SO73583687_Ridge_normalize.ipynb

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      "source": [
        "from sklearn.pipeline import make_pipeline\n",
        "from sklearn.preprocessing import StandardScaler\n",
        "from sklearn.linear_model import Ridge\n",
        "from sklearn.datasets import load_diabetes\n",
        "import pandas as pd\n",
        "\n",
        "# X, y = load_diabetes(return_X_y=True, as_frame=True)\n",
        "\n",
        "data = pd.read_csv('https://drive.google.com/uc?id=1ukCv-bdsggTOLTFQqel4TCmoT1C06DFz', index_col=0)\n",
        "X = data.iloc[:,:15]\n",
        "y = data['target']\n"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "data.head()"
      ],
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        "id": "TvvOMGHzjFDF",
        "outputId": "fa5d30a5-25bb-4914-b497-9c027831d568"
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      "execution_count": 2,
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              "   power_1   power_2     power_3       power_4       power_5       power_6  \\\n",
              "0    290.0   84100.0  24389000.0  7.072810e+09  2.051115e+12  5.948233e+14   \n",
              "1    370.0  136900.0  50653000.0  1.874161e+10  6.934396e+12  2.565726e+15   \n",
              "2    380.0  144400.0  54872000.0  2.085136e+10  7.923517e+12  3.010936e+15   \n",
              "3    384.0  147456.0  56623104.0  2.174327e+10  8.349416e+12  3.206176e+15   \n",
              "4    390.0  152100.0  59319000.0  2.313441e+10  9.022420e+12  3.518744e+15   \n",
              "\n",
              "        power_7       power_8       power_9      power_10      power_11  \\\n",
              "0  1.724988e+17  5.002464e+19  1.450715e+22  4.207072e+24  1.220051e+27   \n",
              "1  9.493188e+17  3.512479e+20  1.299617e+23  4.808584e+25  1.779176e+28   \n",
              "2  1.144156e+18  4.347792e+20  1.652161e+23  6.278212e+25  2.385721e+28   \n",
              "3  1.231172e+18  4.727699e+20  1.815436e+23  6.971275e+25  2.676970e+28   \n",
              "4  1.372310e+18  5.352009e+20  2.087284e+23  8.140406e+25  3.174758e+28   \n",
              "\n",
              "       power_12      power_13      power_14      power_15    target  \n",
              "0  3.538148e+29  1.026063e+32  2.975582e+34  8.629189e+36  221900.0  \n",
              "1  6.582952e+30  2.435692e+33  9.012061e+35  3.334463e+38  538000.0  \n",
              "2  9.065738e+30  3.444980e+33  1.309093e+36  4.974552e+38  180000.0  \n",
              "3  1.027956e+31  3.947353e+33  1.515783e+36  5.820608e+38  604000.0  \n",
              "4  1.238156e+31  4.828807e+33  1.883235e+36  7.344616e+38  510000.0  "
            ],
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              "      <th>power_1</th>\n",
              "      <th>power_2</th>\n",
              "      <th>power_3</th>\n",
              "      <th>power_4</th>\n",
              "      <th>power_5</th>\n",
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              "      <th>power_12</th>\n",
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              "      <th>0</th>\n",
              "      <td>290.0</td>\n",
              "      <td>84100.0</td>\n",
              "      <td>24389000.0</td>\n",
              "      <td>7.072810e+09</td>\n",
              "      <td>2.051115e+12</td>\n",
              "      <td>5.948233e+14</td>\n",
              "      <td>1.724988e+17</td>\n",
              "      <td>5.002464e+19</td>\n",
              "      <td>1.450715e+22</td>\n",
              "      <td>4.207072e+24</td>\n",
              "      <td>1.220051e+27</td>\n",
              "      <td>3.538148e+29</td>\n",
              "      <td>1.026063e+32</td>\n",
              "      <td>2.975582e+34</td>\n",
              "      <td>8.629189e+36</td>\n",
              "      <td>221900.0</td>\n",
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              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>370.0</td>\n",
              "      <td>136900.0</td>\n",
              "      <td>50653000.0</td>\n",
              "      <td>1.874161e+10</td>\n",
              "      <td>6.934396e+12</td>\n",
              "      <td>2.565726e+15</td>\n",
              "      <td>9.493188e+17</td>\n",
              "      <td>3.512479e+20</td>\n",
              "      <td>1.299617e+23</td>\n",
              "      <td>4.808584e+25</td>\n",
              "      <td>1.779176e+28</td>\n",
              "      <td>6.582952e+30</td>\n",
              "      <td>2.435692e+33</td>\n",
              "      <td>9.012061e+35</td>\n",
              "      <td>3.334463e+38</td>\n",
              "      <td>538000.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>380.0</td>\n",
              "      <td>144400.0</td>\n",
              "      <td>54872000.0</td>\n",
              "      <td>2.085136e+10</td>\n",
              "      <td>7.923517e+12</td>\n",
              "      <td>3.010936e+15</td>\n",
              "      <td>1.144156e+18</td>\n",
              "      <td>4.347792e+20</td>\n",
              "      <td>1.652161e+23</td>\n",
              "      <td>6.278212e+25</td>\n",
              "      <td>2.385721e+28</td>\n",
              "      <td>9.065738e+30</td>\n",
              "      <td>3.444980e+33</td>\n",
              "      <td>1.309093e+36</td>\n",
              "      <td>4.974552e+38</td>\n",
              "      <td>180000.0</td>\n",
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              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>384.0</td>\n",
              "      <td>147456.0</td>\n",
              "      <td>56623104.0</td>\n",
              "      <td>2.174327e+10</td>\n",
              "      <td>8.349416e+12</td>\n",
              "      <td>3.206176e+15</td>\n",
              "      <td>1.231172e+18</td>\n",
              "      <td>4.727699e+20</td>\n",
              "      <td>1.815436e+23</td>\n",
              "      <td>6.971275e+25</td>\n",
              "      <td>2.676970e+28</td>\n",
              "      <td>1.027956e+31</td>\n",
              "      <td>3.947353e+33</td>\n",
              "      <td>1.515783e+36</td>\n",
              "      <td>5.820608e+38</td>\n",
              "      <td>604000.0</td>\n",
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              "      <th>4</th>\n",
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              "      <td>1.372310e+18</td>\n",
              "      <td>5.352009e+20</td>\n",
              "      <td>2.087284e+23</td>\n",
              "      <td>8.140406e+25</td>\n",
              "      <td>3.174758e+28</td>\n",
              "      <td>1.238156e+31</td>\n",
              "      <td>4.828807e+33</td>\n",
              "      <td>1.883235e+36</td>\n",
              "      <td>7.344616e+38</td>\n",
              "      <td>510000.0</td>\n",
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          "metadata": {},
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      ]
    },
    {
      "cell_type": "code",
      "source": [
        "penalty = 1.5e-5\n",
        "A = Ridge(normalize=True, alpha=penalty).fit(X, y)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "OWbR5yj8i88_",
        "outputId": "e1f8bf5a-6989-4481-8d21-ac05413be369"
      },
      "execution_count": 3,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "/usr/local/lib/python3.7/dist-packages/sklearn/linear_model/_base.py:145: FutureWarning: 'normalize' was deprecated in version 1.0 and will be removed in 1.2.\n",
            "If you wish to scale the data, use Pipeline with a StandardScaler in a preprocessing stage. To reproduce the previous behavior:\n",
            "\n",
            "from sklearn.pipeline import make_pipeline\n",
            "\n",
            "model = make_pipeline(StandardScaler(with_mean=False), Ridge())\n",
            "\n",
            "If you wish to pass a sample_weight parameter, you need to pass it as a fit parameter to each step of the pipeline as follows:\n",
            "\n",
            "kwargs = {s[0] + '__sample_weight': sample_weight for s in model.steps}\n",
            "model.fit(X, y, **kwargs)\n",
            "\n",
            "Set parameter alpha to: original_alpha * n_samples. \n",
            "  FutureWarning,\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "from sklearn.pipeline import make_pipeline\n",
        "\n",
        "B = make_pipeline(StandardScaler(with_mean=False), Ridge(alpha=penalty * X.shape[0]))\n",
        "B.fit(X, y)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "ebrdc3y1CC_9",
        "outputId": "f7bc6860-a959-4d0e-ce41-dde1000fd546"
      },
      "execution_count": 4,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Pipeline(steps=[('standardscaler', StandardScaler(with_mean=False)),\n",
              "                ('ridge', Ridge(alpha=0.324195))])"
            ]
          },
          "metadata": {},
          "execution_count": 4
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "for i in range(X.shape[1]):\n",
        "    print(A.coef_[i], B[1].coef_[i] / B[0].scale_[i])\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "YtSbOwbZCM02",
        "outputId": "8d8adef6-cfa5-479e-ef41-2b827c95dcb0"
      },
      "execution_count": 5,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "-27.146695104574537 -27.146695104434496\n",
            "0.004539501338651588 0.004539501338546368\n",
            "2.1818777212039407e-06 2.181877721236087e-06\n",
            "-3.138752250904223e-10 -3.1387522509374534e-10\n",
            "1.146994194901286e-15 1.1469941947734586e-15\n",
            "8.702444221177161e-19 8.7024442213974e-19\n",
            "-8.12615496452096e-24 -8.126154962012825e-24\n",
            "-4.49757556285541e-27 -4.4975755629786446e-27\n",
            "-2.3328447957008473e-31 -2.3328447959212177e-31\n",
            "6.325894579997212e-36 6.32589457999304e-36\n",
            "2.0555391095672096e-39 2.055539109687643e-39\n",
            "1.920104055323069e-43 1.9201040553530566e-43\n",
            "9.623468025047094e-48 9.623468024730885e-48\n",
            "-1.6321932842749238e-52 -1.6321932845806583e-52\n",
            "-1.0919777695190494e-55 -1.0919777695016982e-55\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "import numpy as np\n",
        "np.allclose(A.coef_, B[1].coef_ / B[0].scale_)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "bDYbs750Eh_Y",
        "outputId": "64464597-4fa1-4021-ee7f-79877c611085"
      },
      "execution_count": 6,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "True"
            ]
          },
          "metadata": {},
          "execution_count": 6
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "A.coef_[0] * X.iloc[:, 0].std()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "JTaK0ae9CO0u",
        "outputId": "09830efc-4ec9-4899-c013-c3bdaa462a7c"
      },
      "execution_count": 7,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "-24932.635003701726"
            ]
          },
          "metadata": {},
          "execution_count": 7
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [],
      "metadata": {
        "id": "9n6ZOrkXCqY0"
      },
      "execution_count": 7,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [],
      "metadata": {
        "id": "ZR3An68rltsm"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "# SO 73623958, RidgeCV analogue"
      ],
      "metadata": {
        "id": "SnvsPI8HoNPS"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "from sklearn.linear_model import RidgeCV\n",
        "alphas = [10**(i/6 - 2.5) for i in range(30)]\n",
        "m = RidgeCV(alphas=alphas, normalize=True).fit(X, y)\n",
        "n = make_pipeline(StandardScaler(with_mean=False), RidgeCV(alphas=[alph * X.shape[0] for alph in alphas])).fit(X, y)\n",
        "m.alpha_, n[-1].alpha_ / X.shape[0]"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "-P5KTgmnlt6q",
        "outputId": "21334e2b-f9d1-483b-9443-4abf3506eef1"
      },
      "execution_count": 19,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "/usr/local/lib/python3.7/dist-packages/sklearn/linear_model/_base.py:145: FutureWarning: 'normalize' was deprecated in version 1.0 and will be removed in 1.2.\n",
            "If you wish to scale the data, use Pipeline with a StandardScaler in a preprocessing stage. To reproduce the previous behavior:\n",
            "\n",
            "from sklearn.pipeline import make_pipeline\n",
            "\n",
            "model = make_pipeline(StandardScaler(with_mean=False), _RidgeGCV())\n",
            "\n",
            "If you wish to pass a sample_weight parameter, you need to pass it as a fit parameter to each step of the pipeline as follows:\n",
            "\n",
            "kwargs = {s[0] + '__sample_weight': sample_weight for s in model.steps}\n",
            "model.fit(X, y, **kwargs)\n",
            "\n",
            "\n",
            "  FutureWarning,\n"
          ]
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(0.03162277660168379, 0.03162277660168379)"
            ]
          },
          "metadata": {},
          "execution_count": 19
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "for i in range(X.shape[1]):\n",
        "    print(m.coef_[i], n[-1].coef_[i] / n[0].scale_[i])\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "kg4I808Blyxu",
        "outputId": "135f4a34-cd66-4cfa-bfc0-8d006e45b7df"
      },
      "execution_count": 18,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "-3.788340164216518 -3.78834016421657\n",
            "0.0027907209078319433 0.002790720907831993\n",
            "3.086829708007345e-07 3.0868297080073657e-07\n",
            "-5.2644249386633055e-12 -5.264424938663628e-12\n",
            "-1.9381424972637724e-15 -1.9381424972638027e-15\n",
            "-1.4860889775068408e-19 -1.486088977506858e-19\n",
            "-7.844734989518523e-24 -7.844734989518563e-24\n",
            "-3.092909920569876e-28 -3.092909920569853e-28\n",
            "-6.061730259183882e-33 -6.061730259183257e-33\n",
            "4.616432700551042e-37 4.616432700551818e-37\n",
            "7.896022347484185e-41 7.89602234748497e-41\n",
            "7.833394304096256e-45 7.833394304096985e-45\n",
            "6.5432469804562646e-49 6.543246980456902e-49\n",
            "5.014190234278271e-53 5.014190234278814e-53\n",
            "3.646772273044989e-57 3.6467722730454364e-57\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [],
      "metadata": {
        "id": "2UMQ9fTom_m9"
      },
      "execution_count": null,
      "outputs": []
    }
  ]
}