TP02_regression_generalisation.ipynb

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      "source": [
        "# TP 2 : Régression et généralisation\n",
        "\n",
        "Dans ce TP, nous allons voir comment :\n",
        "\n",
        "* Ajuster une régression multiple \"à la main\" (avec numpy)\n",
        "* Ajuster des modèles linéaires avec `sklearn`\n",
        "* Sélectionner des hyperparmètres (un modèle) par cross-validation, puis estimer son erreur de généralisation.\n",
        "\n",
        "Il y aura également un **exercice**, qui vous demendera d'effectuer vous-même une recherche d'hyperparamètres avec une regression Ridge, sur un nouveau jeu de données.\n",
        "\n",
        "Pour ce TP, il nous faudra les librairies, modules et objets suivants"
      ],
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    {
      "cell_type": "code",
      "source": [
        "import pandas as pd\n",
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "# Pour les modèles linéaires\n",
        "from sklearn.linear_model import LinearRegression, Lasso, Ridge\n",
        "# Pour séparer les datasets et la recherche des hyperparamètres\n",
        "from sklearn.model_selection import train_test_split, GridSearchCV\n",
        "# Pour faire des scores (l'opposé des fonctions de pertes) lisibles par sklearn\n",
        "from sklearn.metrics import make_scorer"
      ],
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      "execution_count": 1,
      "outputs": []
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    {
      "cell_type": "markdown",
      "source": [
        "---"
      ],
      "metadata": {
        "id": "3P24qIGwmxog"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Chargement et traitement des données\n",
        "\n",
        "Commençons par définir le chemin à notre jeu de données \"cancer_reg.csv\" (https://github.com/Arnab777as3uj/STAT6021-Cancer-Prediction-Project) et chargeons le. Ce jeu de données contient de nombreuses variables concernant des localités aux États-Unis, avec en particulier la variable **TARGET_deathRate** contenant la mortalité moyenne par année (sur 100'000 habitants) due au cancer."
      ],
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        "id": "hwrM8U3trTc3"
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              "      avgAnnCount  avgDeathsPerYear  TARGET_deathRate  incidenceRate  \\\n",
              "0     1397.000000               469             164.9     489.800000   \n",
              "1      173.000000                70             161.3     411.600000   \n",
              "2      102.000000                50             174.7     349.700000   \n",
              "3      427.000000               202             194.8     430.400000   \n",
              "4       57.000000                26             144.4     350.100000   \n",
              "...           ...               ...               ...            ...   \n",
              "3042  1962.667684                15             149.6     453.549422   \n",
              "3043  1962.667684                43             150.1     453.549422   \n",
              "3044  1962.667684                46             153.9     453.549422   \n",
              "3045  1962.667684                52             175.0     453.549422   \n",
              "3046  1962.667684                48             213.6     453.549422   \n",
              "\n",
              "      medIncome  popEst2015  povertyPercent  studyPerCap           binnedInc  \\\n",
              "0         61898      260131            11.2   499.748204   (61494.5, 125635]   \n",
              "1         48127       43269            18.6    23.111234  (48021.6, 51046.4]   \n",
              "2         49348       21026            14.6    47.560164  (48021.6, 51046.4]   \n",
              "3         44243       75882            17.1   342.637253    (42724.4, 45201]   \n",
              "4         49955       10321            12.5     0.000000  (48021.6, 51046.4]   \n",
              "...         ...         ...             ...          ...                 ...   \n",
              "3042      46961        6343            12.4     0.000000    (45201, 48021.6]   \n",
              "3043      48609       37118            18.8   377.175494  (48021.6, 51046.4]   \n",
              "3044      51144       34536            15.0  1968.959926  (51046.4, 54545.6]   \n",
              "3045      50745       25609            13.3     0.000000  (48021.6, 51046.4]   \n",
              "3046      41193       37030            13.9     0.000000  (40362.7, 42724.4]   \n",
              "\n",
              "      MedianAge  ...  PctPrivateCoverageAlone  PctEmpPrivCoverage  \\\n",
              "0          39.3  ...                      NaN                41.6   \n",
              "1          33.0  ...                     53.8                43.6   \n",
              "2          45.0  ...                     43.5                34.9   \n",
              "3          42.8  ...                     40.3                35.0   \n",
              "4          48.3  ...                     43.9                35.1   \n",
              "...         ...  ...                      ...                 ...   \n",
              "3042       44.2  ...                     54.9                44.6   \n",
              "3043       30.4  ...                     53.3                48.6   \n",
              "3044       30.9  ...                     52.6                47.8   \n",
              "3045       39.0  ...                     56.3                49.6   \n",
              "3046       26.2  ...                     60.3                22.9   \n",
              "\n",
              "     PctPublicCoverage  PctPublicCoverageAlone   PctWhite   PctBlack  \\\n",
              "0                 32.9                    14.0  81.780529   2.594728   \n",
              "1                 31.1                    15.3  89.228509   0.969102   \n",
              "2                 42.1                    21.1  90.922190   0.739673   \n",
              "3                 45.3                    25.0  91.744686   0.782626   \n",
              "4                 44.0                    22.7  94.104024   0.270192   \n",
              "...                ...                     ...        ...        ...   \n",
              "3042              31.7                    13.2  90.280811   3.837754   \n",
              "3043              28.8                    17.7  75.706245   2.326771   \n",
              "3044              26.6                    16.8  87.961629   2.313188   \n",
              "3045              29.5                    14.0  92.905681   1.176562   \n",
              "3046              25.1                    12.6  70.098132  16.590100   \n",
              "\n",
              "      PctAsian  PctOtherRace  PctMarriedHouseholds  BirthRate  \n",
              "0     4.821857      1.843479             52.856076   6.118831  \n",
              "1     2.246233      3.741352             45.372500   4.333096  \n",
              "2     0.465898      2.747358             54.444868   3.729488  \n",
              "3     1.161359      1.362643             51.021514   4.603841  \n",
              "4     0.665830      0.492135             54.027460   6.796657  \n",
              "...        ...           ...                   ...        ...  \n",
              "3042  0.327613      1.700468             51.063830   7.773512  \n",
              "3043  4.044920     14.130288             52.007937   8.186470  \n",
              "3044  1.316472      5.680705             55.153949   7.809192  \n",
              "3045  0.244632      2.131790             58.484232   7.582938  \n",
              "3046  3.177753      1.356457             56.040242   8.981723  \n",
              "\n",
              "[3047 rows x 34 columns]"
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              "      <th></th>\n",
              "      <th>avgAnnCount</th>\n",
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              "      <td>174.7</td>\n",
              "      <td>349.700000</td>\n",
              "      <td>49348</td>\n",
              "      <td>21026</td>\n",
              "      <td>14.6</td>\n",
              "      <td>47.560164</td>\n",
              "      <td>(48021.6, 51046.4]</td>\n",
              "      <td>45.0</td>\n",
              "      <td>...</td>\n",
              "      <td>43.5</td>\n",
              "      <td>34.9</td>\n",
              "      <td>42.1</td>\n",
              "      <td>21.1</td>\n",
              "      <td>90.922190</td>\n",
              "      <td>0.739673</td>\n",
              "      <td>0.465898</td>\n",
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              "      <td>1.362643</td>\n",
              "      <td>51.021514</td>\n",
              "      <td>4.603841</td>\n",
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              "      <th>4</th>\n",
              "      <td>57.000000</td>\n",
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              "      <td>350.100000</td>\n",
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              "      <td>12.5</td>\n",
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              "      <td>48.3</td>\n",
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              "      <td>44.0</td>\n",
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            "application/vnd.google.colaboratory.intrinsic+json": {
              "type": "dataframe",
              "variable_name": "data"
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          },
          "metadata": {},
          "execution_count": 2
        }
      ],
      "source": [
        "file_path = \"drive/MyDrive/Colab Notebooks/ml_data/TP2/cancer_reg.csv\"\n",
        "# L'encodage du fichier est \"latin-1\"\n",
        "data = pd.read_csv(file_path, encoding='latin-1')\n",
        "data"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Remarquons qu'il n'y a que des variables numériques, mis à part **binnedInc** (un intervalle) et **Geography** (nom de la ville) (voir `my_df.dtypes`). Les variables **incidenceRate**, **avgAnnCount**, **avgDeathsPerYear**, **popEst2015** sont des variables qui ont servi à la construction de la variable dépendante ou qui ne sont pas pertinentes. Nous allons enlever toutes ces variables :"
      ],
      "metadata": {
        "id": "5wjey_ZOYhVN"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "data = data.drop([\"binnedInc\", \"Geography\", \"incidenceRate\", \"avgAnnCount\",\n",
        "                  \"avgDeathsPerYear\", \"popEst2015\"], axis=1)"
      ],
      "metadata": {
        "id": "i_ErIJLUW5mi"
      },
      "execution_count": 3,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "data"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 444
        },
        "id": "T-w_SNIdLvVR",
        "outputId": "647fbe01-dda4-4c89-b5f4-8b6b89313f54"
      },
      "execution_count": 4,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "      TARGET_deathRate  medIncome  povertyPercent  studyPerCap  MedianAge  \\\n",
              "0                164.9      61898            11.2   499.748204       39.3   \n",
              "1                161.3      48127            18.6    23.111234       33.0   \n",
              "2                174.7      49348            14.6    47.560164       45.0   \n",
              "3                194.8      44243            17.1   342.637253       42.8   \n",
              "4                144.4      49955            12.5     0.000000       48.3   \n",
              "...                ...        ...             ...          ...        ...   \n",
              "3042             149.6      46961            12.4     0.000000       44.2   \n",
              "3043             150.1      48609            18.8   377.175494       30.4   \n",
              "3044             153.9      51144            15.0  1968.959926       30.9   \n",
              "3045             175.0      50745            13.3     0.000000       39.0   \n",
              "3046             213.6      41193            13.9     0.000000       26.2   \n",
              "\n",
              "      MedianAgeMale  MedianAgeFemale  AvgHouseholdSize  PercentMarried  \\\n",
              "0              36.9             41.7              2.54            52.5   \n",
              "1              32.2             33.7              2.34            44.5   \n",
              "2              44.0             45.8              2.62            54.2   \n",
              "3              42.2             43.4              2.52            52.7   \n",
              "4              47.8             48.9              2.34            57.8   \n",
              "...             ...              ...               ...             ...   \n",
              "3042           41.1             48.8              2.08            51.0   \n",
              "3043           29.3             31.4              2.90            52.6   \n",
              "3044           30.5             31.2              3.04            54.8   \n",
              "3045           36.9             40.5              2.56            58.8   \n",
              "3046           25.5             27.0              2.83            59.5   \n",
              "\n",
              "      PctNoHS18_24  ...  PctPrivateCoverageAlone  PctEmpPrivCoverage  \\\n",
              "0             11.5  ...                      NaN                41.6   \n",
              "1              6.1  ...                     53.8                43.6   \n",
              "2             24.0  ...                     43.5                34.9   \n",
              "3             20.2  ...                     40.3                35.0   \n",
              "4             14.9  ...                     43.9                35.1   \n",
              "...            ...  ...                      ...                 ...   \n",
              "3042          20.9  ...                     54.9                44.6   \n",
              "3043          26.7  ...                     53.3                48.6   \n",
              "3044          19.7  ...                     52.6                47.8   \n",
              "3045          10.9  ...                     56.3                49.6   \n",
              "3046           8.0  ...                     60.3                22.9   \n",
              "\n",
              "      PctPublicCoverage  PctPublicCoverageAlone   PctWhite   PctBlack  \\\n",
              "0                  32.9                    14.0  81.780529   2.594728   \n",
              "1                  31.1                    15.3  89.228509   0.969102   \n",
              "2                  42.1                    21.1  90.922190   0.739673   \n",
              "3                  45.3                    25.0  91.744686   0.782626   \n",
              "4                  44.0                    22.7  94.104024   0.270192   \n",
              "...                 ...                     ...        ...        ...   \n",
              "3042               31.7                    13.2  90.280811   3.837754   \n",
              "3043               28.8                    17.7  75.706245   2.326771   \n",
              "3044               26.6                    16.8  87.961629   2.313188   \n",
              "3045               29.5                    14.0  92.905681   1.176562   \n",
              "3046               25.1                    12.6  70.098132  16.590100   \n",
              "\n",
              "      PctAsian  PctOtherRace  PctMarriedHouseholds  BirthRate  \n",
              "0     4.821857      1.843479             52.856076   6.118831  \n",
              "1     2.246233      3.741352             45.372500   4.333096  \n",
              "2     0.465898      2.747358             54.444868   3.729488  \n",
              "3     1.161359      1.362643             51.021514   4.603841  \n",
              "4     0.665830      0.492135             54.027460   6.796657  \n",
              "...        ...           ...                   ...        ...  \n",
              "3042  0.327613      1.700468             51.063830   7.773512  \n",
              "3043  4.044920     14.130288             52.007937   8.186470  \n",
              "3044  1.316472      5.680705             55.153949   7.809192  \n",
              "3045  0.244632      2.131790             58.484232   7.582938  \n",
              "3046  3.177753      1.356457             56.040242   8.981723  \n",
              "\n",
              "[3047 rows x 28 columns]"
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              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>TARGET_deathRate</th>\n",
              "      <th>medIncome</th>\n",
              "      <th>povertyPercent</th>\n",
              "      <th>studyPerCap</th>\n",
              "      <th>MedianAge</th>\n",
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              "      <th>AvgHouseholdSize</th>\n",
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              "      <th>PctEmpPrivCoverage</th>\n",
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              "      <th>PctAsian</th>\n",
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              "      <td>39.3</td>\n",
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              "      <td>41.7</td>\n",
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              "      <td>52.5</td>\n",
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              "      <td>161.3</td>\n",
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              "      <td>18.6</td>\n",
              "      <td>23.111234</td>\n",
              "      <td>33.0</td>\n",
              "      <td>32.2</td>\n",
              "      <td>33.7</td>\n",
              "      <td>2.34</td>\n",
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              "      <td>53.8</td>\n",
              "      <td>43.6</td>\n",
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              "      <td>15.3</td>\n",
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              "      <td>2.246233</td>\n",
              "      <td>3.741352</td>\n",
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              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>174.7</td>\n",
              "      <td>49348</td>\n",
              "      <td>14.6</td>\n",
              "      <td>47.560164</td>\n",
              "      <td>45.0</td>\n",
              "      <td>44.0</td>\n",
              "      <td>45.8</td>\n",
              "      <td>2.62</td>\n",
              "      <td>54.2</td>\n",
              "      <td>24.0</td>\n",
              "      <td>...</td>\n",
              "      <td>43.5</td>\n",
              "      <td>34.9</td>\n",
              "      <td>42.1</td>\n",
              "      <td>21.1</td>\n",
              "      <td>90.922190</td>\n",
              "      <td>0.739673</td>\n",
              "      <td>0.465898</td>\n",
              "      <td>2.747358</td>\n",
              "      <td>54.444868</td>\n",
              "      <td>3.729488</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>194.8</td>\n",
              "      <td>44243</td>\n",
              "      <td>17.1</td>\n",
              "      <td>342.637253</td>\n",
              "      <td>42.8</td>\n",
              "      <td>42.2</td>\n",
              "      <td>43.4</td>\n",
              "      <td>2.52</td>\n",
              "      <td>52.7</td>\n",
              "      <td>20.2</td>\n",
              "      <td>...</td>\n",
              "      <td>40.3</td>\n",
              "      <td>35.0</td>\n",
              "      <td>45.3</td>\n",
              "      <td>25.0</td>\n",
              "      <td>91.744686</td>\n",
              "      <td>0.782626</td>\n",
              "      <td>1.161359</td>\n",
              "      <td>1.362643</td>\n",
              "      <td>51.021514</td>\n",
              "      <td>4.603841</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>144.4</td>\n",
              "      <td>49955</td>\n",
              "      <td>12.5</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>48.3</td>\n",
              "      <td>47.8</td>\n",
              "      <td>48.9</td>\n",
              "      <td>2.34</td>\n",
              "      <td>57.8</td>\n",
              "      <td>14.9</td>\n",
              "      <td>...</td>\n",
              "      <td>43.9</td>\n",
              "      <td>35.1</td>\n",
              "      <td>44.0</td>\n",
              "      <td>22.7</td>\n",
              "      <td>94.104024</td>\n",
              "      <td>0.270192</td>\n",
              "      <td>0.665830</td>\n",
              "      <td>0.492135</td>\n",
              "      <td>54.027460</td>\n",
              "      <td>6.796657</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>...</th>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3042</th>\n",
              "      <td>149.6</td>\n",
              "      <td>46961</td>\n",
              "      <td>12.4</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>44.2</td>\n",
              "      <td>41.1</td>\n",
              "      <td>48.8</td>\n",
              "      <td>2.08</td>\n",
              "      <td>51.0</td>\n",
              "      <td>20.9</td>\n",
              "      <td>...</td>\n",
              "      <td>54.9</td>\n",
              "      <td>44.6</td>\n",
              "      <td>31.7</td>\n",
              "      <td>13.2</td>\n",
              "      <td>90.280811</td>\n",
              "      <td>3.837754</td>\n",
              "      <td>0.327613</td>\n",
              "      <td>1.700468</td>\n",
              "      <td>51.063830</td>\n",
              "      <td>7.773512</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3043</th>\n",
              "      <td>150.1</td>\n",
              "      <td>48609</td>\n",
              "      <td>18.8</td>\n",
              "      <td>377.175494</td>\n",
              "      <td>30.4</td>\n",
              "      <td>29.3</td>\n",
              "      <td>31.4</td>\n",
              "      <td>2.90</td>\n",
              "      <td>52.6</td>\n",
              "      <td>26.7</td>\n",
              "      <td>...</td>\n",
              "      <td>53.3</td>\n",
              "      <td>48.6</td>\n",
              "      <td>28.8</td>\n",
              "      <td>17.7</td>\n",
              "      <td>75.706245</td>\n",
              "      <td>2.326771</td>\n",
              "      <td>4.044920</td>\n",
              "      <td>14.130288</td>\n",
              "      <td>52.007937</td>\n",
              "      <td>8.186470</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3044</th>\n",
              "      <td>153.9</td>\n",
              "      <td>51144</td>\n",
              "      <td>15.0</td>\n",
              "      <td>1968.959926</td>\n",
              "      <td>30.9</td>\n",
              "      <td>30.5</td>\n",
              "      <td>31.2</td>\n",
              "      <td>3.04</td>\n",
              "      <td>54.8</td>\n",
              "      <td>19.7</td>\n",
              "      <td>...</td>\n",
              "      <td>52.6</td>\n",
              "      <td>47.8</td>\n",
              "      <td>26.6</td>\n",
              "      <td>16.8</td>\n",
              "      <td>87.961629</td>\n",
              "      <td>2.313188</td>\n",
              "      <td>1.316472</td>\n",
              "      <td>5.680705</td>\n",
              "      <td>55.153949</td>\n",
              "      <td>7.809192</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3045</th>\n",
              "      <td>175.0</td>\n",
              "      <td>50745</td>\n",
              "      <td>13.3</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>39.0</td>\n",
              "      <td>36.9</td>\n",
              "      <td>40.5</td>\n",
              "      <td>2.56</td>\n",
              "      <td>58.8</td>\n",
              "      <td>10.9</td>\n",
              "      <td>...</td>\n",
              "      <td>56.3</td>\n",
              "      <td>49.6</td>\n",
              "      <td>29.5</td>\n",
              "      <td>14.0</td>\n",
              "      <td>92.905681</td>\n",
              "      <td>1.176562</td>\n",
              "      <td>0.244632</td>\n",
              "      <td>2.131790</td>\n",
              "      <td>58.484232</td>\n",
              "      <td>7.582938</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3046</th>\n",
              "      <td>213.6</td>\n",
              "      <td>41193</td>\n",
              "      <td>13.9</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>26.2</td>\n",
              "      <td>25.5</td>\n",
              "      <td>27.0</td>\n",
              "      <td>2.83</td>\n",
              "      <td>59.5</td>\n",
              "      <td>8.0</td>\n",
              "      <td>...</td>\n",
              "      <td>60.3</td>\n",
              "      <td>22.9</td>\n",
              "      <td>25.1</td>\n",
              "      <td>12.6</td>\n",
              "      <td>70.098132</td>\n",
              "      <td>16.590100</td>\n",
              "      <td>3.177753</td>\n",
              "      <td>1.356457</td>\n",
              "      <td>56.040242</td>\n",
              "      <td>8.981723</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "<p>3047 rows × 28 columns</p>\n",
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              "\n",
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            ],
            "application/vnd.google.colaboratory.intrinsic+json": {
              "type": "dataframe",
              "variable_name": "data"
            }
          },
          "metadata": {},
          "execution_count": 4
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Notre jeu de données possède des valeurs manquantes (`NaN`). Certaines instances de méthodes permettent de les prendre en charge, mais ici, nous allons les remplacer par la moyenne de la variable manquante. Pour cela, nous créons un dictionnaire contenant les moyennes des variables, puis on utilise `fillna`"
      ],
      "metadata": {
        "id": "N842Dfi-kRV_"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "var_means = {var_name : data[var_name].mean() for var_name in data.columns}\n",
        "data = data.fillna(value=var_means)\n",
        "var_means"
      ],
      "metadata": {
        "id": "-PKDARZ8k6vi",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "5c6807aa-066c-47b7-848b-be92561bacfe"
      },
      "execution_count": 5,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "{'TARGET_deathRate': 178.66406301279943,\n",
              " 'medIncome': 47063.28191663932,\n",
              " 'povertyPercent': 16.87817525434854,\n",
              " 'studyPerCap': 155.3994153176078,\n",
              " 'MedianAge': 45.27233344273055,\n",
              " 'MedianAgeMale': 39.57072530357729,\n",
              " 'MedianAgeFemale': 42.14532326878897,\n",
              " 'AvgHouseholdSize': 2.4796617984903184,\n",
              " 'PercentMarried': 51.773679028552685,\n",
              " 'PctNoHS18_24': 18.224450278962916,\n",
              " 'PctHS18_24': 35.00206760748277,\n",
              " 'PctSomeCol18_24': 40.977034120734906,\n",
              " 'PctBachDeg18_24': 6.158286839514276,\n",
              " 'PctHS25_Over': 34.80466032162783,\n",
              " 'PctBachDeg25_Over': 13.282015096816542,\n",
              " 'PctEmployed16_Over': 54.15264248704664,\n",
              " 'PctUnemployed16_Over': 7.852412208729898,\n",
              " 'PctPrivateCoverage': 64.35493928454217,\n",
              " 'PctPrivateCoverageAlone': 48.45377358490566,\n",
              " 'PctEmpPrivCoverage': 41.19632425336397,\n",
              " 'PctPublicCoverage': 36.25264194289465,\n",
              " 'PctPublicCoverageAlone': 19.240072202166065,\n",
              " 'PctWhite': 83.6452862348999,\n",
              " 'PctBlack': 9.107977614569412,\n",
              " 'PctAsian': 1.2539649641860848,\n",
              " 'PctOtherRace': 1.9835230038171974,\n",
              " 'PctMarriedHouseholds': 51.24387214146373,\n",
              " 'BirthRate': 5.640305931184445}"
            ]
          },
          "metadata": {},
          "execution_count": 5
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Finalement, nous allons isoler notre variable dépendante des autres variables, et sauvegarder le nombre d'individus et variables dépendantes"
      ],
      "metadata": {
        "id": "IWW84TU0d6Y2"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "outputs = data[\"TARGET_deathRate\"]\n",
        "inputs = data.drop([\"TARGET_deathRate\"], axis=1)\n",
        "n_row, n_col = inputs.shape"
      ],
      "metadata": {
        "id": "ntaT7ortYS1H"
      },
      "execution_count": 6,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "---"
      ],
      "metadata": {
        "id": "i3tcmJdrm6wk"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Régression linéaire avec `numpy`\n",
        "\n",
        "Nous allons faire ici une régression linéaire \"à la main\", à l'aide la la libraire `numpy`. Ainsi, nous pourrons comparer ces résultats avec ceux obtenus grâce à `sklearn`. Tout d'abord, on transforme nos entrées et sorties en Arrays"
      ],
      "metadata": {
        "id": "PvDKk2kqegau"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "inputs_a = inputs.to_numpy()\n",
        "outputs_a = outputs.to_numpy()"
      ],
      "metadata": {
        "id": "ZunXy-e_ek4l"
      },
      "execution_count": 7,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "Pour que nous puissons calculer l'intercept $w_0$, nous allons devoir ajouter une colonne de $1$ à nos entrées"
      ],
      "metadata": {
        "id": "GiFc-cOlgH5v"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "vec_of_ones = np.ones([n_row, 1])\n",
        "x_matrix = np.concatenate([vec_of_ones, inputs_a], axis=1)\n",
        "x_matrix"
      ],
      "metadata": {
        "id": "Vwb0ctKcfjYf",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "29e9479a-aca5-428a-ca45-c8d88f20afb4"
      },
      "execution_count": 8,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[1.00000000e+00, 6.18980000e+04, 1.12000000e+01, ...,\n",
              "        1.84347853e+00, 5.28560759e+01, 6.11883103e+00],\n",
              "       [1.00000000e+00, 4.81270000e+04, 1.86000000e+01, ...,\n",
              "        3.74135153e+00, 4.53725004e+01, 4.33309558e+00],\n",
              "       [1.00000000e+00, 4.93480000e+04, 1.46000000e+01, ...,\n",
              "        2.74735831e+00, 5.44448684e+01, 3.72948782e+00],\n",
              "       ...,\n",
              "       [1.00000000e+00, 5.11440000e+04, 1.50000000e+01, ...,\n",
              "        5.68070519e+00, 5.51539491e+01, 7.80919168e+00],\n",
              "       [1.00000000e+00, 5.07450000e+04, 1.33000000e+01, ...,\n",
              "        2.13179047e+00, 5.84842319e+01, 7.58293839e+00],\n",
              "       [1.00000000e+00, 4.11930000e+04, 1.39000000e+01, ...,\n",
              "        1.35645744e+00, 5.60402421e+01, 8.98172324e+00]])"
            ]
          },
          "metadata": {},
          "execution_count": 8
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Effectuons maintenant la formule de régression $\\textbf{w} = (\\textbf{X}^\\top \\textbf{X})^{-1}\\textbf{X}^\\top \\textbf{y}$ pour trouver les coefficients $\\textbf{w}$"
      ],
      "metadata": {
        "id": "bkIj0RzKiAR0"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "coef = np.linalg.inv(x_matrix.T @ x_matrix) @ x_matrix.T @ outputs_a\n",
        "coef"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "z_S0kujxfrZt",
        "outputId": "9a827b89-a0f7-452e-b106-dc633e499478"
      },
      "execution_count": 9,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([ 2.19718691e+02,  2.19788004e-04,  2.77273746e-01,  9.31363532e-04,\n",
              "        1.85557211e-03, -4.98272280e-01, -3.99391598e-01, -5.67544728e-01,\n",
              "        1.47435223e+00, -2.00329540e-01,  2.92050344e-01,  5.19175769e-02,\n",
              "       -8.22649608e-02,  5.30738029e-01, -1.39614877e+00, -5.63257056e-01,\n",
              "        5.43905976e-01, -1.31379589e-01,  1.08845666e-01,  4.91756992e-01,\n",
              "       -1.20887731e-01,  8.85889619e-01, -7.62392584e-02,  3.44733561e-02,\n",
              "       -2.14858389e-01, -1.29052962e+00, -1.75472216e+00, -1.32999581e+00])"
            ]
          },
          "metadata": {},
          "execution_count": 9
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Calculons maintenant les prédictions et la $MSE$"
      ],
      "metadata": {
        "id": "xImex5j3l22j"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "outputs_pred = x_matrix @ coef\n",
        "mse = np.mean((outputs_pred - outputs_a)**2)\n",
        "mse"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "ypeNvQyWhlJP",
        "outputId": "ba3e548c-e319-42bf-8529-5402d5995b47"
      },
      "execution_count": 10,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "458.43606876316204"
            ]
          },
          "metadata": {},
          "execution_count": 10
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Nous allons comparer ces résultats avec ceux obtenus avec `sklearn`.\n",
        "\n",
        "---"
      ],
      "metadata": {
        "id": "WG1Q0KC_mlC1"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Régression linéaire avec `sklearn`\n",
        "\n",
        "Le fonctionnnement usuel de méthodes dans `sklearn` se passe selon les étapes suivantes :\n",
        "\n",
        "* On crée une instance de la classe de la méthode désirée (ici `LinearRegression`)\n",
        "* On fait appelle à la méthode de l'objet `fit`, où l'on fait passer nos données. Cette méthode permet d'entrainer la méthode et trouver les paramètres optimaux.\n",
        "* L'instance initiale va maintenant contenir toutes les informations relative à la méthode, que l'on peut extraire."
      ],
      "metadata": {
        "id": "4iGvAhGEojDu"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "L'entrainement se fait donc de la manière suivante"
      ],
      "metadata": {
        "id": "woWzNjeTp187"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "linear_reg = LinearRegression()\n",
        "linear_reg.fit(inputs, outputs)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 80
        },
        "id": "v-Lq8o3QlgeC",
        "outputId": "4097baef-b7f4-43d0-edf5-fed9d53d72ff"
      },
      "execution_count": 11,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "LinearRegression()"
            ],
            "text/html": [
              "<style>#sk-container-id-1 {\n",
              "  /* Definition of color scheme common for light and dark mode */\n",
              "  --sklearn-color-text: black;\n",
              "  --sklearn-color-line: gray;\n",
              "  /* Definition of color scheme for unfitted estimators */\n",
              "  --sklearn-color-unfitted-level-0: #fff5e6;\n",
              "  --sklearn-color-unfitted-level-1: #f6e4d2;\n",
              "  --sklearn-color-unfitted-level-2: #ffe0b3;\n",
              "  --sklearn-color-unfitted-level-3: chocolate;\n",
              "  /* Definition of color scheme for fitted estimators */\n",
              "  --sklearn-color-fitted-level-0: #f0f8ff;\n",
              "  --sklearn-color-fitted-level-1: #d4ebff;\n",
              "  --sklearn-color-fitted-level-2: #b3dbfd;\n",
              "  --sklearn-color-fitted-level-3: cornflowerblue;\n",
              "\n",
              "  /* Specific color for light theme */\n",
              "  --sklearn-color-text-on-default-background: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, black)));\n",
              "  --sklearn-color-background: var(--sg-background-color, var(--theme-background, var(--jp-layout-color0, white)));\n",
              "  --sklearn-color-border-box: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, black)));\n",
              "  --sklearn-color-icon: #696969;\n",
              "\n",
              "  @media (prefers-color-scheme: dark) {\n",
              "    /* Redefinition of color scheme for dark theme */\n",
              "    --sklearn-color-text-on-default-background: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, white)));\n",
              "    --sklearn-color-background: var(--sg-background-color, var(--theme-background, var(--jp-layout-color0, #111)));\n",
              "    --sklearn-color-border-box: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, white)));\n",
              "    --sklearn-color-icon: #878787;\n",
              "  }\n",
              "}\n",
              "\n",
              "#sk-container-id-1 {\n",
              "  color: var(--sklearn-color-text);\n",
              "}\n",
              "\n",
              "#sk-container-id-1 pre {\n",
              "  padding: 0;\n",
              "}\n",
              "\n",
              "#sk-container-id-1 input.sk-hidden--visually {\n",
              "  border: 0;\n",
              "  clip: rect(1px 1px 1px 1px);\n",
              "  clip: rect(1px, 1px, 1px, 1px);\n",
              "  height: 1px;\n",
              "  margin: -1px;\n",
              "  overflow: hidden;\n",
              "  padding: 0;\n",
              "  position: absolute;\n",
              "  width: 1px;\n",
              "}\n",
              "\n",
              "#sk-container-id-1 div.sk-dashed-wrapped {\n",
              "  border: 1px dashed var(--sklearn-color-line);\n",
              "  margin: 0 0.4em 0.5em 0.4em;\n",
              "  box-sizing: border-box;\n",
              "  padding-bottom: 0.4em;\n",
              "  background-color: var(--sklearn-color-background);\n",
              "}\n",
              "\n",
              "#sk-container-id-1 div.sk-container {\n",
              "  /* jupyter's `normalize.less` sets `[hidden] { display: none; }`\n",
              "     but bootstrap.min.css set `[hidden] { display: none !important; }`\n",
              "     so we also need the `!important` here to be able to override the\n",
              "     default hidden behavior on the sphinx rendered scikit-learn.org.\n",
              "     See: https://github.com/scikit-learn/scikit-learn/issues/21755 */\n",
              "  display: inline-block !important;\n",
              "  position: relative;\n",
              "}\n",
              "\n",
              "#sk-container-id-1 div.sk-text-repr-fallback {\n",
              "  display: none;\n",
              "}\n",
              "\n",
              "div.sk-parallel-item,\n",
              "div.sk-serial,\n",
              "div.sk-item {\n",
              "  /* draw centered vertical line to link estimators */\n",
              "  background-image: linear-gradient(var(--sklearn-color-text-on-default-background), var(--sklearn-color-text-on-default-background));\n",
              "  background-size: 2px 100%;\n",
              "  background-repeat: no-repeat;\n",
              "  background-position: center center;\n",
              "}\n",
              "\n",
              "/* Parallel-specific style estimator block */\n",
              "\n",
              "#sk-container-id-1 div.sk-parallel-item::after {\n",
              "  content: \"\";\n",
              "  width: 100%;\n",
              "  border-bottom: 2px solid var(--sklearn-color-text-on-default-background);\n",
              "  flex-grow: 1;\n",
              "}\n",
              "\n",
              "#sk-container-id-1 div.sk-parallel {\n",
              "  display: flex;\n",
              "  align-items: stretch;\n",
              "  justify-content: center;\n",
              "  background-color: var(--sklearn-color-background);\n",
              "  position: relative;\n",
              "}\n",
              "\n",
              "#sk-container-id-1 div.sk-parallel-item {\n",
              "  display: flex;\n",
              "  flex-direction: column;\n",
              "}\n",
              "\n",
              "#sk-container-id-1 div.sk-parallel-item:first-child::after {\n",
              "  align-self: flex-end;\n",
              "  width: 50%;\n",
              "}\n",
              "\n",
              "#sk-container-id-1 div.sk-parallel-item:last-child::after {\n",
              "  align-self: flex-start;\n",
              "  width: 50%;\n",
              "}\n",
              "\n",
              "#sk-container-id-1 div.sk-parallel-item:only-child::after {\n",
              "  width: 0;\n",
              "}\n",
              "\n",
              "/* Serial-specific style estimator block */\n",
              "\n",
              "#sk-container-id-1 div.sk-serial {\n",
              "  display: flex;\n",
              "  flex-direction: column;\n",
              "  align-items: center;\n",
              "  background-color: var(--sklearn-color-background);\n",
              "  padding-right: 1em;\n",
              "  padding-left: 1em;\n",
              "}\n",
              "\n",
              "\n",
              "/* Toggleable style: style used for estimator/Pipeline/ColumnTransformer box that is\n",
              "clickable and can be expanded/collapsed.\n",
              "- Pipeline and ColumnTransformer use this feature and define the default style\n",
              "- Estimators will overwrite some part of the style using the `sk-estimator` class\n",
              "*/\n",
              "\n",
              "/* Pipeline and ColumnTransformer style (default) */\n",
              "\n",
              "#sk-container-id-1 div.sk-toggleable {\n",
              "  /* Default theme specific background. It is overwritten whether we have a\n",
              "  specific estimator or a Pipeline/ColumnTransformer */\n",
              "  background-color: var(--sklearn-color-background);\n",
              "}\n",
              "\n",
              "/* Toggleable label */\n",
              "#sk-container-id-1 label.sk-toggleable__label {\n",
              "  cursor: pointer;\n",
              "  display: block;\n",
              "  width: 100%;\n",
              "  margin-bottom: 0;\n",
              "  padding: 0.5em;\n",
              "  box-sizing: border-box;\n",
              "  text-align: center;\n",
              "}\n",
              "\n",
              "#sk-container-id-1 label.sk-toggleable__label-arrow:before {\n",
              "  /* Arrow on the left of the label */\n",
              "  content: \"▸\";\n",
              "  float: left;\n",
              "  margin-right: 0.25em;\n",
              "  color: var(--sklearn-color-icon);\n",
              "}\n",
              "\n",
              "#sk-container-id-1 label.sk-toggleable__label-arrow:hover:before {\n",
              "  color: var(--sklearn-color-text);\n",
              "}\n",
              "\n",
              "/* Toggleable content - dropdown */\n",
              "\n",
              "#sk-container-id-1 div.sk-toggleable__content {\n",
              "  max-height: 0;\n",
              "  max-width: 0;\n",
              "  overflow: hidden;\n",
              "  text-align: left;\n",
              "  /* unfitted */\n",
              "  background-color: var(--sklearn-color-unfitted-level-0);\n",
              "}\n",
              "\n",
              "#sk-container-id-1 div.sk-toggleable__content.fitted {\n",
              "  /* fitted */\n",
              "  background-color: var(--sklearn-color-fitted-level-0);\n",
              "}\n",
              "\n",
              "#sk-container-id-1 div.sk-toggleable__content pre {\n",
              "  margin: 0.2em;\n",
              "  border-radius: 0.25em;\n",
              "  color: var(--sklearn-color-text);\n",
              "  /* unfitted */\n",
              "  background-color: var(--sklearn-color-unfitted-level-0);\n",
              "}\n",
              "\n",
              "#sk-container-id-1 div.sk-toggleable__content.fitted pre {\n",
              "  /* unfitted */\n",
              "  background-color: var(--sklearn-color-fitted-level-0);\n",
              "}\n",
              "\n",
              "#sk-container-id-1 input.sk-toggleable__control:checked~div.sk-toggleable__content {\n",
              "  /* Expand drop-down */\n",
              "  max-height: 200px;\n",
              "  max-width: 100%;\n",
              "  overflow: auto;\n",
              "}\n",
              "\n",
              "#sk-container-id-1 input.sk-toggleable__control:checked~label.sk-toggleable__label-arrow:before {\n",
              "  content: \"▾\";\n",
              "}\n",
              "\n",
              "/* Pipeline/ColumnTransformer-specific style */\n",
              "\n",
              "#sk-container-id-1 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
              "  color: var(--sklearn-color-text);\n",
              "  background-color: var(--sklearn-color-unfitted-level-2);\n",
              "}\n",
              "\n",
              "#sk-container-id-1 div.sk-label.fitted input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
              "  background-color: var(--sklearn-color-fitted-level-2);\n",
              "}\n",
              "\n",
              "/* Estimator-specific style */\n",
              "\n",
              "/* Colorize estimator box */\n",
              "#sk-container-id-1 div.sk-estimator input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
              "  /* unfitted */\n",
              "  background-color: var(--sklearn-color-unfitted-level-2);\n",
              "}\n",
              "\n",
              "#sk-container-id-1 div.sk-estimator.fitted input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
              "  /* fitted */\n",
              "  background-color: var(--sklearn-color-fitted-level-2);\n",
              "}\n",
              "\n",
              "#sk-container-id-1 div.sk-label label.sk-toggleable__label,\n",
              "#sk-container-id-1 div.sk-label label {\n",
              "  /* The background is the default theme color */\n",
              "  color: var(--sklearn-color-text-on-default-background);\n",
              "}\n",
              "\n",
              "/* On hover, darken the color of the background */\n",
              "#sk-container-id-1 div.sk-label:hover label.sk-toggleable__label {\n",
              "  color: var(--sklearn-color-text);\n",
              "  background-color: var(--sklearn-color-unfitted-level-2);\n",
              "}\n",
              "\n",
              "/* Label box, darken color on hover, fitted */\n",
              "#sk-container-id-1 div.sk-label.fitted:hover label.sk-toggleable__label.fitted {\n",
              "  color: var(--sklearn-color-text);\n",
              "  background-color: var(--sklearn-color-fitted-level-2);\n",
              "}\n",
              "\n",
              "/* Estimator label */\n",
              "\n",
              "#sk-container-id-1 div.sk-label label {\n",
              "  font-family: monospace;\n",
              "  font-weight: bold;\n",
              "  display: inline-block;\n",
              "  line-height: 1.2em;\n",
              "}\n",
              "\n",
              "#sk-container-id-1 div.sk-label-container {\n",
              "  text-align: center;\n",
              "}\n",
              "\n",
              "/* Estimator-specific */\n",
              "#sk-container-id-1 div.sk-estimator {\n",
              "  font-family: monospace;\n",
              "  border: 1px dotted var(--sklearn-color-border-box);\n",
              "  border-radius: 0.25em;\n",
              "  box-sizing: border-box;\n",
              "  margin-bottom: 0.5em;\n",
              "  /* unfitted */\n",
              "  background-color: var(--sklearn-color-unfitted-level-0);\n",
              "}\n",
              "\n",
              "#sk-container-id-1 div.sk-estimator.fitted {\n",
              "  /* fitted */\n",
              "  background-color: var(--sklearn-color-fitted-level-0);\n",
              "}\n",
              "\n",
              "/* on hover */\n",
              "#sk-container-id-1 div.sk-estimator:hover {\n",
              "  /* unfitted */\n",
              "  background-color: var(--sklearn-color-unfitted-level-2);\n",
              "}\n",
              "\n",
              "#sk-container-id-1 div.sk-estimator.fitted:hover {\n",
              "  /* fitted */\n",
              "  background-color: var(--sklearn-color-fitted-level-2);\n",
              "}\n",
              "\n",
              "/* Specification for estimator info (e.g. \"i\" and \"?\") */\n",
              "\n",
              "/* Common style for \"i\" and \"?\" */\n",
              "\n",
              ".sk-estimator-doc-link,\n",
              "a:link.sk-estimator-doc-link,\n",
              "a:visited.sk-estimator-doc-link {\n",
              "  float: right;\n",
              "  font-size: smaller;\n",
              "  line-height: 1em;\n",
              "  font-family: monospace;\n",
              "  background-color: var(--sklearn-color-background);\n",
              "  border-radius: 1em;\n",
              "  height: 1em;\n",
              "  width: 1em;\n",
              "  text-decoration: none !important;\n",
              "  margin-left: 1ex;\n",
              "  /* unfitted */\n",
              "  border: var(--sklearn-color-unfitted-level-1) 1pt solid;\n",
              "  color: var(--sklearn-color-unfitted-level-1);\n",
              "}\n",
              "\n",
              ".sk-estimator-doc-link.fitted,\n",
              "a:link.sk-estimator-doc-link.fitted,\n",
              "a:visited.sk-estimator-doc-link.fitted {\n",
              "  /* fitted */\n",
              "  border: var(--sklearn-color-fitted-level-1) 1pt solid;\n",
              "  color: var(--sklearn-color-fitted-level-1);\n",
              "}\n",
              "\n",
              "/* On hover */\n",
              "div.sk-estimator:hover .sk-estimator-doc-link:hover,\n",
              ".sk-estimator-doc-link:hover,\n",
              "div.sk-label-container:hover .sk-estimator-doc-link:hover,\n",
              ".sk-estimator-doc-link:hover {\n",
              "  /* unfitted */\n",
              "  background-color: var(--sklearn-color-unfitted-level-3);\n",
              "  color: var(--sklearn-color-background);\n",
              "  text-decoration: none;\n",
              "}\n",
              "\n",
              "div.sk-estimator.fitted:hover .sk-estimator-doc-link.fitted:hover,\n",
              ".sk-estimator-doc-link.fitted:hover,\n",
              "div.sk-label-container:hover .sk-estimator-doc-link.fitted:hover,\n",
              ".sk-estimator-doc-link.fitted:hover {\n",
              "  /* fitted */\n",
              "  background-color: var(--sklearn-color-fitted-level-3);\n",
              "  color: var(--sklearn-color-background);\n",
              "  text-decoration: none;\n",
              "}\n",
              "\n",
              "/* Span, style for the box shown on hovering the info icon */\n",
              ".sk-estimator-doc-link span {\n",
              "  display: none;\n",
              "  z-index: 9999;\n",
              "  position: relative;\n",
              "  font-weight: normal;\n",
              "  right: .2ex;\n",
              "  padding: .5ex;\n",
              "  margin: .5ex;\n",
              "  width: min-content;\n",
              "  min-width: 20ex;\n",
              "  max-width: 50ex;\n",
              "  color: var(--sklearn-color-text);\n",
              "  box-shadow: 2pt 2pt 4pt #999;\n",
              "  /* unfitted */\n",
              "  background: var(--sklearn-color-unfitted-level-0);\n",
              "  border: .5pt solid var(--sklearn-color-unfitted-level-3);\n",
              "}\n",
              "\n",
              ".sk-estimator-doc-link.fitted span {\n",
              "  /* fitted */\n",
              "  background: var(--sklearn-color-fitted-level-0);\n",
              "  border: var(--sklearn-color-fitted-level-3);\n",
              "}\n",
              "\n",
              ".sk-estimator-doc-link:hover span {\n",
              "  display: block;\n",
              "}\n",
              "\n",
              "/* \"?\"-specific style due to the `<a>` HTML tag */\n",
              "\n",
              "#sk-container-id-1 a.estimator_doc_link {\n",
              "  float: right;\n",
              "  font-size: 1rem;\n",
              "  line-height: 1em;\n",
              "  font-family: monospace;\n",
              "  background-color: var(--sklearn-color-background);\n",
              "  border-radius: 1rem;\n",
              "  height: 1rem;\n",
              "  width: 1rem;\n",
              "  text-decoration: none;\n",
              "  /* unfitted */\n",
              "  color: var(--sklearn-color-unfitted-level-1);\n",
              "  border: var(--sklearn-color-unfitted-level-1) 1pt solid;\n",
              "}\n",
              "\n",
              "#sk-container-id-1 a.estimator_doc_link.fitted {\n",
              "  /* fitted */\n",
              "  border: var(--sklearn-color-fitted-level-1) 1pt solid;\n",
              "  color: var(--sklearn-color-fitted-level-1);\n",
              "}\n",
              "\n",
              "/* On hover */\n",
              "#sk-container-id-1 a.estimator_doc_link:hover {\n",
              "  /* unfitted */\n",
              "  background-color: var(--sklearn-color-unfitted-level-3);\n",
              "  color: var(--sklearn-color-background);\n",
              "  text-decoration: none;\n",
              "}\n",
              "\n",
              "#sk-container-id-1 a.estimator_doc_link.fitted:hover {\n",
              "  /* fitted */\n",
              "  background-color: var(--sklearn-color-fitted-level-3);\n",
              "}\n",
              "</style><div id=\"sk-container-id-1\" class=\"sk-top-container\"><div class=\"sk-text-repr-fallback\"><pre>LinearRegression()</pre><b>In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook. <br />On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.</b></div><div class=\"sk-container\" hidden><div class=\"sk-item\"><div class=\"sk-estimator fitted sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-1\" type=\"checkbox\" checked><label for=\"sk-estimator-id-1\" class=\"sk-toggleable__label fitted sk-toggleable__label-arrow fitted\">&nbsp;&nbsp;LinearRegression<a class=\"sk-estimator-doc-link fitted\" rel=\"noreferrer\" target=\"_blank\" href=\"https://scikit-learn.org/1.5/modules/generated/sklearn.linear_model.LinearRegression.html\">?<span>Documentation for LinearRegression</span></a><span class=\"sk-estimator-doc-link fitted\">i<span>Fitted</span></span></label><div class=\"sk-toggleable__content fitted\"><pre>LinearRegression()</pre></div> </div></div></div></div>"
            ]
          },
          "metadata": {},
          "execution_count": 11
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Puis on peut extraire l'intercept"
      ],
      "metadata": {
        "id": "cVTKdbtrqUGo"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "linear_reg.intercept_"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "kIEYYikPqC9m",
        "outputId": "5ca093a6-14ef-40ed-9804-0916e021ec02"
      },
      "execution_count": 12,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "219.7186906539548"
            ]
          },
          "metadata": {},
          "execution_count": 12
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "ou les coefficients"
      ],
      "metadata": {
        "id": "Tpu2T_hdqgfn"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "linear_reg.coef_"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "ibEzSJkaqdDo",
        "outputId": "dc32233e-f249-49db-c898-bd70b2e7dbf4"
      },
      "execution_count": 13,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([ 2.19788004e-04,  2.77273746e-01,  9.31363532e-04,  1.85557211e-03,\n",
              "       -4.98272280e-01, -3.99391598e-01, -5.67544728e-01,  1.47435223e+00,\n",
              "       -2.00329540e-01,  2.92050344e-01,  5.19175769e-02, -8.22649608e-02,\n",
              "        5.30738029e-01, -1.39614877e+00, -5.63257056e-01,  5.43905976e-01,\n",
              "       -1.31379589e-01,  1.08845666e-01,  4.91756992e-01, -1.20887731e-01,\n",
              "        8.85889619e-01, -7.62392584e-02,  3.44733561e-02, -2.14858389e-01,\n",
              "       -1.29052962e+00, -1.75472216e+00, -1.32999581e+00])"
            ]
          },
          "metadata": {},
          "execution_count": 13
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Comparons avec le résultat obtenu avec `numpy`"
      ],
      "metadata": {
        "id": "6ual12zGqrG8"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "coef - np.append(linear_reg.intercept_, linear_reg.coef_)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "o2VHD9BsqqMn",
        "outputId": "bab2a328-d15f-48eb-e371-29e783646af0"
      },
      "execution_count": 14,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([-1.20110144e-10, -4.58861464e-16, -5.91637850e-13, -1.03660570e-15,\n",
              "       -6.45620710e-15,  2.78665979e-14,  8.05966405e-13,  1.53578261e-11,\n",
              "       -2.82662782e-13,  1.45855550e-13, -2.22044605e-16, -5.07920095e-13,\n",
              "       -2.77347589e-13, -2.24598118e-13, -9.39248679e-14,  2.27706742e-13,\n",
              "        7.13540338e-13,  1.66316960e-12, -6.94194702e-13, -3.11695114e-13,\n",
              "       -1.48336898e-12,  1.74227299e-12,  1.64521174e-13,  4.49085213e-14,\n",
              "        1.20570220e-13,  4.27213820e-13, -1.65423231e-13,  2.52908805e-13])"
            ]
          },
          "metadata": {},
          "execution_count": 14
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "on voit que les résultats sont similaires. Qu'en est-il des prédictions et de la $MSE$ ?"
      ],
      "metadata": {
        "id": "WEa1T8-1rOuc"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "sk_outputs_pred = linear_reg.predict(inputs)\n",
        "sk_mse = np.mean((sk_outputs_pred - outputs)**2)\n",
        "print(f\"MSE numpy = {mse}, MSE sklearn = {sk_mse}\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "3B2GQbiLqk9Q",
        "outputId": "9d377cd0-3064-42a2-fd78-2b03d7c2d7be"
      },
      "execution_count": 15,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "MSE numpy = 458.43606876316204, MSE sklearn = 458.43606876316204\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "L'erreur est quasiment identique et on peut être rassuré sur les capacités de `sklearn` ! Pour plus d'information sur `LinearRegression`, voir https://scikit-learn.org/stable/modules/generated/sklearn.linear_model.LinearRegression.html.\n",
        "\n",
        "---"
      ],
      "metadata": {
        "id": "xHNf1RmSsuFW"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## La sélection des hyperparamètres pour une regression *Lasso* par cross-validation\n",
        "\n",
        "Dans les parties précédentes, nous avons utilisé toutes les variables du jeux de données. Ici, grâce à une régression régularisée de type *Lasso* (L1), nous allons voir si certaines variables peuvent être omises. Pour cela, nous allons définir un paramètre optimal $\\lambda$ par cross-validation, et évaluer le modèle retenu."
      ],
      "metadata": {
        "id": "lyJ7-F2uuUFP"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "On commence par scinder aléatoirement le jeu de données en deux, avec d'un côte le jeu de données entrainement/validation (servant à la cross-validation), et de l'autre le jeu de test. La taille du jeu de test est posée à 20%. Nous pouvons utiliser pour cela la fonction `train_test_split` de `sklearn.model_selection`"
      ],
      "metadata": {
        "id": "kEEImyrSv9zZ"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "inputs_train_val, inputs_test, outputs_train_val, outputs_test = \\\n",
        "    train_test_split(inputs, outputs, test_size=0.2)\n",
        "# On sauvegarde les tailles\n",
        "n_row_train_val = inputs_train_val.shape[0]\n",
        "n_row_test = inputs_test.shape[0]\n",
        "n_row_test"
      ],
      "metadata": {
        "id": "mXcPrrK1sIhV",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "2f422e03-6361-46d5-b938-3eb6a5a6ca2a"
      },
      "execution_count": 16,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "610"
            ]
          },
          "metadata": {},
          "execution_count": 16
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Posons maintenant les valeurs de $\\lambda$ qui vont être testées (50 valeurs entre 0.001 et 1, la valeur 0 ne fonctionne pas bien avec Lasso de `sklearn`), ainsi que le nombre de folds $k$"
      ],
      "metadata": {
        "id": "RHKcJCNv0caB"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "hyp_lambdas = np.linspace(0.001, 1, 50)\n",
        "k = 5\n",
        "hyp_lambdas"
      ],
      "metadata": {
        "id": "l6GBP61Rw1Vl",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "190eec34-06ad-4c67-b0ee-df7c409eb8e3"
      },
      "execution_count": 17,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([0.001     , 0.02138776, 0.04177551, 0.06216327, 0.08255102,\n",
              "       0.10293878, 0.12332653, 0.14371429, 0.16410204, 0.1844898 ,\n",
              "       0.20487755, 0.22526531, 0.24565306, 0.26604082, 0.28642857,\n",
              "       0.30681633, 0.32720408, 0.34759184, 0.36797959, 0.38836735,\n",
              "       0.4087551 , 0.42914286, 0.44953061, 0.46991837, 0.49030612,\n",
              "       0.51069388, 0.53108163, 0.55146939, 0.57185714, 0.5922449 ,\n",
              "       0.61263265, 0.63302041, 0.65340816, 0.67379592, 0.69418367,\n",
              "       0.71457143, 0.73495918, 0.75534694, 0.77573469, 0.79612245,\n",
              "       0.8165102 , 0.83689796, 0.85728571, 0.87767347, 0.89806122,\n",
              "       0.91844898, 0.93883673, 0.95922449, 0.97961224, 1.        ])"
            ]
          },
          "metadata": {},
          "execution_count": 17
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Nous tirons maintenant aléatoirement les attributions des individus dans les folds (sur le jeu d'entrainement/validation)"
      ],
      "metadata": {
        "id": "PhjvZ71lH_Lf"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Un vecteur contenant 0, 1, 2, ..., k répèté assez de fois pour\n",
        "# dépasser n_row_train_val\n",
        "fold_membs = np.tile(np.arange(k), int(np.ceil(n_row_train_val / k)))\n",
        "# On ne garde que les n_row_train_val premiers éléments\n",
        "fold_membs = fold_membs[:n_row_train_val]\n",
        "# On mélange le vecteur\n",
        "np.random.shuffle(fold_membs)"
      ],
      "metadata": {
        "id": "kG7oBgYuxi20"
      },
      "execution_count": 18,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "Passons maintenant aux boucles formant le coeur de la cross-validation. La boucle extérieure va tester toutes les valeurs de $\\lambda$, et pour chaque valeur, la boucle intérieure va entrainer et valider un modèle selon les folds.\n",
        "Les résultats finaux de cette double boucle sont deux listes contenant les valeurs moyennes de $MSE_\\text{train}$ et $MSE_\\text{valid}$ pour chaque $\\lambda$."
      ],
      "metadata": {
        "id": "5faMRdRicG9p"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Pour stocker la moyenne du mse pour chaque paramètre\n",
        "train_mse_means, val_mse_means = [], []\n",
        "\n",
        "# Boucle sur les lambdas\n",
        "for hyp_lambda in hyp_lambdas:\n",
        "\n",
        "  # Pour stocker la valeur du mse sur chaque fold\n",
        "  train_mses, val_mses = [], []\n",
        "\n",
        "  # Boucle sur les folds\n",
        "  for fold in range(k):\n",
        "\n",
        "    # On trouve les indices des folds\n",
        "    indices_train = np.where(fold_membs != fold)[0]\n",
        "    indices_val = np.where(fold_membs == fold)[0]\n",
        "\n",
        "    # On sépare le jeu en 2 groupes : entrainement - validation\n",
        "    inputs_train = inputs_train_val.iloc[indices_train, ]\n",
        "    inputs_val = inputs_train_val.iloc[indices_val, ]\n",
        "    outputs_train = outputs_train_val.iloc[indices_train]\n",
        "    outputs_val = outputs_train_val.iloc[indices_val]\n",
        "\n",
        "    # On entraine le modèle (\"alpha\" est le paramètre de régularisation)\n",
        "    lasso_reg = Lasso(alpha=hyp_lambda)\n",
        "    lasso_reg.fit(inputs_train, outputs_train)\n",
        "\n",
        "    # On calcule la train_mse et val_mse\n",
        "    train_mse = np.mean((lasso_reg.predict(inputs_train) - outputs_train)**2)\n",
        "    val_mse = np.mean((lasso_reg.predict(inputs_val) - outputs_val)**2)\n",
        "\n",
        "    # On sauve les valeurs\n",
        "    train_mses.append(train_mse)\n",
        "    val_mses.append(val_mse)\n",
        "\n",
        "  # On sauve les moyennes sur les folds\n",
        "  train_mse_means.append(np.mean(train_mses))\n",
        "  val_mse_means.append(np.mean(val_mses))"
      ],
      "metadata": {
        "id": "u5Dz5ElFIK-X"
      },
      "execution_count": 19,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "Observons comment varient $MSE_\\text{train}$ et $MSE_\\text{valid}$ en fonction de $\\lambda$"
      ],
      "metadata": {
        "id": "SkZQNvTqTd6V"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "fig, ax = plt.subplots()\n",
        "ax.plot(hyp_lambdas, train_mse_means, c=\"blue\", label=\"MSE train\")\n",
        "ax.plot(hyp_lambdas, val_mse_means, c=\"red\", label=\"MSE valid\")\n",
        "ax.set_xlabel(\"$\\lambda$\")\n",
        "ax.set_ylabel(\"$MSE$\")\n",
        "ax.legend()\n",
        "plt.plot()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 467
        },
        "id": "AgrbizyuM4Pd",
        "outputId": "56df4108-994b-4613-bbf7-537da4e98091"
      },
      "execution_count": 20,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[]"
            ]
          },
          "metadata": {},
          "execution_count": 20
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "On peut trouver la valeur optimale l'hyperparmètre $\\lambda$ avec"
      ],
      "metadata": {
        "id": "N0Y3n6i3Ujwe"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "index_opt_hyp_lambda = np.where(val_mse_means == min(val_mse_means))[0][0]\n",
        "opt_hyp_lambda = float(hyp_lambdas[index_opt_hyp_lambda])\n",
        "print(f\"La valeur optimale de lambda est : {opt_hyp_lambda}\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "B0xWVEnHNHpY",
        "outputId": "4f6fff89-75de-4ae9-b0cd-641010b48f93"
      },
      "execution_count": 37,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "La valeur optimale de lambda est : 0.3475918367346939\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "On peut donc maintenant calculer l'erreur de généralisation sur le jeu de test"
      ],
      "metadata": {
        "id": "-VL37ChqX6bl"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# On entraine le modèle sur toutes les données d'entrainement - validation\n",
        "opt_lasso_reg = Lasso(alpha=opt_hyp_lambda)\n",
        "opt_lasso_reg.fit(inputs_train_val, outputs_train_val)\n",
        "# On calcul l'erreur\n",
        "test_mse_lasso = np.mean((opt_lasso_reg.predict(inputs_test) - outputs_test)**2)\n",
        "test_mse_lasso"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "bvr6mcm0UzyJ",
        "outputId": "74402d7d-55af-4ad8-d4fb-9fad7dd16e9a"
      },
      "execution_count": 22,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "520.1706191993661"
            ]
          },
          "metadata": {},
          "execution_count": 22
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Si l'on la compare à la régression linéaire \"classique\""
      ],
      "metadata": {
        "id": "n2LS3jhsZE5g"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# On entraine le modèle sur toutes les données d'entrainement - validation\n",
        "lin_reg = LinearRegression()\n",
        "lin_reg.fit(inputs_train_val, outputs_train_val)\n",
        "# On calcul l'erreur\n",
        "test_mse_lin = np.mean((lin_reg.predict(inputs_test) - outputs_test)**2)\n",
        "test_mse_lin"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "P0CeIlPjU1Al",
        "outputId": "dee62066-f40b-4efb-fcc5-8170c50828c9"
      },
      "execution_count": 38,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "524.3465800240581"
            ]
          },
          "metadata": {},
          "execution_count": 38
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "On voit que les prédictions sont (normalement et légèrement) meilleures. Que valent nos coefficients ?"
      ],
      "metadata": {
        "id": "it9CE_gqZda2"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "reg_coef = np.append(lin_reg.intercept_, lin_reg.coef_)\n",
        "lasso_coef = np.append(opt_lasso_reg.intercept_, opt_lasso_reg.coef_)\n",
        "pd.DataFrame({\"Variables\" : [\"intercept\"] + list(inputs.columns),\n",
        "              \"Coefficient Reg\": reg_coef,\n",
        "             \"Coefficient Lasso\": lasso_coef})"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 928
        },
        "id": "SBGXHimIZU38",
        "outputId": "e3478b24-72e9-4bbc-94a3-d2997c754905"
      },
      "execution_count": 39,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "                  Variables  Coefficient Reg  Coefficient Lasso\n",
              "0                 intercept       229.265467         222.614715\n",
              "1                 medIncome         0.000230           0.000178\n",
              "2            povertyPercent         0.346368           0.310546\n",
              "3               studyPerCap         0.000276           0.000242\n",
              "4                 MedianAge         0.010991           0.010497\n",
              "5             MedianAgeMale        -0.970279          -0.889918\n",
              "6           MedianAgeFemale        -0.103150          -0.087550\n",
              "7          AvgHouseholdSize        -1.298090          -0.000000\n",
              "8            PercentMarried         1.840391           1.647363\n",
              "9              PctNoHS18_24        -0.223353          -0.216874\n",
              "10               PctHS18_24         0.223401           0.220806\n",
              "11          PctSomeCol18_24         0.045434           0.026080\n",
              "12          PctBachDeg18_24        -0.166398          -0.142517\n",
              "13             PctHS25_Over         0.566228           0.564436\n",
              "14        PctBachDeg25_Over        -1.311923          -1.285766\n",
              "15       PctEmployed16_Over        -0.577414          -0.526584\n",
              "16     PctUnemployed16_Over         0.437417           0.400168\n",
              "17       PctPrivateCoverage        -0.268758          -0.241020\n",
              "18  PctPrivateCoverageAlone         0.076874           0.052775\n",
              "19       PctEmpPrivCoverage         0.585739           0.569160\n",
              "20        PctPublicCoverage        -0.020185           0.000000\n",
              "21   PctPublicCoverageAlone         0.653907           0.630760\n",
              "22                 PctWhite        -0.057289          -0.032277\n",
              "23                 PctBlack         0.069242           0.090446\n",
              "24                 PctAsian        -0.116764          -0.018980\n",
              "25             PctOtherRace        -1.286000          -1.250280\n",
              "26     PctMarriedHouseholds        -2.022609          -1.883495\n",
              "27                BirthRate        -1.465250          -1.335273"
            ],
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              "\n",
              "  <div id=\"df-e45604cc-e6ba-4109-9071-b5a7717a2f8b\" class=\"colab-df-container\">\n",
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              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>Variables</th>\n",
              "      <th>Coefficient Reg</th>\n",
              "      <th>Coefficient Lasso</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>intercept</td>\n",
              "      <td>229.265467</td>\n",
              "      <td>222.614715</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>medIncome</td>\n",
              "      <td>0.000230</td>\n",
              "      <td>0.000178</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>povertyPercent</td>\n",
              "      <td>0.346368</td>\n",
              "      <td>0.310546</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>studyPerCap</td>\n",
              "      <td>0.000276</td>\n",
              "      <td>0.000242</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>MedianAge</td>\n",
              "      <td>0.010991</td>\n",
              "      <td>0.010497</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>5</th>\n",
              "      <td>MedianAgeMale</td>\n",
              "      <td>-0.970279</td>\n",
              "      <td>-0.889918</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>6</th>\n",
              "      <td>MedianAgeFemale</td>\n",
              "      <td>-0.103150</td>\n",
              "      <td>-0.087550</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>7</th>\n",
              "      <td>AvgHouseholdSize</td>\n",
              "      <td>-1.298090</td>\n",
              "      <td>-0.000000</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>8</th>\n",
              "      <td>PercentMarried</td>\n",
              "      <td>1.840391</td>\n",
              "      <td>1.647363</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>9</th>\n",
              "      <td>PctNoHS18_24</td>\n",
              "      <td>-0.223353</td>\n",
              "      <td>-0.216874</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>10</th>\n",
              "      <td>PctHS18_24</td>\n",
              "      <td>0.223401</td>\n",
              "      <td>0.220806</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>11</th>\n",
              "      <td>PctSomeCol18_24</td>\n",
              "      <td>0.045434</td>\n",
              "      <td>0.026080</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>12</th>\n",
              "      <td>PctBachDeg18_24</td>\n",
              "      <td>-0.166398</td>\n",
              "      <td>-0.142517</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>13</th>\n",
              "      <td>PctHS25_Over</td>\n",
              "      <td>0.566228</td>\n",
              "      <td>0.564436</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>14</th>\n",
              "      <td>PctBachDeg25_Over</td>\n",
              "      <td>-1.311923</td>\n",
              "      <td>-1.285766</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>15</th>\n",
              "      <td>PctEmployed16_Over</td>\n",
              "      <td>-0.577414</td>\n",
              "      <td>-0.526584</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>16</th>\n",
              "      <td>PctUnemployed16_Over</td>\n",
              "      <td>0.437417</td>\n",
              "      <td>0.400168</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>17</th>\n",
              "      <td>PctPrivateCoverage</td>\n",
              "      <td>-0.268758</td>\n",
              "      <td>-0.241020</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>18</th>\n",
              "      <td>PctPrivateCoverageAlone</td>\n",
              "      <td>0.076874</td>\n",
              "      <td>0.052775</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>19</th>\n",
              "      <td>PctEmpPrivCoverage</td>\n",
              "      <td>0.585739</td>\n",
              "      <td>0.569160</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>20</th>\n",
              "      <td>PctPublicCoverage</td>\n",
              "      <td>-0.020185</td>\n",
              "      <td>0.000000</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>21</th>\n",
              "      <td>PctPublicCoverageAlone</td>\n",
              "      <td>0.653907</td>\n",
              "      <td>0.630760</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>22</th>\n",
              "      <td>PctWhite</td>\n",
              "      <td>-0.057289</td>\n",
              "      <td>-0.032277</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>23</th>\n",
              "      <td>PctBlack</td>\n",
              "      <td>0.069242</td>\n",
              "      <td>0.090446</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>24</th>\n",
              "      <td>PctAsian</td>\n",
              "      <td>-0.116764</td>\n",
              "      <td>-0.018980</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>25</th>\n",
              "      <td>PctOtherRace</td>\n",
              "      <td>-1.286000</td>\n",
              "      <td>-1.250280</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>26</th>\n",
              "      <td>PctMarriedHouseholds</td>\n",
              "      <td>-2.022609</td>\n",
              "      <td>-1.883495</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>27</th>\n",
              "      <td>BirthRate</td>\n",
              "      <td>-1.465250</td>\n",
              "      <td>-1.335273</td>\n",
              "    </tr>\n",
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            "application/vnd.google.colaboratory.intrinsic+json": {
              "type": "dataframe",
              "summary": "{\n  \"name\": \"             \\\"Coefficient Lasso\\\": lasso_coef})\",\n  \"rows\": 28,\n  \"fields\": [\n    {\n      \"column\": \"Variables\",\n      \"properties\": {\n        \"dtype\": \"string\",\n        \"num_unique_values\": 28,\n        \"samples\": [\n          \"PctNoHS18_24\",\n          \"PctOtherRace\",\n          \"PercentMarried\"\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"Coefficient Reg\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 43.36943087344182,\n        \"min\": -2.0226089717333924,\n        \"max\": 229.2654673020072,\n        \"num_unique_values\": 28,\n        \"samples\": [\n          -0.22335258434732244,\n          -1.2860003218418428,\n          1.8403912807180658\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"Coefficient Lasso\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 42.09982743864593,\n        \"min\": -1.8834950446100782,\n        \"max\": 222.61471515091193,\n        \"num_unique_values\": 27,\n        \"samples\": [\n          1.6473627801399493,\n          0.5644357913572513,\n          -0.21687388852596529\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    }\n  ]\n}"
            }
          },
          "metadata": {},
          "execution_count": 39
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "On voit que certains ont été annulés, d'autres sont très faibles et la pluparts (mais pas forcement tous) ont été réduits. L'annulation de certains coefficients est typique de la régression Lasso.\n",
        "\n",
        "---"
      ],
      "metadata": {
        "id": "puVAqF42dUI5"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## La sélection des hyperparamètres avec `sklearn`\n",
        "\n",
        "La libraire `sklearn` offre une interface qui permet d'effectuer la recherche de paramètre optimaux via une cross-validation. Le code est beaucoup plus compact ainsi (pour plus de détails, voir https://scikit-learn.org/stable/modules/grid_search.html#grid-search)"
      ],
      "metadata": {
        "id": "rE-BQz8ipoDF"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# On doit entrer les différents hyperparamètres à tester dans un dictionnaire\n",
        "# Ici, il n'y a que \"alpha\"\n",
        "param_dict = {\"alpha\": hyp_lambdas}\n",
        "\n",
        "# On construit une fonction pour notre perte. Sinon, sklearn utilise la fonction\n",
        "# de \"score\" par défaut contenu dans la méthode utilisée\n",
        "def mse_loss(y_true, y_pred):\n",
        "  return np.mean((y_true - y_pred)**2)\n",
        "\n",
        "# On transforme cette fonction de perte (petit est meilleur) fonction de score\n",
        "# (grand est meilleur), ainsi que dans une fonction lisible par sklearn\n",
        "mse_score = make_scorer(mse_loss, greater_is_better=False)\n",
        "\n",
        "# La recherche des paramètres s'effectue ainsi\n",
        "lasso = Lasso()\n",
        "gride_search = GridSearchCV(lasso,\n",
        "                            param_dict,\n",
        "                            scoring=mse_score,\n",
        "                            cv=k,\n",
        "                            return_train_score=True)\n",
        "gride_search.fit(inputs_train_val, outputs_train_val)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 136
        },
        "id": "Z0obIW2ide-M",
        "outputId": "e8e5ceb3-6673-4df8-d70d-f6d1789caef1"
      },
      "execution_count": 40,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "GridSearchCV(cv=5, estimator=Lasso(),\n",
              "             param_grid={'alpha': array([0.001     , 0.02138776, 0.04177551, 0.06216327, 0.08255102,\n",
              "       0.10293878, 0.12332653, 0.14371429, 0.16410204, 0.1844898 ,\n",
              "       0.20487755, 0.22526531, 0.24565306, 0.26604082, 0.28642857,\n",
              "       0.30681633, 0.32720408, 0.34759184, 0.36797959, 0.38836735,\n",
              "       0.4087551 , 0.42914286, 0.44953061, 0.46991837, 0.49030612,\n",
              "       0.51069388, 0.531081...0.55146939, 0.57185714, 0.5922449 ,\n",
              "       0.61263265, 0.63302041, 0.65340816, 0.67379592, 0.69418367,\n",
              "       0.71457143, 0.73495918, 0.75534694, 0.77573469, 0.79612245,\n",
              "       0.8165102 , 0.83689796, 0.85728571, 0.87767347, 0.89806122,\n",
              "       0.91844898, 0.93883673, 0.95922449, 0.97961224, 1.        ])},\n",
              "             return_train_score=True,\n",
              "             scoring=make_scorer(mse_loss, greater_is_better=False, response_method='predict'))"
            ],
            "text/html": [
              "<style>#sk-container-id-3 {\n",
              "  /* Definition of color scheme common for light and dark mode */\n",
              "  --sklearn-color-text: black;\n",
              "  --sklearn-color-line: gray;\n",
              "  /* Definition of color scheme for unfitted estimators */\n",
              "  --sklearn-color-unfitted-level-0: #fff5e6;\n",
              "  --sklearn-color-unfitted-level-1: #f6e4d2;\n",
              "  --sklearn-color-unfitted-level-2: #ffe0b3;\n",
              "  --sklearn-color-unfitted-level-3: chocolate;\n",
              "  /* Definition of color scheme for fitted estimators */\n",
              "  --sklearn-color-fitted-level-0: #f0f8ff;\n",
              "  --sklearn-color-fitted-level-1: #d4ebff;\n",
              "  --sklearn-color-fitted-level-2: #b3dbfd;\n",
              "  --sklearn-color-fitted-level-3: cornflowerblue;\n",
              "\n",
              "  /* Specific color for light theme */\n",
              "  --sklearn-color-text-on-default-background: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, black)));\n",
              "  --sklearn-color-background: var(--sg-background-color, var(--theme-background, var(--jp-layout-color0, white)));\n",
              "  --sklearn-color-border-box: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, black)));\n",
              "  --sklearn-color-icon: #696969;\n",
              "\n",
              "  @media (prefers-color-scheme: dark) {\n",
              "    /* Redefinition of color scheme for dark theme */\n",
              "    --sklearn-color-text-on-default-background: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, white)));\n",
              "    --sklearn-color-background: var(--sg-background-color, var(--theme-background, var(--jp-layout-color0, #111)));\n",
              "    --sklearn-color-border-box: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, white)));\n",
              "    --sklearn-color-icon: #878787;\n",
              "  }\n",
              "}\n",
              "\n",
              "#sk-container-id-3 {\n",
              "  color: var(--sklearn-color-text);\n",
              "}\n",
              "\n",
              "#sk-container-id-3 pre {\n",
              "  padding: 0;\n",
              "}\n",
              "\n",
              "#sk-container-id-3 input.sk-hidden--visually {\n",
              "  border: 0;\n",
              "  clip: rect(1px 1px 1px 1px);\n",
              "  clip: rect(1px, 1px, 1px, 1px);\n",
              "  height: 1px;\n",
              "  margin: -1px;\n",
              "  overflow: hidden;\n",
              "  padding: 0;\n",
              "  position: absolute;\n",
              "  width: 1px;\n",
              "}\n",
              "\n",
              "#sk-container-id-3 div.sk-dashed-wrapped {\n",
              "  border: 1px dashed var(--sklearn-color-line);\n",
              "  margin: 0 0.4em 0.5em 0.4em;\n",
              "  box-sizing: border-box;\n",
              "  padding-bottom: 0.4em;\n",
              "  background-color: var(--sklearn-color-background);\n",
              "}\n",
              "\n",
              "#sk-container-id-3 div.sk-container {\n",
              "  /* jupyter's `normalize.less` sets `[hidden] { display: none; }`\n",
              "     but bootstrap.min.css set `[hidden] { display: none !important; }`\n",
              "     so we also need the `!important` here to be able to override the\n",
              "     default hidden behavior on the sphinx rendered scikit-learn.org.\n",
              "     See: https://github.com/scikit-learn/scikit-learn/issues/21755 */\n",
              "  display: inline-block !important;\n",
              "  position: relative;\n",
              "}\n",
              "\n",
              "#sk-container-id-3 div.sk-text-repr-fallback {\n",
              "  display: none;\n",
              "}\n",
              "\n",
              "div.sk-parallel-item,\n",
              "div.sk-serial,\n",
              "div.sk-item {\n",
              "  /* draw centered vertical line to link estimators */\n",
              "  background-image: linear-gradient(var(--sklearn-color-text-on-default-background), var(--sklearn-color-text-on-default-background));\n",
              "  background-size: 2px 100%;\n",
              "  background-repeat: no-repeat;\n",
              "  background-position: center center;\n",
              "}\n",
              "\n",
              "/* Parallel-specific style estimator block */\n",
              "\n",
              "#sk-container-id-3 div.sk-parallel-item::after {\n",
              "  content: \"\";\n",
              "  width: 100%;\n",
              "  border-bottom: 2px solid var(--sklearn-color-text-on-default-background);\n",
              "  flex-grow: 1;\n",
              "}\n",
              "\n",
              "#sk-container-id-3 div.sk-parallel {\n",
              "  display: flex;\n",
              "  align-items: stretch;\n",
              "  justify-content: center;\n",
              "  background-color: var(--sklearn-color-background);\n",
              "  position: relative;\n",
              "}\n",
              "\n",
              "#sk-container-id-3 div.sk-parallel-item {\n",
              "  display: flex;\n",
              "  flex-direction: column;\n",
              "}\n",
              "\n",
              "#sk-container-id-3 div.sk-parallel-item:first-child::after {\n",
              "  align-self: flex-end;\n",
              "  width: 50%;\n",
              "}\n",
              "\n",
              "#sk-container-id-3 div.sk-parallel-item:last-child::after {\n",
              "  align-self: flex-start;\n",
              "  width: 50%;\n",
              "}\n",
              "\n",
              "#sk-container-id-3 div.sk-parallel-item:only-child::after {\n",
              "  width: 0;\n",
              "}\n",
              "\n",
              "/* Serial-specific style estimator block */\n",
              "\n",
              "#sk-container-id-3 div.sk-serial {\n",
              "  display: flex;\n",
              "  flex-direction: column;\n",
              "  align-items: center;\n",
              "  background-color: var(--sklearn-color-background);\n",
              "  padding-right: 1em;\n",
              "  padding-left: 1em;\n",
              "}\n",
              "\n",
              "\n",
              "/* Toggleable style: style used for estimator/Pipeline/ColumnTransformer box that is\n",
              "clickable and can be expanded/collapsed.\n",
              "- Pipeline and ColumnTransformer use this feature and define the default style\n",
              "- Estimators will overwrite some part of the style using the `sk-estimator` class\n",
              "*/\n",
              "\n",
              "/* Pipeline and ColumnTransformer style (default) */\n",
              "\n",
              "#sk-container-id-3 div.sk-toggleable {\n",
              "  /* Default theme specific background. It is overwritten whether we have a\n",
              "  specific estimator or a Pipeline/ColumnTransformer */\n",
              "  background-color: var(--sklearn-color-background);\n",
              "}\n",
              "\n",
              "/* Toggleable label */\n",
              "#sk-container-id-3 label.sk-toggleable__label {\n",
              "  cursor: pointer;\n",
              "  display: block;\n",
              "  width: 100%;\n",
              "  margin-bottom: 0;\n",
              "  padding: 0.5em;\n",
              "  box-sizing: border-box;\n",
              "  text-align: center;\n",
              "}\n",
              "\n",
              "#sk-container-id-3 label.sk-toggleable__label-arrow:before {\n",
              "  /* Arrow on the left of the label */\n",
              "  content: \"▸\";\n",
              "  float: left;\n",
              "  margin-right: 0.25em;\n",
              "  color: var(--sklearn-color-icon);\n",
              "}\n",
              "\n",
              "#sk-container-id-3 label.sk-toggleable__label-arrow:hover:before {\n",
              "  color: var(--sklearn-color-text);\n",
              "}\n",
              "\n",
              "/* Toggleable content - dropdown */\n",
              "\n",
              "#sk-container-id-3 div.sk-toggleable__content {\n",
              "  max-height: 0;\n",
              "  max-width: 0;\n",
              "  overflow: hidden;\n",
              "  text-align: left;\n",
              "  /* unfitted */\n",
              "  background-color: var(--sklearn-color-unfitted-level-0);\n",
              "}\n",
              "\n",
              "#sk-container-id-3 div.sk-toggleable__content.fitted {\n",
              "  /* fitted */\n",
              "  background-color: var(--sklearn-color-fitted-level-0);\n",
              "}\n",
              "\n",
              "#sk-container-id-3 div.sk-toggleable__content pre {\n",
              "  margin: 0.2em;\n",
              "  border-radius: 0.25em;\n",
              "  color: var(--sklearn-color-text);\n",
              "  /* unfitted */\n",
              "  background-color: var(--sklearn-color-unfitted-level-0);\n",
              "}\n",
              "\n",
              "#sk-container-id-3 div.sk-toggleable__content.fitted pre {\n",
              "  /* unfitted */\n",
              "  background-color: var(--sklearn-color-fitted-level-0);\n",
              "}\n",
              "\n",
              "#sk-container-id-3 input.sk-toggleable__control:checked~div.sk-toggleable__content {\n",
              "  /* Expand drop-down */\n",
              "  max-height: 200px;\n",
              "  max-width: 100%;\n",
              "  overflow: auto;\n",
              "}\n",
              "\n",
              "#sk-container-id-3 input.sk-toggleable__control:checked~label.sk-toggleable__label-arrow:before {\n",
              "  content: \"▾\";\n",
              "}\n",
              "\n",
              "/* Pipeline/ColumnTransformer-specific style */\n",
              "\n",
              "#sk-container-id-3 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
              "  color: var(--sklearn-color-text);\n",
              "  background-color: var(--sklearn-color-unfitted-level-2);\n",
              "}\n",
              "\n",
              "#sk-container-id-3 div.sk-label.fitted input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
              "  background-color: var(--sklearn-color-fitted-level-2);\n",
              "}\n",
              "\n",
              "/* Estimator-specific style */\n",
              "\n",
              "/* Colorize estimator box */\n",
              "#sk-container-id-3 div.sk-estimator input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
              "  /* unfitted */\n",
              "  background-color: var(--sklearn-color-unfitted-level-2);\n",
              "}\n",
              "\n",
              "#sk-container-id-3 div.sk-estimator.fitted input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
              "  /* fitted */\n",
              "  background-color: var(--sklearn-color-fitted-level-2);\n",
              "}\n",
              "\n",
              "#sk-container-id-3 div.sk-label label.sk-toggleable__label,\n",
              "#sk-container-id-3 div.sk-label label {\n",
              "  /* The background is the default theme color */\n",
              "  color: var(--sklearn-color-text-on-default-background);\n",
              "}\n",
              "\n",
              "/* On hover, darken the color of the background */\n",
              "#sk-container-id-3 div.sk-label:hover label.sk-toggleable__label {\n",
              "  color: var(--sklearn-color-text);\n",
              "  background-color: var(--sklearn-color-unfitted-level-2);\n",
              "}\n",
              "\n",
              "/* Label box, darken color on hover, fitted */\n",
              "#sk-container-id-3 div.sk-label.fitted:hover label.sk-toggleable__label.fitted {\n",
              "  color: var(--sklearn-color-text);\n",
              "  background-color: var(--sklearn-color-fitted-level-2);\n",
              "}\n",
              "\n",
              "/* Estimator label */\n",
              "\n",
              "#sk-container-id-3 div.sk-label label {\n",
              "  font-family: monospace;\n",
              "  font-weight: bold;\n",
              "  display: inline-block;\n",
              "  line-height: 1.2em;\n",
              "}\n",
              "\n",
              "#sk-container-id-3 div.sk-label-container {\n",
              "  text-align: center;\n",
              "}\n",
              "\n",
              "/* Estimator-specific */\n",
              "#sk-container-id-3 div.sk-estimator {\n",
              "  font-family: monospace;\n",
              "  border: 1px dotted var(--sklearn-color-border-box);\n",
              "  border-radius: 0.25em;\n",
              "  box-sizing: border-box;\n",
              "  margin-bottom: 0.5em;\n",
              "  /* unfitted */\n",
              "  background-color: var(--sklearn-color-unfitted-level-0);\n",
              "}\n",
              "\n",
              "#sk-container-id-3 div.sk-estimator.fitted {\n",
              "  /* fitted */\n",
              "  background-color: var(--sklearn-color-fitted-level-0);\n",
              "}\n",
              "\n",
              "/* on hover */\n",
              "#sk-container-id-3 div.sk-estimator:hover {\n",
              "  /* unfitted */\n",
              "  background-color: var(--sklearn-color-unfitted-level-2);\n",
              "}\n",
              "\n",
              "#sk-container-id-3 div.sk-estimator.fitted:hover {\n",
              "  /* fitted */\n",
              "  background-color: var(--sklearn-color-fitted-level-2);\n",
              "}\n",
              "\n",
              "/* Specification for estimator info (e.g. \"i\" and \"?\") */\n",
              "\n",
              "/* Common style for \"i\" and \"?\" */\n",
              "\n",
              ".sk-estimator-doc-link,\n",
              "a:link.sk-estimator-doc-link,\n",
              "a:visited.sk-estimator-doc-link {\n",
              "  float: right;\n",
              "  font-size: smaller;\n",
              "  line-height: 1em;\n",
              "  font-family: monospace;\n",
              "  background-color: var(--sklearn-color-background);\n",
              "  border-radius: 1em;\n",
              "  height: 1em;\n",
              "  width: 1em;\n",
              "  text-decoration: none !important;\n",
              "  margin-left: 1ex;\n",
              "  /* unfitted */\n",
              "  border: var(--sklearn-color-unfitted-level-1) 1pt solid;\n",
              "  color: var(--sklearn-color-unfitted-level-1);\n",
              "}\n",
              "\n",
              ".sk-estimator-doc-link.fitted,\n",
              "a:link.sk-estimator-doc-link.fitted,\n",
              "a:visited.sk-estimator-doc-link.fitted {\n",
              "  /* fitted */\n",
              "  border: var(--sklearn-color-fitted-level-1) 1pt solid;\n",
              "  color: var(--sklearn-color-fitted-level-1);\n",
              "}\n",
              "\n",
              "/* On hover */\n",
              "div.sk-estimator:hover .sk-estimator-doc-link:hover,\n",
              ".sk-estimator-doc-link:hover,\n",
              "div.sk-label-container:hover .sk-estimator-doc-link:hover,\n",
              ".sk-estimator-doc-link:hover {\n",
              "  /* unfitted */\n",
              "  background-color: var(--sklearn-color-unfitted-level-3);\n",
              "  color: var(--sklearn-color-background);\n",
              "  text-decoration: none;\n",
              "}\n",
              "\n",
              "div.sk-estimator.fitted:hover .sk-estimator-doc-link.fitted:hover,\n",
              ".sk-estimator-doc-link.fitted:hover,\n",
              "div.sk-label-container:hover .sk-estimator-doc-link.fitted:hover,\n",
              ".sk-estimator-doc-link.fitted:hover {\n",
              "  /* fitted */\n",
              "  background-color: var(--sklearn-color-fitted-level-3);\n",
              "  color: var(--sklearn-color-background);\n",
              "  text-decoration: none;\n",
              "}\n",
              "\n",
              "/* Span, style for the box shown on hovering the info icon */\n",
              ".sk-estimator-doc-link span {\n",
              "  display: none;\n",
              "  z-index: 9999;\n",
              "  position: relative;\n",
              "  font-weight: normal;\n",
              "  right: .2ex;\n",
              "  padding: .5ex;\n",
              "  margin: .5ex;\n",
              "  width: min-content;\n",
              "  min-width: 20ex;\n",
              "  max-width: 50ex;\n",
              "  color: var(--sklearn-color-text);\n",
              "  box-shadow: 2pt 2pt 4pt #999;\n",
              "  /* unfitted */\n",
              "  background: var(--sklearn-color-unfitted-level-0);\n",
              "  border: .5pt solid var(--sklearn-color-unfitted-level-3);\n",
              "}\n",
              "\n",
              ".sk-estimator-doc-link.fitted span {\n",
              "  /* fitted */\n",
              "  background: var(--sklearn-color-fitted-level-0);\n",
              "  border: var(--sklearn-color-fitted-level-3);\n",
              "}\n",
              "\n",
              ".sk-estimator-doc-link:hover span {\n",
              "  display: block;\n",
              "}\n",
              "\n",
              "/* \"?\"-specific style due to the `<a>` HTML tag */\n",
              "\n",
              "#sk-container-id-3 a.estimator_doc_link {\n",
              "  float: right;\n",
              "  font-size: 1rem;\n",
              "  line-height: 1em;\n",
              "  font-family: monospace;\n",
              "  background-color: var(--sklearn-color-background);\n",
              "  border-radius: 1rem;\n",
              "  height: 1rem;\n",
              "  width: 1rem;\n",
              "  text-decoration: none;\n",
              "  /* unfitted */\n",
              "  color: var(--sklearn-color-unfitted-level-1);\n",
              "  border: var(--sklearn-color-unfitted-level-1) 1pt solid;\n",
              "}\n",
              "\n",
              "#sk-container-id-3 a.estimator_doc_link.fitted {\n",
              "  /* fitted */\n",
              "  border: var(--sklearn-color-fitted-level-1) 1pt solid;\n",
              "  color: var(--sklearn-color-fitted-level-1);\n",
              "}\n",
              "\n",
              "/* On hover */\n",
              "#sk-container-id-3 a.estimator_doc_link:hover {\n",
              "  /* unfitted */\n",
              "  background-color: var(--sklearn-color-unfitted-level-3);\n",
              "  color: var(--sklearn-color-background);\n",
              "  text-decoration: none;\n",
              "}\n",
              "\n",
              "#sk-container-id-3 a.estimator_doc_link.fitted:hover {\n",
              "  /* fitted */\n",
              "  background-color: var(--sklearn-color-fitted-level-3);\n",
              "}\n",
              "</style><div id=\"sk-container-id-3\" class=\"sk-top-container\"><div class=\"sk-text-repr-fallback\"><pre>GridSearchCV(cv=5, estimator=Lasso(),\n",
              "             param_grid={&#x27;alpha&#x27;: array([0.001     , 0.02138776, 0.04177551, 0.06216327, 0.08255102,\n",
              "       0.10293878, 0.12332653, 0.14371429, 0.16410204, 0.1844898 ,\n",
              "       0.20487755, 0.22526531, 0.24565306, 0.26604082, 0.28642857,\n",
              "       0.30681633, 0.32720408, 0.34759184, 0.36797959, 0.38836735,\n",
              "       0.4087551 , 0.42914286, 0.44953061, 0.46991837, 0.49030612,\n",
              "       0.51069388, 0.531081...0.55146939, 0.57185714, 0.5922449 ,\n",
              "       0.61263265, 0.63302041, 0.65340816, 0.67379592, 0.69418367,\n",
              "       0.71457143, 0.73495918, 0.75534694, 0.77573469, 0.79612245,\n",
              "       0.8165102 , 0.83689796, 0.85728571, 0.87767347, 0.89806122,\n",
              "       0.91844898, 0.93883673, 0.95922449, 0.97961224, 1.        ])},\n",
              "             return_train_score=True,\n",
              "             scoring=make_scorer(mse_loss, greater_is_better=False, response_method=&#x27;predict&#x27;))</pre><b>In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook. <br />On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.</b></div><div class=\"sk-container\" hidden><div class=\"sk-item sk-dashed-wrapped\"><div class=\"sk-label-container\"><div class=\"sk-label fitted sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-5\" type=\"checkbox\" ><label for=\"sk-estimator-id-5\" class=\"sk-toggleable__label fitted sk-toggleable__label-arrow fitted\">&nbsp;&nbsp;GridSearchCV<a class=\"sk-estimator-doc-link fitted\" rel=\"noreferrer\" target=\"_blank\" href=\"https://scikit-learn.org/1.5/modules/generated/sklearn.model_selection.GridSearchCV.html\">?<span>Documentation for GridSearchCV</span></a><span class=\"sk-estimator-doc-link fitted\">i<span>Fitted</span></span></label><div class=\"sk-toggleable__content fitted\"><pre>GridSearchCV(cv=5, estimator=Lasso(),\n",
              "             param_grid={&#x27;alpha&#x27;: array([0.001     , 0.02138776, 0.04177551, 0.06216327, 0.08255102,\n",
              "       0.10293878, 0.12332653, 0.14371429, 0.16410204, 0.1844898 ,\n",
              "       0.20487755, 0.22526531, 0.24565306, 0.26604082, 0.28642857,\n",
              "       0.30681633, 0.32720408, 0.34759184, 0.36797959, 0.38836735,\n",
              "       0.4087551 , 0.42914286, 0.44953061, 0.46991837, 0.49030612,\n",
              "       0.51069388, 0.531081...0.55146939, 0.57185714, 0.5922449 ,\n",
              "       0.61263265, 0.63302041, 0.65340816, 0.67379592, 0.69418367,\n",
              "       0.71457143, 0.73495918, 0.75534694, 0.77573469, 0.79612245,\n",
              "       0.8165102 , 0.83689796, 0.85728571, 0.87767347, 0.89806122,\n",
              "       0.91844898, 0.93883673, 0.95922449, 0.97961224, 1.        ])},\n",
              "             return_train_score=True,\n",
              "             scoring=make_scorer(mse_loss, greater_is_better=False, response_method=&#x27;predict&#x27;))</pre></div> </div></div><div class=\"sk-parallel\"><div class=\"sk-parallel-item\"><div class=\"sk-item\"><div class=\"sk-label-container\"><div class=\"sk-label fitted sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-6\" type=\"checkbox\" ><label for=\"sk-estimator-id-6\" class=\"sk-toggleable__label fitted sk-toggleable__label-arrow fitted\">best_estimator_: Lasso</label><div class=\"sk-toggleable__content fitted\"><pre>Lasso(alpha=0.26604081632653065)</pre></div> </div></div><div class=\"sk-serial\"><div class=\"sk-item\"><div class=\"sk-estimator fitted sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-7\" type=\"checkbox\" ><label for=\"sk-estimator-id-7\" class=\"sk-toggleable__label fitted sk-toggleable__label-arrow fitted\">&nbsp;Lasso<a class=\"sk-estimator-doc-link fitted\" rel=\"noreferrer\" target=\"_blank\" href=\"https://scikit-learn.org/1.5/modules/generated/sklearn.linear_model.Lasso.html\">?<span>Documentation for Lasso</span></a></label><div class=\"sk-toggleable__content fitted\"><pre>Lasso(alpha=0.26604081632653065)</pre></div> </div></div></div></div></div></div></div></div></div>"
            ]
          },
          "metadata": {},
          "execution_count": 40
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Pour sortir le meilleur paramètre\n",
        "print(gride_search.best_params_)\n",
        "# Les différents scores sont là\n",
        "train_score = gride_search.cv_results_[\"mean_train_score\"]\n",
        "val_score = gride_search.cv_results_[\"mean_test_score\"]\n",
        "# Le graphique\n",
        "fig, ax = plt.subplots()\n",
        "ax.plot(hyp_lambdas, -train_score, c=\"blue\", label=\"MSE score train\")\n",
        "ax.plot(hyp_lambdas, -val_score, c=\"red\", label=\"MSE score valid\")\n",
        "ax.set_xlabel(\"$\\lambda$\")\n",
        "ax.set_ylabel(\"$MSE score$\")\n",
        "ax.legend()\n",
        "plt.plot()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 485
        },
        "id": "MAxPXmeTrcMO",
        "outputId": "477bcf6c-9e47-4a35-8f66-0100417e2d4d"
      },
      "execution_count": 26,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "{'alpha': 0.26604081632653065}\n"
          ]
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[]"
            ]
          },
          "metadata": {},
          "execution_count": 26
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "---"
      ],
      "metadata": {
        "id": "70NTioUYw_wi"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Exercice : recherche d'hyperparamètres avec une regression Ridge, sur le dataset *winequality*\n",
        "\n",
        "Vous avez à disposition deux jeux de données sur les vins : **winequality-red.csv** et **winequality-white.csv**. Ces deux jeux contiennent plusieurs variables concernant la composition des vins, et un score dénotant sa qualité"
      ],
      "metadata": {
        "id": "TfVMzWK2w9-d"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "file_path = \"drive/MyDrive/Colab Notebooks/ml_data/TP2/winequality-red.csv\"\n",
        "# Pour les blancs\n",
        "#file_path = \"drive/MyDrive/Colab Notebooks/ml_data/TP2/winequality-white.csv\"\n",
        "wine_data = pd.read_csv(file_path, sep=\";\")\n",
        "wine_data"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 424
        },
        "id": "CM15YHeSv2Ad",
        "outputId": "de3f33ab-005b-482a-c762-1fae9ee905f8"
      },
      "execution_count": 27,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "      fixed acidity  volatile acidity  citric acid  residual sugar  chlorides  \\\n",
              "0               7.4             0.700         0.00             1.9      0.076   \n",
              "1               7.8             0.880         0.00             2.6      0.098   \n",
              "2               7.8             0.760         0.04             2.3      0.092   \n",
              "3              11.2             0.280         0.56             1.9      0.075   \n",
              "4               7.4             0.700         0.00             1.9      0.076   \n",
              "...             ...               ...          ...             ...        ...   \n",
              "1594            6.2             0.600         0.08             2.0      0.090   \n",
              "1595            5.9             0.550         0.10             2.2      0.062   \n",
              "1596            6.3             0.510         0.13             2.3      0.076   \n",
              "1597            5.9             0.645         0.12             2.0      0.075   \n",
              "1598            6.0             0.310         0.47             3.6      0.067   \n",
              "\n",
              "      free sulfur dioxide  total sulfur dioxide  density    pH  sulphates  \\\n",
              "0                    11.0                  34.0  0.99780  3.51       0.56   \n",
              "1                    25.0                  67.0  0.99680  3.20       0.68   \n",
              "2                    15.0                  54.0  0.99700  3.26       0.65   \n",
              "3                    17.0                  60.0  0.99800  3.16       0.58   \n",
              "4                    11.0                  34.0  0.99780  3.51       0.56   \n",
              "...                   ...                   ...      ...   ...        ...   \n",
              "1594                 32.0                  44.0  0.99490  3.45       0.58   \n",
              "1595                 39.0                  51.0  0.99512  3.52       0.76   \n",
              "1596                 29.0                  40.0  0.99574  3.42       0.75   \n",
              "1597                 32.0                  44.0  0.99547  3.57       0.71   \n",
              "1598                 18.0                  42.0  0.99549  3.39       0.66   \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  \n",
              "...       ...      ...  \n",
              "1594     10.5        5  \n",
              "1595     11.2        6  \n",
              "1596     11.0        6  \n",
              "1597     10.2        5  \n",
              "1598     11.0        6  \n",
              "\n",
              "[1599 rows x 12 columns]"
            ],
            "text/html": [
              "\n",
              "  <div id=\"df-c92219b1-0a52-4fd7-9c6b-8c6b7571c187\" class=\"colab-df-container\">\n",
              "    <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>0.700</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>0.99780</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>0.880</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>0.99680</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>0.760</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>0.99700</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>0.280</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>0.99800</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>0.700</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>0.99780</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>...</th>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1594</th>\n",
              "      <td>6.2</td>\n",
              "      <td>0.600</td>\n",
              "      <td>0.08</td>\n",
              "      <td>2.0</td>\n",
              "      <td>0.090</td>\n",
              "      <td>32.0</td>\n",
              "      <td>44.0</td>\n",
              "      <td>0.99490</td>\n",
              "      <td>3.45</td>\n",
              "      <td>0.58</td>\n",
              "      <td>10.5</td>\n",
              "      <td>5</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1595</th>\n",
              "      <td>5.9</td>\n",
              "      <td>0.550</td>\n",
              "      <td>0.10</td>\n",
              "      <td>2.2</td>\n",
              "      <td>0.062</td>\n",
              "      <td>39.0</td>\n",
              "      <td>51.0</td>\n",
              "      <td>0.99512</td>\n",
              "      <td>3.52</td>\n",
              "      <td>0.76</td>\n",
              "      <td>11.2</td>\n",
              "      <td>6</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1596</th>\n",
              "      <td>6.3</td>\n",
              "      <td>0.510</td>\n",
              "      <td>0.13</td>\n",
              "      <td>2.3</td>\n",
              "      <td>0.076</td>\n",
              "      <td>29.0</td>\n",
              "      <td>40.0</td>\n",
              "      <td>0.99574</td>\n",
              "      <td>3.42</td>\n",
              "      <td>0.75</td>\n",
              "      <td>11.0</td>\n",
              "      <td>6</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1597</th>\n",
              "      <td>5.9</td>\n",
              "      <td>0.645</td>\n",
              "      <td>0.12</td>\n",
              "      <td>2.0</td>\n",
              "      <td>0.075</td>\n",
              "      <td>32.0</td>\n",
              "      <td>44.0</td>\n",
              "      <td>0.99547</td>\n",
              "      <td>3.57</td>\n",
              "      <td>0.71</td>\n",
              "      <td>10.2</td>\n",
              "      <td>5</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1598</th>\n",
              "      <td>6.0</td>\n",
              "      <td>0.310</td>\n",
              "      <td>0.47</td>\n",
              "      <td>3.6</td>\n",
              "      <td>0.067</td>\n",
              "      <td>18.0</td>\n",
              "      <td>42.0</td>\n",
              "      <td>0.99549</td>\n",
              "      <td>3.39</td>\n",
              "      <td>0.66</td>\n",
              "      <td>11.0</td>\n",
              "      <td>6</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "<p>1599 rows × 12 columns</p>\n",
              "</div>\n",
              "    <div class=\"colab-df-buttons\">\n",
              "\n",
              "  <div class=\"colab-df-container\">\n",
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              "\n",
              "    .colab-df-convert:hover {\n",
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              "        document.querySelector('#df-c92219b1-0a52-4fd7-9c6b-8c6b7571c187 button.colab-df-convert');\n",
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              "        const element = document.querySelector('#df-c92219b1-0a52-4fd7-9c6b-8c6b7571c187');\n",
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              "                                                    [key], {});\n",
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              "        const docLinkHtml = 'Like what you see? Visit the ' +\n",
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              "        element.innerHTML = '';\n",
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              "\n",
              "  .colab-df-quickchart {\n",
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              "\n",
              "  .colab-df-quickchart-complete:disabled,\n",
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              "    background-color: var(--disabled-bg-color);\n",
              "    fill: var(--disabled-fill-color);\n",
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              "\n",
              "  .colab-df-spinner {\n",
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              "\n",
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              "      border-color: transparent;\n",
              "      border-right-color: var(--fill-color);\n",
              "      border-top-color: var(--fill-color);\n",
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              "    60% {\n",
              "      border-color: transparent;\n",
              "      border-right-color: var(--fill-color);\n",
              "    }\n",
              "    80% {\n",
              "      border-color: transparent;\n",
              "      border-right-color: var(--fill-color);\n",
              "      border-bottom-color: var(--fill-color);\n",
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              "      border-bottom-color: var(--fill-color);\n",
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              "  }\n",
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              "\n",
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              "    async function quickchart(key) {\n",
              "      const quickchartButtonEl =\n",
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              "      quickchartButtonEl.classList.add('colab-df-spinner');\n",
              "      try {\n",
              "        const charts = await google.colab.kernel.invokeFunction(\n",
              "            'suggestCharts', [key], {});\n",
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              "        console.error('Error during call to suggestCharts:', error);\n",
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              "      quickchartButtonEl.classList.remove('colab-df-spinner');\n",
              "      quickchartButtonEl.classList.add('colab-df-quickchart-complete');\n",
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              "\n",
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              "        fill: #1967D2;\n",
              "        height: 32px;\n",
              "        padding: 0 0 0 0;\n",
              "        width: 32px;\n",
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              "\n",
              "      .colab-df-generate:hover {\n",
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              "        box-shadow: 0px 1px 2px rgba(60, 64, 67, 0.3), 0px 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
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              "      [theme=dark] .colab-df-generate {\n",
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              "    <button class=\"colab-df-generate\" onclick=\"generateWithVariable('wine_data')\"\n",
              "            title=\"Generate code using this dataframe.\"\n",
              "            style=\"display:none;\">\n",
              "\n",
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              "      buttonEl.onclick = () => {\n",
              "        google.colab.notebook.generateWithVariable('wine_data');\n",
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              "\n",
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            "application/vnd.google.colaboratory.intrinsic+json": {
              "type": "dataframe",
              "variable_name": "wine_data",
              "summary": "{\n  \"name\": \"wine_data\",\n  \"rows\": 1599,\n  \"fields\": [\n    {\n      \"column\": \"fixed acidity\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 1.7410963181276953,\n        \"min\": 4.6,\n        \"max\": 15.9,\n        \"num_unique_values\": 96,\n        \"samples\": [\n          5.3,\n          12.7,\n          12.6\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"volatile acidity\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 0.17905970415353537,\n        \"min\": 0.12,\n        \"max\": 1.58,\n        \"num_unique_values\": 143,\n        \"samples\": [\n          1.025,\n          0.4,\n          0.87\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"citric acid\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 0.19480113740531857,\n        \"min\": 0.0,\n        \"max\": 1.0,\n        \"num_unique_values\": 80,\n        \"samples\": [\n          0.37,\n          0.0,\n          0.09\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"residual sugar\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 1.4099280595072798,\n        \"min\": 0.9,\n        \"max\": 15.5,\n        \"num_unique_values\": 91,\n        \"samples\": [\n          11.0,\n          3.0,\n          15.5\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"chlorides\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 0.0470653020100901,\n        \"min\": 0.012,\n        \"max\": 0.611,\n        \"num_unique_values\": 153,\n        \"samples\": [\n          0.096,\n          0.343,\n          0.159\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"free sulfur dioxide\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 10.460156969809725,\n        \"min\": 1.0,\n        \"max\": 72.0,\n        \"num_unique_values\": 60,\n        \"samples\": [\n          11.0,\n          9.0,\n          32.0\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"total sulfur dioxide\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 32.895324478299074,\n        \"min\": 6.0,\n        \"max\": 289.0,\n        \"num_unique_values\": 144,\n        \"samples\": [\n          68.0,\n          35.0,\n          101.0\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"density\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 0.0018873339538425554,\n        \"min\": 0.99007,\n        \"max\": 1.00369,\n        \"num_unique_values\": 436,\n        \"samples\": [\n          0.99974,\n          1.0001,\n          0.99471\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"pH\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 0.15438646490354277,\n        \"min\": 2.74,\n        \"max\": 4.01,\n        \"num_unique_values\": 89,\n        \"samples\": [\n          3.07,\n          3.0,\n          3.15\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"sulphates\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 0.16950697959010996,\n        \"min\": 0.33,\n        \"max\": 2.0,\n        \"num_unique_values\": 96,\n        \"samples\": [\n          1.07,\n          1.04,\n          1.18\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"alcohol\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 1.0656675818473946,\n        \"min\": 8.4,\n        \"max\": 14.9,\n        \"num_unique_values\": 65,\n        \"samples\": [\n          8.5,\n          9.95,\n          9.4\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"quality\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 0,\n        \"min\": 3,\n        \"max\": 8,\n        \"num_unique_values\": 6,\n        \"samples\": [\n          5,\n          6,\n          3\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    }\n  ]\n}"
            }
          },
          "metadata": {},
          "execution_count": 27
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Votre but sera de trouver un \"bon\" modèle pour prédire la variable **quality** en fonction des autres. Nous allons considérer les modèles de la famille **régression Ridge**. Il vous faudra :\n",
        "\n",
        "1. Séparer le jeu de données en train/validation et test (20% pour test).\n",
        "2. Faire une cross-validation (5-folds) sur train/validation à la recherche de l'hyperparamètre $\\lambda$ minimisant la $MSE$ (parmi les valeurs allant de 0 à 0.3, à vous de voir le nombre d'étapes).\n",
        "3. Tracer le graphique des $MSE_\\text{train}$ et $MSE_\\text{valid}$.\n",
        "4. Trouver l'hyperparamètre optimal et estimer la perte de généralisation.\n",
        "\n",
        "A vous de jouer !"
      ],
      "metadata": {
        "id": "FLHYa2y5zXmd"
      }
    }
  ]
}