset https://archive.ics.uci.edu/ml/machine-learning-databases/wine-quality/winequality-red.csv\n",
    "\n",
    "Nous allons chercher le meilleur modèle en optimisant la MSE (erreur quadratique moyenne) et le R2 via une grid search.\n",
    "Nous comparerons enfin les performances à l’aide d’une baseline naïve ainsi que les différentes heuristiques."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# coding: utf-8\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "from sklearn import dummy\n",
    "from sklearn import model_selection\n",
    "from sklearn.model_selection import KFold\n",
    "from sklearn import preprocessing\n",
    "from sklearn import neighbors, metrics\n",
    "\n",
    "import warnings\n",
    "warnings.filterwarnings(action='ignore')\n",
    "\n",
    "seed = 42"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Chargement et préparation des données"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>fixed acidity</th>\n",
       "      <th>volatile acidity</th>\n",
       "      <th>citric acid</th>\n",
       "      <th>residual sugar</th>\n",
       "      <th>chlorides</th>\n",
       "      <th>free sulfur dioxide</th>\n",
       "      <th>total sulfur dioxide</th>\n",
       "      <th>density</th>\n",
       "      <th>pH</th>\n",
       "      <th>sulphates</th>\n",
       "      <th>alcohol</th>\n",
       "      <th>quality</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>7.4</td>\n",
       "      <td>0.70</td>\n",
       "      <td>0.00</td>\n",
       "      <td>1.9</td>\n",
       "      <td>0.076</td>\n",
       "      <td>11.0</td>\n",
       "      <td>34.0</td>\n",
       "      <td>0.9978</td>\n",
       "      <td>3.51</td>\n",
       "      <td>0.56</td>\n",
       "      <td>9.4</td>\n",
       "      <td>5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>7.8</td>\n",
       "      <td>0.88</td>\n",
       "      <td>0.00</td>\n",
       "      <td>2.6</td>\n",
       "      <td>0.098</td>\n",
       "      <td>25.0</td>\n",
       "      <td>67.0</td>\n",
       "      <td>0.9968</td>\n",
       "      <td>3.20</td>\n",
       "      <td>0.68</td>\n",
       "      <td>9.8</td>\n",
       "      <td>5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>7.8</td>\n",
       "      <td>0.76</td>\n",
       "      <td>0.04</td>\n",
       "      <td>2.3</td>\n",
       "      <td>0.092</td>\n",
       "      <td>15.0</td>\n",
       "      <td>54.0</td>\n",
       "      <td>0.9970</td>\n",
       "      <td>3.26</td>\n",
       "      <td>0.65</td>\n",
       "      <td>9.8</td>\n",
       "      <td>5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>11.2</td>\n",
       "      <td>0.28</td>\n",
       "      <td>0.56</td>\n",
       "      <td>1.9</td>\n",
       "      <td>0.075</td>\n",
       "      <td>17.0</td>\n",
       "      <td>60.0</td>\n",
       "      <td>0.9980</td>\n",
       "      <td>3.16</td>\n",
       "      <td>0.58</td>\n",
       "      <td>9.8</td>\n",
       "      <td>6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>7.4</td>\n",
       "      <td>0.70</td>\n",
       "      <td>0.00</td>\n",
       "      <td>1.9</td>\n",
       "      <td>0.076</td>\n",
       "      <td>11.0</td>\n",
       "      <td>34.0</td>\n",
       "      <td>0.9978</td>\n",
       "      <td>3.51</td>\n",
       "      <td>0.56</td>\n",
       "      <td>9.4</td>\n",
       "      <td>5</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   fixed acidity  volatile acidity  citric acid  residual sugar  chlorides  \\\n",
       "0            7.4              0.70         0.00             1.9      0.076   \n",
       "1            7.8              0.88         0.00             2.6      0.098   \n",
       "2            7.8              0.76         0.04             2.3      0.092   \n",
       "3           11.2              0.28         0.56             1.9      0.075   \n",
       "4            7.4              0.70         0.00             1.9      0.076   \n",
       "\n",
       "   free sulfur dioxide  total sulfur dioxide  density    pH  sulphates  \\\n",
       "0                 11.0                  34.0   0.9978  3.51       0.56   \n",
       "1                 25.0                  67.0   0.9968  3.20       0.68   \n",
       "2                 15.0                  54.0   0.9970  3.26       0.65   \n",
       "3                 17.0                  60.0   0.9980  3.16       0.58   \n",
       "4                 11.0                  34.0   0.9978  3.51       0.56   \n",
       "\n",
       "   alcohol  quality  \n",
       "0      9.4        5  \n",
       "1      9.8        5  \n",
       "2      9.8        5  \n",
       "3      9.8        6  \n",
       "4      9.4        5  "
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data = pd.read_csv('winequality-red.csv', sep=\";\")\n",
    "data.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Nos données contiennent 12 colonnes, 11 qui correspondent à divers indicateurs physico-chimiques et 1 qui est la qualité du vin.\n",
    "\n",
    "Nous allons extraire deux arrays numpy de ces données, un qui contient les points et l’autre qui contient les étiquettes :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "X = data.as_matrix(data.columns[:-1])\n",
    "y_m = data.as_matrix([data.columns[-1]])\n",
    "y = y_m.flatten()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "On peut maintenant afficher un histogramme pour chacune de nos variables :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1152x864 with 12 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(16, 12))\n",
    "for feat_idx in range(X.shape[1]):\n",
    "    ax = fig.add_subplot(3,4, (feat_idx+1))\n",
    "    h = ax.hist(X[:, feat_idx], bins=50, color='steelblue',\n",
    "                normed=True, edgecolor='none')\n",
    "    ax.set_title(data.columns[feat_idx], fontsize=14)\n",
    "\n",
    "ax = fig.add_subplot(3,4, 12)\n",
    "h = ax.hist(y, bins=50, color='steelblue',\n",
    "            normed=True, edgecolor='none')\n",
    "ax.set_title('Quality', fontsize=14)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "On remarque en particulier que ces variables prennent des valeurs dans des ensembles différents. Par exemple, “alcohol” varie de 0 à 0.6 tandis que “density” varie de 0 à 120. Il va donc nous falloir standardiser les données pour que la deuxième ne domine pas complètement la première."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Séparons nos données en un jeu d’entraînement et un jeu de test. Le jeu de test contiendra 30% des données.\n",
    "On paramètre 'random_state' avec la valeur du seed pour que la séparation des données soit fixe et reproductible."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "X_train, X_test, y_train, y_test = \\\n",
    "    model_selection.train_test_split(X, y,\n",
    "                                    test_size=0.3, # 30% des données dans le jeu de test\n",
    "                                     random_state = seed\n",
    "                                    )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Nous pouvons maintenant standardiser les données d’entraînement et appliquer la même transformation aux données de test :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "std_scale = preprocessing.StandardScaler().fit(X_train)\n",
    "X_train_std = std_scale.transform(X_train)\n",
    "X_test_std = std_scale.transform(X_test)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#  Sélection de modèles avec une Grid Search"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "On commence par créer la fonction qui va effectuer la validation croisée :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "def cvf(X, y, n_neighbors, n_fold, weights, verbose=False):\n",
    "    \"\"\"\n",
    "    X : données\n",
    "    y : valeur à prédire \n",
    "    n_neighbors : liste des K à tester pour le K-NN\n",
    "    n_fold : nombre de folds à créer\n",
    "    weights : fonction de poids utilisée pour la prédiction\n",
    "    verbose : False par défaut, permet d'afficher dees informations du code\n",
    "    \"\"\"\n",
    "    \n",
    "    # on recrée les folds. Etant donné que pour l'exercice on va utiliser n_fold = 5 comme dans la partie 1,\n",
    "    # et qu'on utilise la même seed, on aura les mêmes folds que dans la partie 1.\n",
    "    kf = KFold(n_splits=n_fold, shuffle=True, random_state=seed)\n",
    "    if verbose: \n",
    "        for train_index, test_index in kf.split(X):\n",
    "            print(\"TRAIN:\", \"taille\", len(train_index), \", 5ers indices\", train_index[0:5], \n",
    "                  \"|| TEST:\", \"taille\", len(test_index), \", 5ers indices\", test_index[0:5])\n",
    "    \n",
    "    # on initialise les listes qui contiendront les différents résultats de MSE et R2\n",
    "    MSE = [] \n",
    "    R2 = []\n",
    "    \n",
    "    # on boucle pour tester les différentes valeurs de K pour le KNN\n",
    "    for kn in n_neighbors:\n",
    "        if verbose: print(\"kn\", kn)    \n",
    "        knn = neighbors.KNeighborsRegressor(kn, weights=weights) # initialisation du classifieur\n",
    "        \n",
    "        MSE_fold = [] # initialisation d'une liste qui contiendra la MSE pour chaque k-fold et chaque knn\n",
    "        R2_fold = []\n",
    "        \n",
    "        # on boucle sur les différents folds\n",
    "        for train_index, test_index in kf.split(X):\n",
    "            if verbose: print(\"TRAIN:\", \"taille\", len(train_index), \", 5ers indices\", train_index[0:5], \n",
    "                      \"|| TEST:\", \"taille\", len(test_index), \", 5ers indices\", test_index[0:5])\n",
    "            X_train, X_test = X[train_index], X[test_index]\n",
    "            y_train, y_test = y[train_index], y[test_index]\n",
    "                        \n",
    "            # on fit le knn sur le fold d'entrainement\n",
    "            knn.fit(X_train, y_train)\n",
    "            \n",
    "            # on calcule les y prédits sur le fold de test\n",
    "            y_pred = knn.predict(X_test)\n",
    "            \n",
    "            # on calcule le MSE et le R2 sur le fold de test et on l'ajoute aux listes :\n",
    "            #accuracy_fold.append([knn.score(X_train_std_test, y_train_test)])\n",
    "            MSE_fold.append([metrics.mean_squared_error(y_test, y_pred)])\n",
    "            R2_fold.append([knn.score(X_test, y_test)])\n",
    "            \n",
    "        if verbose: \n",
    "            print(np.mean(MSE_fold))\n",
    "            print(np.mean(R2_fold))\n",
    "        \n",
    "        # on aggrège les résultats en ne gardant que la moyenne des accuracy des différents folds pour chaque k\n",
    "        #accuracy.append([kn, round(np.mean(accuracy_fold), 3)])\n",
    "        MSE.append([kn, round(np.mean(MSE_fold), 3)])\n",
    "        R2.append([kn, round(np.mean(R2_fold), 3)])\n",
    "    \n",
    "    return MSE, R2           "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "On fait tourner notre fonction avec les hyper-paramètres que nous souhaitons tester. Ici il est demandé de tester le nombre de voisins, mais nous allons également comparer les résultats avec 2 fonctions de poids différentes pour la prédiction ('uniform' et 'distance'). \n",
    "\n",
    "Commençons avec la fonction de poids 'uniform' :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "n_neighbors = [3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49]\n",
    "weights='uniform'\n",
    "n_fold = 5\n",
    "\n",
    "cvf_unif = cvf(X_train_std, y_train, n_neighbors, n_fold, weights, verbose=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "On concatène les résultats pour mieux les observer :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>k</th>\n",
       "      <th>MSE</th>\n",
       "      <th>R2</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>3</td>\n",
       "      <td>0.521</td>\n",
       "      <td>0.199</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>5</td>\n",
       "      <td>0.494</td>\n",
       "      <td>0.239</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>7</td>\n",
       "      <td>0.486</td>\n",
       "      <td>0.252</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>9</td>\n",
       "      <td>0.472</td>\n",
       "      <td>0.275</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>11</td>\n",
       "      <td>0.461</td>\n",
       "      <td>0.292</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>13</td>\n",
       "      <td>0.457</td>\n",
       "      <td>0.299</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>15</td>\n",
       "      <td>0.455</td>\n",
       "      <td>0.302</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>17</td>\n",
       "      <td>0.453</td>\n",
       "      <td>0.305</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>19</td>\n",
       "      <td>0.449</td>\n",
       "      <td>0.311</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>21</td>\n",
       "      <td>0.448</td>\n",
       "      <td>0.313</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>23</td>\n",
       "      <td>0.448</td>\n",
       "      <td>0.313</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>25</td>\n",
       "      <td>0.447</td>\n",
       "      <td>0.313</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>27</td>\n",
       "      <td>0.447</td>\n",
       "      <td>0.315</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>29</td>\n",
       "      <td>0.446</td>\n",
       "      <td>0.316</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>31</td>\n",
       "      <td>0.444</td>\n",
       "      <td>0.318</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>33</td>\n",
       "      <td>0.445</td>\n",
       "      <td>0.317</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>35</td>\n",
       "      <td>0.446</td>\n",
       "      <td>0.316</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>37</td>\n",
       "      <td>0.445</td>\n",
       "      <td>0.316</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>39</td>\n",
       "      <td>0.442</td>\n",
       "      <td>0.322</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>41</td>\n",
       "      <td>0.443</td>\n",
       "      <td>0.321</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>43</td>\n",
       "      <td>0.443</td>\n",
       "      <td>0.320</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>45</td>\n",
       "      <td>0.444</td>\n",
       "      <td>0.319</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>47</td>\n",
       "      <td>0.445</td>\n",
       "      <td>0.317</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>49</td>\n",
       "      <td>0.445</td>\n",
       "      <td>0.318</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     k    MSE     R2\n",
       "0    3  0.521  0.199\n",
       "1    5  0.494  0.239\n",
       "2    7  0.486  0.252\n",
       "3    9  0.472  0.275\n",
       "4   11  0.461  0.292\n",
       "5   13  0.457  0.299\n",
       "6   15  0.455  0.302\n",
       "7   17  0.453  0.305\n",
       "8   19  0.449  0.311\n",
       "9   21  0.448  0.313\n",
       "10  23  0.448  0.313\n",
       "11  25  0.447  0.313\n",
       "12  27  0.447  0.315\n",
       "13  29  0.446  0.316\n",
       "14  31  0.444  0.318\n",
       "15  33  0.445  0.317\n",
       "16  35  0.446  0.316\n",
       "17  37  0.445  0.316\n",
       "18  39  0.442  0.322\n",
       "19  41  0.443  0.321\n",
       "20  43  0.443  0.320\n",
       "21  45  0.444  0.319\n",
       "22  47  0.445  0.317\n",
       "23  49  0.445  0.318"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "MSE_unif = pd.DataFrame(cvf_unif[0], columns=['k', 'MSE'])\n",
    "R2_unif = pd.DataFrame(cvf_unif[1], columns=['k', 'R2'])\n",
    "results_unif = MSE_unif.merge(R2_unif, on='k')\n",
    "results_unif"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "La MSE semble être la plus faible lorsque k = 39.\n",
    "LE R2 semble évoluer de façon inverse à la MSE (le R2 atteint son maximum lorsque la MSE atteint son minimum).\n",
    "\n",
    "Observons cela sur un graphique :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = results_unif['k']\n",
    "y1 = results_unif['MSE']\n",
    "y2 = results_unif['R2']\n",
    "\n",
    "fig, ax1 = plt.subplots()\n",
    "\n",
    "color = 'tab:blue'\n",
    "ax1.set_xlabel('k')\n",
    "ax1.set_ylabel('MSE', color=color)\n",
    "ax1.plot(x, y1, color=color)\n",
    "ax1.tick_params(axis='y', labelcolor=color)\n",
    "\n",
    "ax2 = ax1.twinx()  # instantiate a second axes that shares the same x-axis\n",
    "\n",
    "color = 'tab:green'\n",
    "ax2.set_ylabel('R2', color=color)  # we already handled the x-label with ax1\n",
    "ax2.plot(x, y2, color=color)\n",
    "ax2.tick_params(axis='y', labelcolor=color)\n",
    "\n",
    "ax1.axvline(39, color='red', linestyle='--')\n",
    "\n",
    "fig.tight_layout()  # otherwise the right y-label is slightly clipped\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "La ligne rouge correspond marque la position où le MSE est minimum et le R2 maximum.\n",
    "\n",
    "Regardons maintenant ce qu'il se passe avec la fonction de poids 'distance' :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "n_neighbors = [3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49]\n",
    "weights = 'distance'\n",
    "n_fold = 5\n",
    "\n",
    "cvf_dist = cvf(X_train_std, y_train, n_neighbors, n_fold, weights, verbose=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "On concatène les résultats pour mieux les observer :\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>k</th>\n",
       "      <th>MSE</th>\n",
       "      <th>R2</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>3</td>\n",
       "      <td>0.521</td>\n",
       "      <td>0.283</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>5</td>\n",
       "      <td>0.494</td>\n",
       "      <td>0.337</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>7</td>\n",
       "      <td>0.486</td>\n",
       "      <td>0.355</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>9</td>\n",
       "      <td>0.472</td>\n",
       "      <td>0.371</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>11</td>\n",
       "      <td>0.461</td>\n",
       "      <td>0.387</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>13</td>\n",
       "      <td>0.457</td>\n",
       "      <td>0.394</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>15</td>\n",
       "      <td>0.455</td>\n",
       "      <td>0.396</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>17</td>\n",
       "      <td>0.453</td>\n",
       "      <td>0.398</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>19</td>\n",
       "      <td>0.449</td>\n",
       "      <td>0.403</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>21</td>\n",
       "      <td>0.448</td>\n",
       "      <td>0.406</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>23</td>\n",
       "      <td>0.448</td>\n",
       "      <td>0.406</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>25</td>\n",
       "      <td>0.447</td>\n",
       "      <td>0.407</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>27</td>\n",
       "      <td>0.447</td>\n",
       "      <td>0.409</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>29</td>\n",
       "      <td>0.446</td>\n",
       "      <td>0.409</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>31</td>\n",
       "      <td>0.444</td>\n",
       "      <td>0.411</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>33</td>\n",
       "      <td>0.445</td>\n",
       "      <td>0.412</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>35</td>\n",
       "      <td>0.446</td>\n",
       "      <td>0.411</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>37</td>\n",
       "      <td>0.445</td>\n",
       "      <td>0.412</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>39</td>\n",
       "      <td>0.442</td>\n",
       "      <td>0.416</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>41</td>\n",
       "      <td>0.443</td>\n",
       "      <td>0.415</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>43</td>\n",
       "      <td>0.443</td>\n",
       "      <td>0.414</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>45</td>\n",
       "      <td>0.444</td>\n",
       "      <td>0.413</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>47</td>\n",
       "      <td>0.445</td>\n",
       "      <td>0.413</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>49</td>\n",
       "      <td>0.445</td>\n",
       "      <td>0.413</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     k    MSE     R2\n",
       "0    3  0.521  0.283\n",
       "1    5  0.494  0.337\n",
       "2    7  0.486  0.355\n",
       "3    9  0.472  0.371\n",
       "4   11  0.461  0.387\n",
       "5   13  0.457  0.394\n",
       "6   15  0.455  0.396\n",
       "7   17  0.453  0.398\n",
       "8   19  0.449  0.403\n",
       "9   21  0.448  0.406\n",
       "10  23  0.448  0.406\n",
       "11  25  0.447  0.407\n",
       "12  27  0.447  0.409\n",
       "13  29  0.446  0.409\n",
       "14  31  0.444  0.411\n",
       "15  33  0.445  0.412\n",
       "16  35  0.446  0.411\n",
       "17  37  0.445  0.412\n",
       "18  39  0.442  0.416\n",
       "19  41  0.443  0.415\n",
       "20  43  0.443  0.414\n",
       "21  45  0.444  0.413\n",
       "22  47  0.445  0.413\n",
       "23  49  0.445  0.413"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "MSE_dist = pd.DataFrame(cvf_dist[0], columns=['k', 'MSE'])\n",
    "R2_dist = pd.DataFrame(cvf_dist[1], columns=['k', 'R2'])\n",
    "results_dist = MSE_unif.merge(R2_dist, on='k')\n",
    "results_dist"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "La MSE semble être la plus faible lorsque k = 39, ce qui est cohérent avec nos précédents résultats.\n",
    "LE R2 semble évoluer de façon inverse à la MSE (le R2 atteint son maximum lorsque la MSE atteint son minimum).\n",
    "\n",
    "Observons cela sur un graphique :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = results_dist['k']\n",
    "y1 = results_dist['MSE']\n",
    "y2 = results_dist['R2']\n",
    "\n",
    "fig, ax1 = plt.subplots()\n",
    "\n",
    "color = 'tab:blue'\n",
    "ax1.set_xlabel('k')\n",
    "ax1.set_ylabel('MSE', color=color)\n",
    "ax1.plot(x, y1, color=color)\n",
    "ax1.tick_params(axis='y', labelcolor=color)\n",
    "\n",
    "ax2 = ax1.twinx()  # instantiate a second axes that shares the same x-axis\n",
    "\n",
    "color = 'tab:green'\n",
    "ax2.set_ylabel('R2', color=color)  # we already handled the x-label with ax1\n",
    "ax2.plot(x, y2, color=color)\n",
    "ax2.tick_params(axis='y', labelcolor=color)\n",
    "\n",
    "ax1.axvline(39, color='red', linestyle='--')\n",
    "\n",
    "fig.tight_layout()  # otherwise the right y-label is slightly clipped\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "De la même façon que tout à l'heure, la ligne rouge correspond à la position où le MSE est minimun et le R2 maximum. \n",
    "\n",
    "Nous allons donc retenir le modèle avec les 39 plus proches voisins.\n",
    "Entrainons donc un knn avec k = 39 sur les données d'entrainements :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "KNeighborsRegressor(algorithm='auto', leaf_size=30, metric='minkowski',\n",
       "          metric_params=None, n_jobs=None, n_neighbors=39, p=2,\n",
       "          weights='uniform')"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "knn39 = neighbors.KNeighborsRegressor(n_neighbors=39)\n",
    "knn39.fit(X_train_std, y_train)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Et appliquons le pour prédire les étiquettes de notre jeu de test, et la RMSE correspondante :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "RMSE : 0.66\n"
     ]
    }
   ],
   "source": [
    "y_pred = knn39.predict(X_test_std)\n",
    "print(\"RMSE : %.2f\" % np.sqrt(metrics.mean_squared_error(y_test, y_pred)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Nos étiquettes étant des nombres entiers, nous faisons en moyenne une erreur inférieure à la plus petite différence possible entre deux notes.\n",
    "\n",
    "Nous pouvons visualiser les résultats sur un graphique, en représentant en abscisse les vraies valeurs des étiquettes, et en ordonnée les valeurs prédites.\n",
    "Comme nos étiquettes prennent des valeurs entières entre 3 et 8, nous avons beaucoup de points superposés aux même coordonnées. Pour mieux visualiser les données, nous pouvons utiliser un swarplot qui va étaler les points positionnés aux mêmes valeurs de x pour les rendre visibles :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "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": [
    "sns.swarmplot(y_test, y_pred, size=3)\n",
    "sns.despine()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "On remarque que les notes extrêmes (3, 4, 8) sont mal prédites. Le modèle n'est pas très précis dans ses prédictions.\n",
    "\n",
    "Pour mieux comprendre notre modèle, comparons-le à une première approche naïve, qui consiste à prédire des valeurs aléatoires, distribuées uniformément entre les valeurs basse et haute des étiquettes du jeu de données d'entraînement."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "y_pred_random = np.random.randint(np.min(y), np.max(y), y_test.size)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Calculons la RMSE correspondante :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "RMSE : 1.71\n"
     ]
    }
   ],
   "source": [
    "print(\"RMSE : %.2f\" % np.sqrt(metrics.mean_squared_error(y_test, y_pred_random)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Nous obtenons une RMSE de 1.74, ce qui est bien supérieur à la RMSE obtenue par notre modèle kNN. Notre modèle a ainsi réussi à bien mieux apprendre qu'un modèle aléatoire.\n",
    "\n",
    "Cependant, beaucoup de nos vins ont une note de 5 et 6, et beaucoup de nos prédictions sont autour de cette valeur. Comparons maintenant notre modèle à un modèle aléatoire qui retourne systématiquement la valeur moyenne des étiquettes du jeu de données d'entraînement.\n",
    "\n",
    "Nous pouvons utiliser pour cela la fonction correspondante du module \"dummy\" de scikit-learn :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "RMSE : 0.80\n"
     ]
    }
   ],
   "source": [
    "dum = dummy.DummyRegressor(strategy='mean')\n",
    "\n",
    "# Entraînement\n",
    "dum.fit(X_train_std, y_train)\n",
    "\n",
    "# Prédiction sur le jeu de test\n",
    "y_pred_dum = dum.predict(X_test_std)\n",
    "\n",
    "# Evaluate\n",
    "print(\"RMSE : %.2f\" % np.sqrt(metrics.mean_squared_error(y_test, y_pred_dum)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "nous obtenons une RMSE de 0.80, qui est supérieure à celle de 0.66 obtenue par le kNN. Le kNN a donc appris plus que la moyenne des étiquettes."
   ]
  }
 ],
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