custom_enet_example.ipynb

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      "name": "python"
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  "cells": [
    {
      "cell_type": "markdown",
      "source": [
        "This notebook is an example for CustomENet and CustomENetCV. First import these two classes and some other objects."
      ],
      "metadata": {
        "id": "fpEe6LbLCsE1"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "from custom_enet import CustomENet, CustomENetCV\n",
        "import numpy as np\n",
        "import pandas as pd\n",
        "import matplotlib.pyplot as plt\n",
        "from scipy.optimize import minimize_scalar\n",
        "from sklearn.linear_model import ElasticNetCV\n",
        "from sklearn.preprocessing import StandardScaler\n",
        "from statsmodels.api import OLS, add_constant\n",
        "from sklearn.metrics import mean_squared_error\n",
        "from sklearn.model_selection import RepeatedKFold"
      ],
      "metadata": {
        "id": "7Fcu4wXjCdZ-"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "Generate a toy dataset."
      ],
      "metadata": {
        "id": "rfwNbIyVGA6g"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "def add_randomness(x, rng, loc=0, scale=1):\n",
        "    r = rng.normal(loc, scale, size=x.size).reshape(x.shape)\n",
        "    return x + r\n",
        "\n",
        "#Simulate X    \n",
        "nsp = 400 #n_samples\n",
        "rng = np.random.default_rng(2023)\n",
        "#Continuous variables:\n",
        "X1 = rng.uniform(0, 2, nsp * 20).reshape(nsp, -1) \n",
        "#Categorical variables:\n",
        "C1 = rng.integers(0, 3, nsp)\n",
        "C1 = pd.get_dummies(C1, drop_first=True).to_numpy()\n",
        "C2 = rng.integers(0, 2, nsp)\n",
        "C2 = pd.get_dummies(C2, drop_first=True).to_numpy()\n",
        "C3 = rng.integers(0, 3, nsp)\n",
        "C3 = pd.get_dummies(C3, drop_first=True).to_numpy()\n",
        "#Correlated variables as noise.\n",
        "X2 = add_randomness(X1 ** 2, rng, scale=0.2)\n",
        "X3 = add_randomness(X1 ** 3, rng, scale=0.2)\n",
        "X4 = add_randomness(X1 ** 0.5, rng, scale=0.2)\n",
        "X5 = add_randomness(np.log(X1+1), rng, scale=0.2)\n",
        "X6 = add_randomness(np.exp(X1-1), rng, scale=0.2)\n",
        "X7 = add_randomness(np.sin((X1-1)), rng, scale=0.2)\n",
        "X8 = add_randomness(np.cos((X1-1)), rng, scale=0.2)\n",
        "X9 = add_randomness(np.sin((X1-1)*2), rng, scale=0.2)\n",
        "X10 = add_randomness(np.cos((X1-1)*2), rng, scale=0.2)\n",
        "X11 = add_randomness(np.sin((X1-1)*3), rng, scale=0.2)\n",
        "X12 = add_randomness(np.cos((X1-1)*3), rng, scale=0.2)\n",
        "#Combine all\n",
        "X = np.concatenate([X1, C1, C2, C3, X2, X3, X4, X5, X6, \n",
        "                    X7, X8, X9, X10, X11, X12], axis=1)\n",
        "print(X.shape)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "sKm9Y0idGirt",
        "outputId": "e5330bdd-8e6e-4c26-f0e1-3ba5b29c927a"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "(400, 245)\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "#Simulate coefficients\n",
        "n_dominant = 10 # number of dominant covariates\n",
        "n_cat = 5 # number of categorical covariates\n",
        "n_weak = 10 # number of weak covariates\n",
        "beta = rng.uniform(1, 3, X.shape[1]).reshape(-1, 1) \n",
        "beta[n_dominant:(n_dominant+n_weak)] *= 0.1\n",
        "beta[(n_dominant+n_weak+n_cat):] = .0"
      ],
      "metadata": {
        "id": "_ckBmP7xO_2A"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "#Simulate y\n",
        "y_t = X @ beta #deterministic y\n",
        "y = y_t + rng.normal(0, 2, size = nsp).reshape(-1, 1) #add noise"
      ],
      "metadata": {
        "id": "tTIIfPbVQPuK"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "Assume based on prior knowledge the categorical(dummy) variables have direct relationship with y and we don't want to penalize them. The penalty weight vector can be set as:"
      ],
      "metadata": {
        "id": "tD5OIU7xRy5r"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "penalty = np.ones(X.shape[1]) \n",
        "penalty[(n_dominant+n_weak):(n_dominant+n_weak+n_cat)] = .0"
      ],
      "metadata": {
        "id": "Peu45z3CQGxP"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "Split into train and test data."
      ],
      "metadata": {
        "id": "fxZVSWyiXgmS"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "train_n = 200\n",
        "X_train, X_test = X[:train_n], X[train_n:]\n",
        "y_train, y_test = y[:train_n], y[train_n:]\n",
        "y_t_test = y_t[train_n:]"
      ],
      "metadata": {
        "id": "9rk3RuUSXSfQ"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "Create a CV splitter for train data:"
      ],
      "metadata": {
        "id": "cVdc5MsvZQ4u"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "cv = RepeatedKFold(n_splits=10, n_repeats=3, random_state=2023)"
      ],
      "metadata": {
        "id": "LtbuvbAxZQKD"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "Theoratically minimal RMSE of prediction:"
      ],
      "metadata": {
        "id": "4_4UEZYEYrVH"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "print(mean_squared_error(y_test, y_t_test, squared=False))"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "ihbUbIM_Yqwk",
        "outputId": "9bf5103f-3484-428d-c3bd-9d836cc0894d"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "2.05031561171969\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Now let's start regression. First try OLS."
      ],
      "metadata": {
        "id": "PNdZRj9kYQ0S"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "model_ols = OLS(y_train, add_constant(X_train)).fit()\n",
        "y_pred = model_ols.predict(add_constant(X_test)).reshape(-1, 1)"
      ],
      "metadata": {
        "id": "1WZC1AF8Xsy7"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "Test RMSE of OLS:"
      ],
      "metadata": {
        "id": "XEtqvYBTe5TV"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "print(mean_squared_error(y_test, y_pred, squared=False))"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "N9YGv1Yae_GA",
        "outputId": "41a246f9-eb83-49f8-9243-4dfc419e39fa"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "5.225113897199456\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "OLS did a bad job due to severe overfitting. This is expected since n_features(125) > n_samples(100). Now try regular Lasso with CV:"
      ],
      "metadata": {
        "id": "9ArWDIaJYeRU"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "#Sklearn's Lasso requires X to be standardized.\n",
        "x_scaler = StandardScaler()\n",
        "X_train_s = x_scaler.fit_transform(X_train)\n",
        "X_test_s = x_scaler.transform(X_test)\n",
        "\n",
        "model_lasso = ElasticNetCV(l1_ratio=1, fit_intercept=True, max_iter=10000, cv=cv, \n",
        "                           alphas=None, random_state=2023)\n",
        "model_lasso.fit(X_train_s, y_train.ravel())"
      ],
      "metadata": {
        "id": "BwlibulFYdkl",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 91
        },
        "outputId": "19bab06c-ab06-47f9-cceb-b76b530a9e61"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "ElasticNetCV(cv=RepeatedKFold(n_repeats=3, n_splits=10, random_state=2023),\n",
              "             l1_ratio=1, max_iter=10000, random_state=2023)"
            ],
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              "             l1_ratio=1, max_iter=10000, random_state=2023)</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 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 sk-toggleable__label-arrow\">ElasticNetCV</label><div class=\"sk-toggleable__content\"><pre>ElasticNetCV(cv=RepeatedKFold(n_repeats=3, n_splits=10, random_state=2023),\n",
              "             l1_ratio=1, max_iter=10000, random_state=2023)</pre></div></div></div></div></div>"
            ]
          },
          "metadata": {},
          "execution_count": null
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Plot CV errors vs. alphas in train data:"
      ],
      "metadata": {
        "id": "iUXL1KHnbbh1"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "def path_stats(alphas, cv_errs, plot=True, \n",
        "               title=None, figsize=None):\n",
        "    err_mean = pd.Series(cv_errs.mean(axis=1), index = alphas)\n",
        "    err_std = pd.Series(cv_errs.std(axis=1), index = alphas)\n",
        "    if plot:\n",
        "        plt.figure(figsize=figsize)\n",
        "        if title:\n",
        "            plt.title(title)\n",
        "        err_mean.plot(yerr=err_std, logx=True, \n",
        "                      ecolor='grey', elinewidth=0.5, capsize=1)\n",
        "    return err_mean, err_std\n",
        "\n",
        "lasso_path_err, _ = path_stats(model_lasso.alphas_, model_lasso.mse_path_, \n",
        "                               title='regular lasso mse')"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 457
        },
        "id": "EPbwFJUEbLjB",
        "outputId": "6eb91ec1-eddd-47f1-ea14-0d55aa10abfa"
      },
      "execution_count": null,
      "outputs": [
        {
          "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": [
        "Test RMSE of regular Lasso:"
      ],
      "metadata": {
        "id": "eOokcL7uefzI"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "y_pred = model_lasso.predict(X_test_s).reshape(-1, 1)\n",
        "print(mean_squared_error(y_test, y_pred, squared=False))"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "zsnFYcEAebk5",
        "outputId": "102a7732-b424-4250-c814-e571efcce00c"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "2.5791273808053528\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Much better than OLS. Now run Lasso with customized penalties:"
      ],
      "metadata": {
        "id": "-fix4zsEfZC1"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "model_cl = CustomENetCV(cv, l1_ratio=1, standardize=True, fit_intercept=True, \n",
        "                        alphas=None, tol=1e-4, max_iter=10000, random_state=2023)\n",
        "model_cl.fit(X_train, y_train, penalty)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "w-m5ASo3fRA_",
        "outputId": "309bb3c4-c2dd-42c4-a7a3-e6ce6f70f0a1"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "CV round 1\n",
            "CV round 2\n",
            "CV round 3\n",
            "CV round 4\n",
            "CV round 5\n",
            "CV round 6\n",
            "CV round 7\n",
            "CV round 8\n",
            "CV round 9\n",
            "CV round 10\n",
            "CV round 11\n",
            "CV round 12\n",
            "CV round 13\n",
            "CV round 14\n",
            "CV round 15\n",
            "CV round 16\n",
            "CV round 17\n",
            "CV round 18\n",
            "CV round 19\n",
            "CV round 20\n",
            "CV round 21\n",
            "CV round 22\n",
            "CV round 23\n",
            "CV round 24\n",
            "CV round 25\n",
            "CV round 26\n",
            "CV round 27\n",
            "CV round 28\n",
            "CV round 29\n",
            "CV round 30\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Path plot:"
      ],
      "metadata": {
        "id": "aLaGwWbZgPIy"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "cl_path_err, _ = path_stats(model_cl.alphas, model_cl.cv_errs, \n",
        "                               title='custom lasso mse')"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 457
        },
        "id": "E5WOLOiFgSZH",
        "outputId": "1179a3d5-1c53-446b-a902-17474613a5cf"
      },
      "execution_count": null,
      "outputs": [
        {
          "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": [
        "Compare paths of regular Lasso and custom Lasso:"
      ],
      "metadata": {
        "id": "PM3dNhSfgypc"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "lasso_path_err.plot(logx=True, label='regular lasso')\n",
        "cl_path_err.plot(logx=True, label='custom lasso')\n",
        "plt.legend()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 451
        },
        "id": "qtjgrWa6g369",
        "outputId": "d6c1093b-2e85-4746-efd1-aa5a251c7791"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.legend.Legend at 0x7f7636fe56d0>"
            ]
          },
          "metadata": {},
          "execution_count": null
        },
        {
          "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": [
        "Test RMSE of custom Lasso:"
      ],
      "metadata": {
        "id": "thsnygeyiJl5"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "y_pred = model_cl.predict(X_test).reshape(-1, 1)\n",
        "print(mean_squared_error(y_test, y_pred, squared=False))"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "TfMACDI-iH-R",
        "outputId": "68527d85-2538-4e7c-91a7-68d1c73eefd6"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "2.5205751542255346\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Custom Lasso performed better than regular Lasso as expected. \n",
        "\n",
        "Of couse, we don't need to limit the model to Lasso. Let's try ElasticNet with customized penalties and tune the l1_ratio parameter. First generate a rough plot of l1_ratio vs. CV error:"
      ],
      "metadata": {
        "id": "K8GW3PqXkc3E"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "#Define an objective function\n",
        "def l1_r_opt_fun(r):\n",
        "    model = CustomENetCV(cv, alphas=None, l1_ratio=r, standardize=True, \n",
        "                         fit_intercept=True, max_iter=10000, refit=False,\n",
        "                         verbose=False, random_state=2023)\n",
        "    model.fit(X_train, y_train, penalty)\n",
        "    return model.cv_min_err\n",
        "\n",
        "r_v = np.linspace(0.1, 1, 5)\n",
        "l1_r_errs = []\n",
        "for i, r in enumerate(r_v):\n",
        "    print(r)\n",
        "    l1_r_errs.append(l1_r_opt_fun(r))"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "iJptQcwkYlRh",
        "outputId": "94866245-8727-42fe-f71d-43d610cd1095"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "0.1\n",
            "0.325\n",
            "0.55\n",
            "0.775\n",
            "1.0\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "plt.plot(r_v, l1_r_errs)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 449
        },
        "id": "TziCFVcOaitC",
        "outputId": "d9301ff6-3b27-49a2-bcb4-ed9a8ceed748"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x7f26b0a17f10>]"
            ]
          },
          "metadata": {},
          "execution_count": null
        },
        {
          "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": [
        "Seems like the optimal value is around 0.8. Further zoom in:"
      ],
      "metadata": {
        "id": "Dwlwfd-znRpS"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "r_v = np.linspace(0.5, 1, 6)\n",
        "l1_r_errs = []\n",
        "for i, r in enumerate(r_v):\n",
        "    print(r)\n",
        "    l1_r_errs.append(l1_r_opt_fun(r))\n",
        "\n",
        "plt.plot(r_v, l1_r_errs)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 551
        },
        "id": "W4_o34m9nP1A",
        "outputId": "b9af3d0d-498c-4ae4-d9c2-5c601ecd7611"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "0.5\n",
            "0.6\n",
            "0.7\n",
            "0.8\n",
            "0.9\n",
            "1.0\n"
          ]
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x7f6b4ec0b5b0>]"
            ]
          },
          "metadata": {},
          "execution_count": null
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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8wa28TU7kWlRYREREmsGSTfs4UFgzgv+mQTFmx3E5KiwiIiJN7FhpJYvWpgEw81KN4G8IFRYREZEmtmhtGsXl1XSLCOSavhrB3xAqLCIiIk0o+2gZ//f1fgBmjUnEqhH8DaLCIiIi0oSe/mwPlTY7g+PbMaxLe7PjuCwVFhERkSayPbeQ5Sl5AMwe0w2LRXtXGkqFRUREpAmcPoL/6j6RGsF/nlRYREREmsCG1CN8lVYzgv+ey7qaHcflqbCIiIg0stNH8N84MJqothrBf75UWERERBrZ8m257DpQRICvJ9M0gr9RqLCIiIg0otNH8N8xIp42rTWCvzGosIiIiDSi1zftI6+wnIggX24eHGN2HLehwiIiItJIjpdpBH9TUWERERFpJIvWplFUXk1ieADXXdDR7DhuRYVFRESkEWQfLeP1TTUj+P+iEfyNToVFRESkESxYvZdKm51Bce0YkRBidhy3o8IiIiJynmpG8OcCGsHfVFRYREREztOTq3ZjGHBV70h6dtQI/qagwiIiInIeNuw9zJepR/CyWrh3tEbwNxUVFhERkQaynz6C/6IYjeBvQiosIiIiDfTBD7nsPFBEgI8n0y7WCP6mpMIiIiLSAOVVNuZ/uheA20fG0VYj+JuUCouIiEgD/Pvr/eQeP0F4oC9/GNzZ7DhuT4VFRETEQYVlVTx/agT/ZRrB3xxUWERERBz0wro0Ck9U0TUsgOs1gr9ZqLCIiIg4IPf4CV7btA+AWRrB32xUWERERBzw9Gd7qKy2c1FsW0Z01Qj+5qLCIiIico525hXx/jaN4DeDCouIiMg5euLkCP4re0XQOyrY7DgtigqLiIjIOdiYeoQNew9rBL9JVFhERER+hd1uMO+TXQBMTo4mul1rkxO1PCosIiIiv+LDH/PYkVczgv//aQS/KVRYREREzqKi2sZTn+4B4M8j4mjn72NyopZJhUVEROQs/v31fnKOnSAs0Ecj+E2kwiIiIlKPwhOnjeC/NAE/b43gN4sKi4iISD0Wr0vneFkVCWH+GsFvMhUWERGRM8g7foJXv8oE4C+XJ+Jp1UemmbT1RUREzmDB6r1UVttJ7tyWixNDzY7T4qmwiIiI/I9dB4p49/scAGZfoRH8zkCFRURE5H88eXIE/9ieEfTRCH6noMIiIiJymk1pR1i35zCeHhrB70xUWERERE6qGcG/G4DJyZ2Iaa8R/M5ChUVEROSkD3/M46fcQvx9PPl/l3QxO46cRoVFRESEmhH88z+rGcH/p2GxtNcIfqeiwiIiIgL8Z3MW2UdPEBrgwy1DNYLf2aiwiIhIi1d4oornv0gFYMalCbTy9jQ5kfwvFRYREWnxXlyfzrGyKuJD/RnfTyP4nZEKi4iItGgHCk/w6kaN4Hd2+lMREZEWbcFne6motjMgpi2jumkEv7NSYRERkRZr98GfR/DPuiJRI/idmEOFZe7cuVgsljpLYmJivevv2LGD66+/npiYGCwWCwsXLjzr6z/xxBNYLBamT5/uSCwREZEGefKT3dgNuKJnOBd0amN2HDkLh0+DTkpK4vPPP//5BTzrf4mysjJiY2MZP348M2bMOOvrfvvtt7z00kv06tXL0UgiIiIO25R+hLW1I/jr/8+3OAeHDwl5enoSHh5eu7Rv377edfv3789TTz3FxIkT8fGpfwBPSUkJkydP5pVXXqFNGzVcERFpWna7wRMnR/D/NrkTnTWC3+k5XFhSU1OJjIwkNjaWyZMnk5WVdd4hpk6dytixYxk1atQ5P6eiooKioqI6i4iIyLn4+KcD/JhTSGtvK3dqBL9LcKiwJCcns2TJElatWsXixYvJzMxk6NChFBcXNzjA0qVL+f7775k3b55Dz5s3bx5BQUG1S1RUVIMziIhIy1FZbeepT0+O4B8epxH8LsKhwjJmzBjGjx9Pr169GD16NCtXruT48eMsW7asQd88Ozubu+66izfeeANfX1+Hnjt79mwKCwtrl+zs7AZlEBGRluWNb/aTdbSMkAAf/qgR/C7jvGYPBwcHk5CQQFpaWoOev3XrVg4dOsQFF1xQ+5jNZmPDhg08//zzVFRUYLVaz/hcHx+fs54XIyIi8r+Kyqv4x5qTI/hHaQS/KzmvP6mSkhLS09O58cYbG/T8Sy65hJ9++qnOYzfffDOJiYn85S9/qbesiIiINMRLJ0fwx4W05oYLNYLflThUWO655x7GjRtHdHQ0eXl5zJkzB6vVyqRJkwCYMmUKHTp0qD0fpbKykp07d9b+Ojc3l5SUFPz9/YmPjycgIIAePXrU+R6tW7emXbt2v3hcRETkfBwsLOdfGsHvshwqLDk5OUyaNImCggJCQkIYMmQImzdvJiQkBICsrCw8PH7+AcjLy6Nv3761X8+fP5/58+czfPhw1q1b1zjvQERE5Bw8s3ov5VV2Loxuw6Xdw8yOIw6yGIZhmB2iMRQVFREUFERhYSGBgYFmxxERESeyN7+YyxduwG7Au7cPol+0Zn45i3P9/Nb+MBERcXunRvBfnhSusuKiVFhERMStbc4oYM3uQ1g9LNx3eVez40gDqbCIiIjbMgyDeSt3ATBpQBSxIf4mJ5KGUmERERG39fFPB/ghp5BW3lbuuiTB7DhyHlRYRETELZ0+gv+2YbGEBGjYqCtTYREREbf05jf72V9QRnt/H24dGmt2HDlPKiwiIuJ2isur+McXNbeNmT6qC619NILf1amwiIiI23lpfQZHSyuJDWnNhP5RZseRRqDCIiIibiW/qJx/bswA4L7RiXhpBL9b0J+iiIi4lVMj+PtFt2F0kkbwuwsVFhERcRup+cUs+y4bgPuvSMRisZicSBqLCouIiLiNJ1fVjOAfnRRGv+i2ZseRRqTCIiIibuGbjAI+33VqBH+i2XGkkamwiIiIyzMMg3mf7AZgQv8o4jSC3+2osIiIiMv7ZPtBUrKP08rbyvRRXcyOI01AhUVERFxalc3O31fV7F3549BYQgN8TU4kTUGFRUREXNp/t2Sxr6CM9v7e3DZMI/jdlQqLiIi4rJKKap79PBWAuy7pgr9G8LstFRYREXFZL69Pp6C0ks7tWzNxQCez40gTUmERERGXlH20jFe+zATgvtFdNYLfzelPV0REXI7NbjBzWQonqmz0j2nD5T3CzY4kTUyFRUREXM7idWl8u+8Y/j6ePD2+j0bwtwAqLCIi4lJSso/zzMkTbR+6KolO7VqZnEiagwqLiIi4jNKKaqYv3YbNbnBlrwiuu6CD2ZGkmaiwiIiIy3j4w53sKygjMsiXx67pqUNBLYgKi4iIuIRV2w/w1nfZWCywYEIfglp5mR1JmpEKi4iIOL2DheXMeu8nAP48PI6LYtuZnEiamwqLiIg4Nbvd4O63UzheVkXPDkHMGJVgdiQxgQqLiIg4tVe/yuSrtAL8vKwsnNgHb099dLVE+lMXERGntSOvkL+v2gPAg1d2Jy7E3+REYhYVFhERcUrlVTbuWppCpc3Opd3DmDQgyuxIYiIVFhERcUrzVu4i7VAJIQE+PHGdLmFu6VRYRETE6azdfYjXv94PwPzxvWnn72NyIjGbCouIiDiVIyUV3PvODwDcPDiG4QkhJicSZ6DCIiIiTsMwDO5750eOlFTSNSyAv1yeaHYkcRIqLCIi4jT+s3k/X+w+hLenB89O6oOvl9XsSOIkVFhERMQppB0q5tGPdwEw6/JEEsMDTU4kzkSFRURETFdRbePO/6ZQUW1nWEIIvx8UY3YkcTIqLCIiYroFn+1l54Ei2rb2Zv5veuHhoUuYpS4VFhERMdVXaUd4aUMGAE9c15PQQF+TE4kzUmERERHTHC+r5O5lNZcwTxrQicuSwk1OJM5KhUVERExhGAaz3/uJg0XlxLZvzYNXdjM7kjgxFRYRETHF21tz+GT7QTw9LDw7sS+tvD3NjiROTIVFRESa3b4jpTy0YgcAMy9LoGfHIJMTibNTYRERkWZVZbMz/a0USittJHduy5+GxZkdSVyACouIiDSr59akkpJ9nABfTxZM6INVlzDLOVBhERGRZvPdvqM8vzYNgMev7UmHYD+TE4mrUGEREZFmUVRexfS3UrAbcN0FHRjXO9LsSOJCVFhERKRZzP1gBznHThDV1o+HrkoyO464GBUWERFpch+k5PLetlw8LLBwQh8CfL3MjiQuRoVFRESaVM6xMv66fDsA0y7uQr/otiYnElekwiIiIk3GZjeYuewHisur6dspmDsvjjc7krgoFRYREWkyL65PZ0vmUVp7W1k4oQ+eVn3sSMPoJ0dERJrEjznHeWb1XgDmXpVEdLvWJicSV6bCIiIija6sspq7lqZQbTcY2zOC3/TraHYkcXEqLCIi0uge+WgnmUdKiQjy5bFre2CxaJqtnB8VFhERaVSf7jjIf7dkY7HA0zf0JriVt9mRxA2osIiISKPJLypn1rs/AnDbsFgGxbU3OZG4CxUWERFpFHa7wT1v/8CxsiqSIgO5+9KuZkcSN6LCIiIijeK1Tfv4MvUIvl4ePDuxD96e+oiRxuPQT9PcuXOxWCx1lsTExHrX37FjB9dffz0xMTFYLBYWLlz4i3XmzZtH//79CQgIIDQ0lGuuuYY9e/Y4/EZERMQ8uw4U8eQnuwH469juxIcGmJxI3I3D9TcpKYkDBw7ULhs3bqx33bKyMmJjY3niiScIDw8/4zrr169n6tSpbN68mdWrV1NVVcVll11GaWmpo9FERMQE5VU2pi9NodJmZ1S3UCYndzI7krghT4ef4OlZb/n4X/3796d///4AzJo164zrrFq1qs7XS5YsITQ0lK1btzJs2DBH44mISDN74pPd7Mkvpr2/D09c30uXMEuTcHgPS2pqKpGRkcTGxjJ58mSysrIaNVBhYSEAbdue/eZYFRUVFBUV1VlERKR5rdtziCWb9gHw1PhetPf3MTeQuC2HCktycjJLlixh1apVLF68mMzMTIYOHUpxcXGjhLHb7UyfPp3BgwfTo0ePs647b948goKCapeoqKhGySAiIuemoKSCe96uuYT594NiGNk11ORE4s4cOiQ0ZsyY2l/36tWL5ORkoqOjWbZsGbfccst5h5k6dSrbt28/63kxp8yePZuZM2fWfl1UVKTSIiLSTAzD4C/v/siRkgoSwvyZNab+CzBEGoPD57CcLjg4mISEBNLS0s47yLRp0/joo4/YsGEDHTv++j0nfHx88PHRrkcRETO8uSWLz3cdwtvqwbMT++LrZTU7kri587pIvqSkhPT0dCIiIhr8GoZhMG3aNN5//32++OILOnfufD6RRESkiaUdKuGRj3YCcN/lXekWEWhyImkJHNrDcs899zBu3Diio6PJy8tjzpw5WK1WJk2aBMCUKVPo0KED8+bNA6CyspKdO3fW/jo3N5eUlBT8/f2Jj48Hag4Dvfnmm3zwwQcEBARw8OBBAIKCgvDz82u0NyoiIuevstrO9Le2UV5lZ0h8e/4wWP/JlObhUGHJyclh0qRJFBQUEBISwpAhQ9i8eTMhISEAZGVl4eHx806bvLw8+vbtW/v1/PnzmT9/PsOHD2fdunUALF68GIARI0bU+V6vvfYav//97xvwlkREpKksWL2X7blFBLfy4ukbeuPhoUuYpXlYDMMwzA7RGIqKiggKCqKwsJDAQO2eFBFpbF+nF/Dbf27GMODF3/Xj8h7nNpNL5GzO9fNbN3oQEZFfVVhWxcxlKRgGTOwfpbIizU6FRUREzsowDO5f/hMHCsvp3L41D17Z3exI0gKpsIiIyFm9930uH/94AE8PCwsn9KG1z3lNxBBpEBUWERGp1/6CUv72wXYAZlyaQO+oYHMDSYulwiIiImdUbbMz460USittDIhpy5+Hx5kdSVowFRYRETmj59em8X3WcQJ8PVkwoTdWXcIsJlJhERGRX9i6/xj/WJMKwKPX9KBjm1YmJ5KWToVFRETqKC6vYvpb27AbcE2fSK7u08HsSCIqLCIiUtfcFTvJPnqCDsF+PHxND7PjiAAqLCIicpqPfszj3e9z8LDAwol9CPT1MjuSCKDCIiIiJ+UdP8H97/0EwNSR8fSPaWtyIpGfqbCIiAg2u8HMZSkUlVfTOyqYOy/pYnYkkTpUWEREhFe+zGBzxlFaeVt5dkIfvKz6eBDnop9IEZEW7qecQp7+bA8Ac8clEdO+tcmJRH5JhUVEpAU7UWnjrre2UWUzGNMjnPEXdjQ7ksgZqbCIiLRgj368k4zDpYQF+vD4tT2xWDTNVpyTCouISAu1emc+b3yTBcCCG/rQprW3yYlE6qfCIiLSAh0qLucv7/4IwG3DYhkc397kRCJnp8IiItLC2O0G97z9I0dLK+keEcjdlyWYHUnkV6mwiIi0MK9/vY8New/j4+nBsxP74ONpNTuSyK9SYRERaUH2HCxm3ie7AXhgbDe6hAWYnEjk3KiwiIi0EOVVNu5auo3Kajsju4Zw40XRZkcSOWcqLCIiLcRTn+5h98Fi2vt78/ff9NYlzOJSVFhERFqADXsP86+NmQA89ZvehAT4mJxIxDEqLCIibu5oaSV3v/0DAFMGRjMyMdTkRCKOU2EREXFjhmHwl3d/5HBxBfGh/tx/RTezI4k0iAqLiIgbW/ptNqt35uNltfDsxD74eukSZnFNKiwiIm4q43AJD3+4E4D7RieSFBlkciKRhlNhERFxQ5XVdu5amsKJKhuD49txy5DOZkcSOS8qLCIibmjh53v5KbeQID8vnh7fBw8PXcIsrk2FRUTEzXyTUcDi9ekAPHFdT8KDfE1OJHL+VFhERNxI4YkqZryVgmHADRd2ZEzPCLMjiTQKFRYRETdhGAZ/Xb6dvMJyYtq1Ys64JLMjiTQaFRYRETexPCWXD3/Iw+ph4ZkJfWjt42l2JJFGo8IiIuIGso+W8eDyHQBMv6QLfTu1MTmRSONSYRERcXHVNjsz3kqhpKKaC6PbcMfIeLMjiTQ6FRYRERf3wrp0vtt/jAAfT56Z0AerLmEWN6TCIiLiwrZlHePZNakAPHJND6LatjI5kUjTUGEREXFRJRXVTH8rBZvd4KrekVzTt4PZkUSajAqLiIiLemjFDvYXlNEh2I9HrulhdhyRJqXCIiLiglb+dIC3t+ZgscCCG3oT5OdldiSRJqXCIiLiYg4UnmD2ez8BcMeIOJJj25mcSKTpqbCIiLgQu93g7mU/UHiiil4dg5g+KsHsSCLNQoVFRMSF/HNjBpvSC/DzsrJwQh+8rPpnXFoG/aSLiLiI7bmFPPXpHgDmjOtObIi/yYlEmo8Ki4iICzhRaWP6WylU2Qwu6x7GhP5RZkcSaVYqLCIiLuDxlbtIO1RCaIAPT1zfC4tF02ylZVFhERFxcmt25fPvzfsBePqG3rRt7W1yIpHmp8IiIuLEDhdXcN87PwJwy5DODO0SYnIiEXOosPyK9XsP81XaEbNjiEgLZBgG973zAwWllSSGB3Dv6K5mRxIxjafZAZxZaUU1f3nnRw4WlXNlrwj+OrY74UG+ZscSkRbi35v3s3bPYXw8PfjHpL74elnNjiRiGu1hOQsDuLxHOB4W+OjHA1zy9Dr++WUGVTa72dFExM2l5hfz2Me7AJg9JpGEsACTE4mYS4XlLPx9PJl7VRIrpg2hb6dgSittPPrxLq78x0a+ySgwO56IuKmKaht3Lk2hotrO8IQQbhoUY3YkEdOpsJyDHh2CePfPg3jy+p60aeXFnvxiJry8mZlvpXC4uMLseCLiZuZ/uoddB4po29qbp8brEmYRUGE5Zx4eFib078Tae0bw2+ROWCzw3rZcLp6/jiVfZVKtw0Qi0gg2ph7hlS8zAfj79b0IDdB5cyKgwuKw4FbePH5tT5bfMZieHYIorqhm7oc7uer5r9i6/5jZ8UTEhR0rreTut1MA+N1FnRjVPczcQCJORIWlgXpHBbN86mAevaYHQX5e7DxQxPWLN3HfOz9wtLTS7Hgi4mIMw2D2ez+RX1RBXEhrHriiu9mRRJyKCst5sHpY+N1F0Xxx93DG9+sIwLLvchg5fx1vfLMfu90wOaGIuIq3v8th1Y6DeFktPDuxL37euoRZ5HQqLI2gnb8PT43vzTt/HkhieACFJ6p44P3tXPvCV/yYc9zseCLi5DKPlDL3wx0A3H1ZV3p0CDI5kYjzUWFpRBfGtOWj/zeEOeO6E+DjyQ85hVy96Cv+uvwnCsuqzI4nIk6oymZn+tJtlFXaGBjbjtuGxpodScQpOVRY5s6di8ViqbMkJibWu/6OHTu4/vrriYmJwWKxsHDhwjOut2jRImJiYvD19SU5OZktW7Y49CaciafVg5sHd2bN3cO5pk8khgH/2ZzFyKfXsey7bB0mEpE6/rEmlR9yCgny8+LpG3rj4aFLmEXOxOE9LElJSRw4cKB22bhxY73rlpWVERsbyxNPPEF4ePgZ13nrrbeYOXMmc+bM4fvvv6d3796MHj2aQ4cOORrNqYQG+rJwYl/+e+tFdAn152hpJfe98yPjX/qanXlFZscTESfw7b6jLFqbBsDj1/YkMtjP5EQizsvhwuLp6Ul4eHjt0r59+3rX7d+/P0899RQTJ07Ex8fnjOssWLCAW2+9lZtvvpnu3bvz4osv0qpVK1599VVHozmlgXHtWHnXUO6/IpFW3la27j/Glc99yUMf7qCoXIeJRFqqovIqpi9NwW7Ab/p1ZGyvCLMjiTg1hwtLamoqkZGRxMbGMnnyZLKyshr8zSsrK9m6dSujRo36OZCHB6NGjeLrr79u8Os6Gy+rB7cNi2PN3cMZ2ysCuwGvfbWPS55ez/JtuRiGDhOJtDR/W76d3OMn6NS2FXOvSjI7jojTc6iwJCcns2TJElatWsXixYvJzMxk6NChFBcXN+ibHzlyBJvNRlhY3eFIYWFhHDx48KzPraiooKioqM7i7CKC/Fj02wv49y0DiG3fmsPFFUx/K4WJL29mb37DtqGIuJ4PUnJZnpKH1cPCMxP64O/jaXYkEafnUGEZM2YM48ePp1evXowePZqVK1dy/Phxli1b1lT56jVv3jyCgoJql6ioqGbP0FBDu4TwyfSh3Du6K75eHnyTeZQrnv2Sx1fuorSi2ux4ItKEso+W8df3twNw58Vd6BfdxuREIq7hvC5rDg4OJiEhgbS0tAY9v3379litVvLz8+s8np+fX+9JuqfMnj2bwsLC2iU7O7tBGczi42ll6sh4Vs8YzmXdw6i2G7y8IYNLnl7Pxz8e0GEiETdksxvcvewHiiuq6Rfdhqkj48yOJOIyzquwlJSUkJ6eTkREw04W8/b2pl+/fqxZs6b2Mbvdzpo1axg4cOBZn+vj40NgYGCdxRVFtW3Fy1Mu5NXfX0intq04WFTO1De/Z8qrW0g/XGJ2PBFpRC+uT2fLvqP4+3jyzA198LRqFJbIuXLob8s999zD+vXr2bdvH5s2beLaa6/FarUyadIkAKZMmcLs2bNr16+srCQlJYWUlBQqKyvJzc0lJSWlzh6ZmTNn8sorr/D666+za9cubr/9dkpLS7n55psb6S26hosTw/hsxjDuuqQL3p4efJl6hMsXbuCpT3dzotJmdjwROU8p2cd5ZvVeAB66KolO7VqZnEjEtTh0pldOTg6TJk2ioKCAkJAQhgwZwubNmwkJCQEgKysLD4+fO1BeXh59+/at/Xr+/PnMnz+f4cOHs27dOgAmTJjA4cOH+dvf/sbBgwfp06cPq1at+sWJuC2Br5eVGZcmcN0FHZi7Ygdr9xxm0dp0lm/L42/junNZ9zAsFg2VEnE1pRXVTF+6jWq7wZW9Irjugg5mRxJxORbDTU6WKCoqIigoiMLCQpc9PHQ6wzD4bGc+D3+4k9zjJwAY2TWEuVclEd2utcnpRMQRs979kaXfZhMZ5Msndw0jqJWX2ZFEnMa5fn7rAKqTslgsjE4KZ/XMYdwxIg4vq4W1ew5z6TMbWPj5XsqrdJhIxBWs2n6Qpd9mY7HAggl9VFZEGkiFxcm18vbkvssTWTV9GEPi21NZbWfh56lc9swG1u527dsXiLi7/KJyZr33IwB/Hh7HRbHtTE4k4rpUWFxEXIg//75lAM//ti9hgT5kHS3j5iXfctv/fUfOsTKz44nI/7CfvIT5eFkVPToEMmNUgtmRRFyaCosLsVgsXNkrkjV3j+C2YbF4elj4bGc+oxasZ9HaNCqqdZhIxFm8+lUmG9OO4OvlwbMT++LtqX9uRc6H/ga5IH8fT+6/ohsr7xrKgM5tKa+y89Snexiz8Es2ph4xO55Ii1ZUXsWitWn8fdUeAP52ZRJxIf4mpxJxfbpKyMUZhsHylFwe+3g3R0oqABjbK4K/ju1GRJBuVS/SXI6WVvLaV5ks2bSP4vKaW2yM6RHOC5Mv0DgCkbM4189vFRY3UVRexYLP9vJ/X+/DbkArbyvTR3Xh5sGd8dI0TZEmk19UzisbMnhzSxZlJ4c8dgn1546RcYzrFalptiK/QoWlhdqRV8iDy7fzfdZxABLC/Hn46h66OkGkkWUfLePF9em8/V0OlTY7AD06BDJtZDyXdQ/Hw0N7VUTOhQpLC2a3G7zzfQ5PfLKbo6WVAFzTJ5L7x3YjNMDX5HQiri3tUAmL16WzPCUXm73mn8/+MW2YOjKe4QkhOvwj4iAVFuF4WSVPfbqHN7dkYRgQ4OPJzMsSuPGiaO2mFnHQjrxCXlibzsrtBzj1r+bQLu2ZNjKeZO3BFGkwFRap9UP2cR78YDs/5hQC0C0ikEevSaJfdFuTk4k4v637j7FobRpfnDao8dLuYUwbGU/vqGDzgom4CRUWqcNmN1j6bRZ/X7WHwhNVAIzv15FZYxJp5+9jcjoR52IYBpvSC3j+izS+zigAwMMCV/aK5I6RcSSG698YkcaiwiJnVFBSwZOrdrPsuxwAgvy8uHd0VyYN6IRVJwlKC2cYBl/sPsRzX6SRkn0cAC+rhev6duT2EXHEtNeNR0UamwqLnNXW/Uf56/Id7DpQBECvjkE8cnUP7eKWFslmN/hk+wEWrU2v/Tvh4+nBpAGduG1YLJHBmmkk0lRUWORXVdvs/Gfzfp7+bC/FFdVYLDBpQCfuG92V4FbeZscTaXJVNjvLt+WyeF06GUdKAWjtbeXGgTHcMqQzIQE6XCrS1FRY5JwdKi5n3srdvL8tF4C2rb2ZdXkiv+nXUbMkxC2VV9l4+7tsXlyfQe7xE0DN4dE/DO7M7wfFENTKy+SEIi2HCos47JuMAh78YDt780sAuKBTMI9c04OkyCCTk4k0jtKKat74Zj+vfJnJ4eKaW1m09/fh1qGdmXxRNP4+niYnFGl5VFikQapsdpZ8tY+Fn++ltNKGhwWmDIxh5mUJBPrqf53imgrLqliyaR+vbcrkeFnNVXIdgv340/BYbrgwCl8vq8kJRVouFRY5LwcLy3n045189OMBoOZ/ofdfkci1fTtokqe4jCMlFfxrYyb//no/JRU1NyTs3L41t4+I45o+HfD21ABFEbOpsEij2Jh6hL+t2E7G4ZoTEgd0bssjV/ega3iAyclE6neg8AQvrc9g6bdZlFfV3OcnMTyAqSPjuaJnhC7hF3EiKizSaCqqbfzzy0ye+yKV8io7Vg8Lfxgcw12jEnTMX5zKviOlvLg+nXe/z6HKVvNPW++oYP7fyHgu6RaqvYMiTkiFRRpd7vETPPzhDj7dkQ9AWKAPfx3bnSt7ReiDQEy1N7+YRWvT+PCHPE7ej5CLYtsybWQXBse308+niBNTYZEms3bPIeau2MH+gjIAhsS3Z+5VScSH+pucTFqaH3OO8/wXaXy2M7/2sZFdQ5h2cbzulSXiIlRYpEmVV9l4cX06L6xLp7LajpfVwh+HxvL/Lo6nlbcOE0nT2pJ5lOfXprFh72EALBYY0yOcO0bE06ODLsMXcSUqLNIssgrKmPvhjto72XYI9uPBK7szOilMu+GlURmGwYbUIyz6Io0t+44CYPWwcHXvmhsSxofqRHARV6TCIs3GMAxW78znoQ931k4NHdE1hLnjknSzODlvdrvBZzvzWbQ2jZ9yCwHwtnrwmws78udhcXRq18rkhCJyPlRYpNmdqLTx/NpUXt6QQZXNwNvTgz8Pj+OOEXEazCUOq7bZ+ejHA7ywLq12+rKfl5XfJnfi1qGxhAf5mpxQRBqDCouYJuNwCXNW7ODL1CMARLX146Grkrg4MczkZOIKKqptvPd9Li+uT689sTvAx5ObBsVw8+AY2vnrhoQi7kSFRUxlGAYrfzrIIx/t5GBROQCXdg/jb1d2J6qtduHLL52otLH02yxe3pDBgcKan5m2rb25ZUhnbhwYrVtDiLgpFRZxCqUV1fxjTSr/2phJtd3A18uDaSPjuXVYLD6eOkwkUFxexb837+dfX2ZSUFoJ1Mz4uXVoLL9N7qSrzkTcnAqLOJW9+cU8uHw732TWXN3RuX1rHroqiWEJISYnE7McK63kta8yWbJpH0XlNff5iWrrx5+Hx/Gbfh1VaEVaCBUWcTqGYbDihzwe/XgXh4srALiiZzgPXtmdiCA/k9NJczlUVM4rX2bwxjdZlFXaAIgP9eeOEXFc1TsST6tuSCjSkqiwiNMqKq/imdV7eX3TPuwGtPK2ctclXbh5cGfdPdeNZR8t46UN6Sz7LofK6pobEiZFBjJtZDyjk8Lx0A0JRVokFRZxejvzinjwg+1s3X8MgJh2rRjQuS3xof7EhdQsUW1b6c66Li79cAkvrE3ng5Rcqk/e6OfC6DZMvTieEQkhGjAo0sKpsIhLsNsN3v0+hyc+2V17wuXpvK0edG7fmrjQ1sSH+BN3sszEhrTWyZhObmdeEYvWpbHypwOc+ldmSHx7pl0cT3LntioqIgKosJgdRxxUeKKKDXsPk3aohPTDJaQfLiXjcAkVJw8dnEmHYL+TBaY1cSH+tXtm2vt768PQRN9nHWPRF2msOXm7BoBR3cKYdnE8faKCzQsmIk5JhUVcns1ukHf8xGklpuTkr0s5eoa9MacE+Xn9osTEhfoT1cZPJ3Q2EcMw+Dq9gOfXprEpvQAADwuM7RXJHSPi6Bahv5MicmYqLOLWjpZW1pSYQ3WLTPaxMur7ifa2ehDTvlXdInPy8FJrHx1eagjDMPhi9yGeX5vGtqzjAHh6WLjugg7cPiKezrqXlIj8inP9/Na/0uKS2rb2pm3rtvSPaVvn8fIqG5lHSuuUmPRDJWQcKaG8ys7e/JLa+9KcLjLIt/b8mLhQ/5Pny7QmxN9Hh5fOwGY3+GT7ARatTWfXgSIAvD09mNg/ituGxdKxjaYZi0jj0h4WaRHsdoPc4yd+UWTSD5ec8WTfUwJ9PX8uMrV7ZlrTqW2rFnl4qcpm54OUPF5Yl0bG4VIAWntb+d1F0dwytDOhAbohoYg4RoeERM7RsVOHl06e7HvqnJnso2XY6/nb4WW1ENPutPNkQlvXlhp3PLxUXmXj7a05vLQ+nZxjJ4Cac4V+f/KGhMGtvE1OKCKuSoVF5DyVV9nYV1BK+qHTDzHVLOVV9V+9FBHkW2dvzKlfhwS43uGl0opq3vwmi1e+zODQyenE7f29+ePQWH53UTT+bljORKR5qbCINBG73SCv8ESdvTGnDi8dKan/8FKAr2ftXpjT58p0atsKLyc7vFR4oorXN+3jta8yOVZWBdSc53PbsFgmDuiEr5fu8yMijUOFRcQEx8tOXb1Ud69M1q8cXopu1/qMl2I39x6MIyUV/GtjJv/+ej8lFTU3JIxp14rbR8Rxbd+OunWCiDQ6FRYRJ1JRbWPfkbLavTFpp86ZOVTKiSpbvc8LD/T9xZTf+FB/Qhv58NKBwhO8tD6Dpd9m1R7u6hoWwB0j4xjbM6JFnmAsIs1DhUXEBdjtBgeKymtKTJ0BeaUcKamo93n+Pp41e2RC/evslYlu59jhpf0Fpby4Pp13tuZQZav5p6B3xyCmjoxnVLcw3ZBQRJqcCouIiyssqyL9yGlF5uRhpv0FpfUeXvL0sBDdrtX/zJOpOfk3wNerdr29+cW8sDaNFT/k1b5Wcue2TLs4niHx7V3u5GARcV0qLCJuqqLaxv6Csl9M+U0/XEJZZf2Hl8ICfYgL8cfT6sGGvYdrHx/RNYSpI+N/MYRPRKQ5aNKtiJvy8bSSEBZAQlhAnccNw+BAYXndS7APlZJ2uITDxRXkF9Usp1yeFM7UkfH07BjU3G9BRMRhKiwibsJisRAZ7EdksB9Du4TU+b3CE1VknCwyh0squLRbGF3+p/CIiDgzFRaRFiDIz4u+ndrQt1Mbs6OIiDSIrlUUERERp6fCIiIiIk5PhUVEREScngqLiIiIOD0VFhEREXF6KiwiIiLi9FRYRERExOmpsIiIiIjTU2ERERERp6fCIiIiIk7PocIyd+5cLBZLnSUxMfGsz3n77bdJTEzE19eXnj17snLlyjq/X1JSwrRp0+jYsSN+fn50796dF1980fF3IiIiIm7L4T0sSUlJHDhwoHbZuHFjvetu2rSJSZMmccstt7Bt2zauueYarrnmGrZv3167zsyZM1m1ahX/+c9/2LVrF9OnT2fatGmsWLGiYe9IRERE3I7DhcXT05Pw8PDapX379vWu++yzz3L55Zdz77330q1bNx555BEuuOACnn/++dp1Nm3axE033cSIESOIiYnhtttuo3fv3mzZsqVh70hERETcjsN3a05NTSUyMhJfX18GDhzIvHnz6NSp0xnX/frrr5k5c2adx0aPHs3y5ctrvx40aBArVqzgD3/4A5GRkaxbt469e/fyzDPPnDVHRUUFFRUVtV8XFhYCUFRU5OhbEhEREZOc+tw2DOPsKxoOWLlypbFs2TLjhx9+MFatWmUMHDjQ6NSpk1FUVHTG9b28vIw333yzzmOLFi0yQkNDa78uLy83pkyZYgCGp6en4e3tbbz++uu/mmXOnDkGoEWLFi1atGhxgyU7O/usn/sO7WEZM2ZM7a979epFcnIy0dHRLFu2jFtuucWRl6r13HPPsXnzZlasWEF0dDQbNmxg6tSpREZGMmrUqHqfN3v27Dp7b+x2O0ePHqVdu3ZYLJYGZTmToqIioqKiyM7OJjAwsNFeV+rSdm4+2tbNQ9u5eWg7N4+m3M6GYVBcXExkZORZ13P4kNDpgoODSUhIIC0t7Yy/Hx4eTn5+fp3H8vPzCQ8PB+DEiRPcf//9vP/++4wdOxaoKUIpKSnMnz//rIXFx8cHHx+fX+RpKoGBgfrL0Ay0nZuPtnXz0HZuHtrOzaOptnNQUNCvrnNec1hKSkpIT08nIiLijL8/cOBA1qxZU+ex1atXM3DgQACqqqqoqqrCw6NuDKvVit1uP59oIiIi4kYc2sNyzz33MG7cOKKjo8nLy2POnDlYrVYmTZoEwJQpU+jQoQPz5s0D4K677mL48OE8/fTTjB07lqVLl/Ldd9/x8ssvAzVNbfjw4dx77734+fkRHR3N+vXr+b//+z8WLFjQyG9VREREXJVDhSUnJ4dJkyZRUFBASEgIQ4YMYfPmzYSEhACQlZVVZ2/JoEGDePPNN/nrX//K/fffT5cuXVi+fDk9evSoXWfp0qXMnj2byZMnc/ToUaKjo3nsscf485//3Ehv8fz4+PgwZ86cXxx+ksal7dx8tK2bh7Zz89B2bh7OsJ0thvFr1xGJiIiImEv3EhIRERGnp8IiIiIiTk+FRURERJyeCouIiIg4PRUWYNGiRcTExODr60tycvJZb7y4ZMkSLBZLncXX17cZ07ouR7YzwPHjx5k6dSoRERH4+PiQkJDAypUrmymt63JkO48YMeIXP88Wi6V2kKOcnaM/0wsXLqRr1674+fkRFRXFjBkzKC8vb6a0rsuR7VxVVcXDDz9MXFwcvr6+9O7dm1WrVjVjWte0YcMGxo0bR2RkJBaLpc49/+qzbt06LrjgAnx8fIiPj2fJkiVNG/JXb9rj5pYuXWp4e3sbr776qrFjxw7j1ltvNYKDg438/Pwzrv/aa68ZgYGBxoEDB2qXgwcPNnNq1+Podq6oqDAuvPBC44orrjA2btxoZGZmGuvWrTNSUlKaOblrcXQ7FxQU1PlZ3r59u2G1Wo3XXnuteYO7IEe39RtvvGH4+PgYb7zxhpGZmWl8+umnRkREhDFjxoxmTu5aHN3O9913nxEZGWl8/PHHRnp6uvHCCy8Yvr6+xvfff9/MyV3LypUrjQceeMB47733DMB4//33z7p+RkaG0apVK2PmzJnGzp07jeeee86wWq3GqlWrmixjiy8sAwYMMKZOnVr7tc1mMyIjI4158+adcf3XXnvNCAoKaqZ07sPR7bx48WIjNjbWqKysbK6IbsHR7fy/nnnmGSMgIMAoKSlpqohuw9FtPXXqVOPiiy+u89jMmTONwYMHN2lOV+fodo6IiDCef/75Oo9dd911xuTJk5s0pzs5l8Jy3333GUlJSXUemzBhgjF69Ogmy9WiDwlVVlaydevWOvcs8vDwYNSoUXz99df1Pq+kpITo6GiioqK4+uqr2bFjR3PEdVkN2c4rVqxg4MCBTJ06lbCwMHr06MHjjz+OzWZrrtgup6E/z6f717/+xcSJE2ndunVTxXQLDdnWgwYNYuvWrbWHMzIyMli5ciVXXHFFs2R2RQ3ZzhUVFb84TO/n58fGjRubNGtL8/XXX//ifn+jR48+539rGqJFF5YjR45gs9kICwur83hYWBgHDx4843O6du3Kq6++ygcffMB//vMf7HY7gwYNIicnpzkiu6SGbOeMjAzeeecdbDYbK1eu5MEHH+Tpp5/m0UcfbY7ILqkh2/l0W7ZsYfv27fzxj39sqohuoyHb+re//S0PP/wwQ4YMwcvLi7i4OEaMGMH999/fHJFdUkO28+jRo1mwYAGpqanY7XZWr17Ne++9x4EDB5ojcotx8ODBM/65FBUVceLEiSb5ni26sDTEwIEDmTJlCn369GH48OG89957hISE8NJLL5kdza3Y7XZCQ0N5+eWX6devHxMmTOCBBx7gxRdfNDua2/rXv/5Fz549GTBggNlR3NK6det4/PHHeeGFF/j+++957733+Pjjj3nkkUfMjuZWnn32Wbp06UJiYiLe3t5MmzaNm2+++Rc32RXX49C9hNxN+/btsVqt5Ofn13k8Pz+f8PDwc3oNLy8v+vbtS1paWlNEdAsN2c4RERF4eXlhtVprH+vWrRsHDx6ksrISb2/vJs3sis7n57m0tJSlS5fy8MMPN2VEt9GQbf3ggw9y44031u7B6tmzJ6Wlpdx222088MAD+kA9g4Zs55CQEJYvX055eTkFBQVERkYya9YsYmNjmyNyixEeHn7GP5fAwED8/Pya5Hu26L8h3t7e9OvXjzVr1tQ+ZrfbWbNmDQMHDjyn17DZbPz0009EREQ0VUyX15DtPHjwYNLS0rDb7bWP7d27l4iICJWVepzPz/Pbb79NRUUFv/vd75o6pltoyLYuKyv7RSk5VcgN3dLtjM7nZ9rX15cOHTpQXV3Nu+++y9VXX93UcVuUgQMH1vlzAVi9evU5f3Y2SJOdzusili5davj4+BhLliwxdu7cadx2221GcHBw7aXKN954ozFr1qza9R966CHj008/NdLT042tW7caEydONHx9fY0dO3aY9RZcgqPbOSsrywgICDCmTZtm7Nmzx/joo4+M0NBQ49FHHzXrLbgER7fzKUOGDDEmTJjQ3HFdmqPbes6cOUZAQIDx3//+18jIyDA+++wzIy4uzrjhhhvMegsuwdHtvHnzZuPdd9810tPTjQ0bNhgXX3yx0blzZ+PYsWMmvQPXUFxcbGzbts3Ytm2bARgLFiwwtm3bZuzfv98wDMOYNWuWceONN9auf+qy5nvvvdfYtWuXsWjRIl3W3Byee+45o1OnToa3t7cxYMAAY/PmzbW/N3z4cOOmm26q/Xr69Om164aFhRlXXHGFru8/R45sZ8MwjE2bNhnJycmGj4+PERsbazz22GNGdXV1M6d2PY5u5927dxuA8dlnnzVzUtfnyLauqqoy5s6da8TFxRm+vr5GVFSUcccdd+iD9Bw4sp3XrVtndOvWzfDx8THatWtn3HjjjUZubq4JqV3L2rVrDeAXy6lte9NNNxnDhw//xXP69OljeHt7G7GxsU0+v8liGNoXKSIiIs6tRZ/DIiIiIq5BhUVEREScngqLiIiIOD0VFhEREXF6KiwiIiLi9FRYRERExOmpsIiIiIjTU2ERERERp6fCIiIiIk5PhUVEREScngqLiIiIOD0VFhEREXF6/x8heb2LxzrCRgAAAABJRU5ErkJggg==\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "It's clear the optimal value lies between 0.6 and 0.8. Finally we can fine-tune l1_ratio by optimization algorithm (this may take a while):"
      ],
      "metadata": {
        "id": "JNphpEscp--U"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "ce_opt_res = minimize_scalar(l1_r_opt_fun, bounds = (.6, .8), tol=1e-4, \n",
        "                             options={'maxiter':100, 'disp':True})\n",
        "l1_r_best = ce_opt_res.x\n",
        "print(l1_r_best)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "4HB-Jdbqqbui",
        "outputId": "da55ea4b-a416-4141-d5cd-02ba5b1dc9a7"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "/usr/local/lib/python3.9/dist-packages/scipy/optimize/_minimize.py:892: RuntimeWarning: Method 'bounded' does not support relative tolerance in x; defaulting to absolute tolerance.\n",
            "  warn(\"Method 'bounded' does not support relative tolerance in x; \"\n"
          ]
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "\n",
            "Optimization terminated successfully;\n",
            "The returned value satisfies the termination criteria\n",
            "(using xtol =  0.0001 )\n",
            "0.6645052789645336\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Use the optimal l1_ratio to fit the custom ElasticNet model:"
      ],
      "metadata": {
        "id": "Vi021nIhuHT_"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "model_ce = CustomENetCV(cv, l1_ratio=l1_r_best, standardize=True, fit_intercept=True, \n",
        "                        alphas=None, tol=1e-4, max_iter=10000, random_state=2023)\n",
        "model_ce.fit(X_train, y_train, penalty)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Po-yDR0csrZB",
        "outputId": "c116846f-28ad-4c20-86c8-16d6d41f9e23"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "CV round 1\n",
            "CV round 2\n",
            "CV round 3\n",
            "CV round 4\n",
            "CV round 5\n",
            "CV round 6\n",
            "CV round 7\n",
            "CV round 8\n",
            "CV round 9\n",
            "CV round 10\n",
            "CV round 11\n",
            "CV round 12\n",
            "CV round 13\n",
            "CV round 14\n",
            "CV round 15\n",
            "CV round 16\n",
            "CV round 17\n",
            "CV round 18\n",
            "CV round 19\n",
            "CV round 20\n",
            "CV round 21\n",
            "CV round 22\n",
            "CV round 23\n",
            "CV round 24\n",
            "CV round 25\n",
            "CV round 26\n",
            "CV round 27\n",
            "CV round 28\n",
            "CV round 29\n",
            "CV round 30\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Test RMSE:"
      ],
      "metadata": {
        "id": "uXGJFJ6TuY6b"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "y_pred = model_ce.predict(X_test).reshape(-1, 1)\n",
        "print(mean_squared_error(y_test, y_pred, squared=False))"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "nqdd0BfJs_tM",
        "outputId": "60d43ce0-eea8-406f-df28-0648e7f5cd44"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "2.4728960379551017\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Customized penalty allows one to suppress certain variables. We first plot the the coefficients of the model:"
      ],
      "metadata": {
        "id": "jwlPVA-5HRX-"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "xtks = np.arange(X.shape[1])\n",
        "plt.bar(xtks, model_ce.w[:-1], width=0.4)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 447
        },
        "id": "wPOO0iKqHNxl",
        "outputId": "9897c182-2308-4364-ea44-4d7c854ee0b3"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<BarContainer object of 245 artists>"
            ]
          },
          "metadata": {},
          "execution_count": null
        },
        {
          "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": [
        "Suppose we want to suppress variables after 40, we can do:"
      ],
      "metadata": {
        "id": "uElXdd9II_Om"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "new_penalty = penalty.copy()\n",
        "new_penalty[40:] = 2\n",
        "\n",
        "model_ce_new = CustomENet(alpha=model_ce.alpha_best, l1_ratio=l1_r_best, standardize=True, fit_intercept=True, tol=1e-4, max_iter=10000, random_state=2023)\n",
        "model_ce_new.fit(X_train, y_train, new_penalty)\n",
        "plt.bar(xtks, model_ce_new.w[:-1], width=0.4)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 447
        },
        "id": "XSfF3YPRIVXu",
        "outputId": "a220a7ea-b40d-485b-ea0e-90d084ceebf8"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<BarContainer object of 245 artists>"
            ]
          },
          "metadata": {},
          "execution_count": null
        },
        {
          "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": [
        "Setting the penalty to infinite literally means to set the coefficient to 0."
      ],
      "metadata": {
        "id": "iiEr3FP0KVJ_"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "new_penalty = penalty.copy()\n",
        "new_penalty[40:] = np.inf\n",
        "\n",
        "model_ce_new = CustomENet(alpha=model_ce.alpha_best, l1_ratio=l1_r_best, standardize=True, fit_intercept=True, tol=1e-4, max_iter=10000, random_state=2023)\n",
        "model_ce_new.fit(X_train, y_train, new_penalty)\n",
        "plt.bar(xtks, model_ce_new.w[:-1], width=0.4)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 447
        },
        "id": "0fh_FuwWKLXP",
        "outputId": "c233cf98-42f9-44e6-b2a7-74648f27554e"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<BarContainer object of 245 artists>"
            ]
          },
          "metadata": {},
          "execution_count": null
        },
        {
          "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": [
        "In contrast to sklearn's ElasticNet, CustomENet and CustomENet incorporate Ridge regression. Simply set l1_ratio to 0. But for Ridge we need to provide the alphas."
      ],
      "metadata": {
        "id": "gAmSH0iaLTXn"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "alphas = np.geomspace(0.01, 10, num=100)\n",
        "model_rd = CustomENetCV(cv, l1_ratio=0, standardize=True, fit_intercept=True, \n",
        "                        alphas=alphas, tol=1e-4, max_iter=10000, random_state=2023)\n",
        "model_rd.fit(X_train, y_train, penalty)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "_mMScqVqJY0u",
        "outputId": "e029ae0f-00cd-4ca8-840f-daae077a38d3"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "CV round 1\n",
            "CV round 2\n",
            "CV round 3\n",
            "CV round 4\n",
            "CV round 5\n",
            "CV round 6\n",
            "CV round 7\n",
            "CV round 8\n",
            "CV round 9\n",
            "CV round 10\n",
            "CV round 11\n",
            "CV round 12\n",
            "CV round 13\n",
            "CV round 14\n",
            "CV round 15\n",
            "CV round 16\n",
            "CV round 17\n",
            "CV round 18\n",
            "CV round 19\n",
            "CV round 20\n",
            "CV round 21\n",
            "CV round 22\n",
            "CV round 23\n",
            "CV round 24\n",
            "CV round 25\n",
            "CV round 26\n",
            "CV round 27\n",
            "CV round 28\n",
            "CV round 29\n",
            "CV round 30\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Path plot of Ridge:"
      ],
      "metadata": {
        "id": "_DGmgw1QM0sC"
      }
    },
    {
      "cell_type": "code",
      "source": [
        " _ = path_stats(model_rd.alphas, model_rd.cv_errs, title='custom ridge mse')"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 457
        },
        "id": "BXIql0emM0DA",
        "outputId": "cd63096d-9378-4c86-851f-5984813fa484"
      },
      "execution_count": null,
      "outputs": [
        {
          "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": [
        "Test RMSE:"
      ],
      "metadata": {
        "id": "pQaoFySemOGn"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "y_pred = model_rd.predict(X_test).reshape(-1, 1)\n",
        "print(mean_squared_error(y_test, y_pred, squared=False))"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "LU63AB_TlrVX",
        "outputId": "ca6019c6-4550-4009-c7df-26713afd949b"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "2.509452892037787\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Custom penalty allows us to do basic two-stage adaptive Lasso regression. Use coefficients of Ridge as the initial estimator to generate the penalty weight vector: "
      ],
      "metadata": {
        "id": "ZOxzN8a8mXlw"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "init_beta = model_rd.w[:-1]\n",
        "nz_f = init_beta != .0\n",
        "adt_penalty = np.full(X.shape[1], np.inf)\n",
        "adt_penalty[nz_f] = 1 / np.abs(init_beta[nz_f])\n",
        "adt_penalty[(n_dominant+n_weak):(n_dominant+n_weak+n_cat)] = .0"
      ],
      "metadata": {
        "id": "P4TfdlCsmWGu"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "Run adaptive Lasso regression:"
      ],
      "metadata": {
        "id": "8uBFq07g4mnO"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "model_cl_adt = CustomENetCV(cv, l1_ratio=1, standardize=True, fit_intercept=True, \n",
        "                            alphas=None, tol=1e-4, max_iter=10000, random_state=2023)\n",
        "model_cl_adt.fit(X_train, y_train, adt_penalty)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "FtPJgvBRo1uh",
        "outputId": "4237b651-373f-4801-9f8f-a384c78114d3"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "CV round 1\n",
            "CV round 2\n",
            "CV round 3\n",
            "CV round 4\n",
            "CV round 5\n",
            "CV round 6\n",
            "CV round 7\n",
            "CV round 8\n",
            "CV round 9\n",
            "CV round 10\n",
            "CV round 11\n",
            "CV round 12\n",
            "CV round 13\n",
            "CV round 14\n",
            "CV round 15\n",
            "CV round 16\n",
            "CV round 17\n",
            "CV round 18\n",
            "CV round 19\n",
            "CV round 20\n",
            "CV round 21\n",
            "CV round 22\n",
            "CV round 23\n",
            "CV round 24\n",
            "CV round 25\n",
            "CV round 26\n",
            "CV round 27\n",
            "CV round 28\n",
            "CV round 29\n",
            "CV round 30\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "_ = path_stats(model_ce_adt.alphas, model_cl.cv_errs, title='adaptive custom lasso mse')"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 457
        },
        "id": "NCIob5FNuluG",
        "outputId": "a1d13d8a-4605-48c1-b157-96e09c334537"
      },
      "execution_count": null,
      "outputs": [
        {
          "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": [
        "Test RMSE:"
      ],
      "metadata": {
        "id": "uEaQ1kcbRBuj"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "y_pred = model_ce_adt.predict(X_test).reshape(-1, 1)\n",
        "print(mean_squared_error(y_test, y_pred, squared=False))"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "nLWboba2r_Jc",
        "outputId": "5638ed7a-7e24-4efa-bc85-b992cae032c9"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "2.6196033069031475\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "The preformance is even worse. If we plot the coefficients, we see that large coefficients were relaxed as expceted. However, these also include many noise varaibles which introduced more noise to the prediction."
      ],
      "metadata": {
        "id": "cddQRwCzRNd7"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "xtks = np.arange(X.shape[1])\n",
        "plt.bar(xtks, model_ce_adt.w[:-1], width=0.4)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 447
        },
        "id": "og1FMJt8pM1h",
        "outputId": "a7f314ae-032d-483a-c6cb-8b247ca3ffc7"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<BarContainer object of 245 artists>"
            ]
          },
          "metadata": {},
          "execution_count": null
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {}
        }
      ]
    }
  ]
}