Book_Chapter4.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "provenance": [],
      "authorship_tag": "ABX9TyNqTOY8VX0Ub85VZZ1POLIT",
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/Mateusz-best-creator/Learning_ML/blob/main/Book_Chapter4.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "72OvO8s07ZXt"
      },
      "outputs": [],
      "source": [
        "import numpy as np\n",
        "\n",
        "np.random.seed(42)\n",
        "m = 100\n",
        "X = 2 * np.random.rand(m, 1)\n",
        "y = 4 + 3 * X + np.random.randn(m, 1)"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "import matplotlib.pyplot as plt\n",
        "\n",
        "plt.scatter(X, y)\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 430
        },
        "id": "LtHAkEB_B3Oq",
        "outputId": "0c0825ce-c2a8-44d4-e278-12589a261d5c"
      },
      "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": [
        "## Normal Equation"
      ],
      "metadata": {
        "id": "PPMebPRzFhjT"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "from sklearn.preprocessing import add_dummy_feature\n",
        "from scipy.linalg import inv\n",
        "\n",
        "X_b = add_dummy_feature(X)\n",
        "theta_best = inv(X_b.T @ X_b) @ X_b.T @ y\n",
        "theta_best"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "dg7HNw-4CKsZ",
        "outputId": "7ab4120a-f11e-4e94-ad35-9dd870e4047e"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[4.21509616],\n",
              "       [2.77011339]])"
            ]
          },
          "metadata": {},
          "execution_count": 11
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "X_new = [[0], [2]]\n",
        "X_new_b = add_dummy_feature(X_new)\n",
        "y_predict = X_new_b @ theta_best\n",
        "y_predict"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "uIDp2_KHCfj1",
        "outputId": "b0c7bca2-892a-40d6-d28c-fd28da7dc429"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[4.21509616],\n",
              "       [9.75532293]])"
            ]
          },
          "metadata": {},
          "execution_count": 14
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "plt.plot(X_new, y_predict, \"r-\", label=\"Predictions\")\n",
        "plt.plot(X, y, \"b.\")\n",
        "plt.legend()\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 430
        },
        "id": "c2W0IlcdDJy9",
        "outputId": "fdd6cdde-8264-4607-d224-2e7f0b81b950"
      },
      "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": "code",
      "source": [
        "from sklearn.linear_model import LinearRegression\n",
        "\n",
        "lr = LinearRegression()\n",
        "lr.fit(X, y)\n",
        "lr.coef_, lr.intercept_"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "4M8I-1BrEGoa",
        "outputId": "8c9f0764-5dff-42fa-ebdd-6dc2795220ff"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(array([[0.84362064]]), array([3.56401543]))"
            ]
          },
          "metadata": {},
          "execution_count": 63
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Gradient Descent"
      ],
      "metadata": {
        "id": "jW5BCnLCEtfk"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Batch Gradient Descent"
      ],
      "metadata": {
        "id": "yjZaezxiG0kC"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "eta = 0.1\n",
        "lr = 0.05\n",
        "n_epochs = 1000\n",
        "m = len(X_b)\n",
        "\n",
        "np.random.seed(42)\n",
        "theta = np.random.rand(2, 1)\n",
        "\n",
        "for epoch in range(n_epochs):\n",
        "  gradients = 2 / m * X_b.T @ (X_b @ theta - y)\n",
        "  theta = theta - lr * gradients\n",
        "\n",
        "print(f\"Learned Parameters:\\n{theta}\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "SCpcphmGFluE",
        "outputId": "1321a377-516a-46d4-ccbb-1f5889fafe12"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Learned Parameters:\n",
            "[[1.03315353]\n",
            " [2.5308619 ]]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Stochastic Gradient Descent"
      ],
      "metadata": {
        "id": "V2_QTJixFlw0"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "n_epochs = 50\n",
        "t0, t1 = 5, 50 # Learning schedule hyperparameters\n",
        "\n",
        "def learning_schedule(t):\n",
        "  return t0 / (t + t1)\n",
        "\n",
        "np.random.seed(42)\n",
        "theta = np.random.randn(2, 1)\n",
        "\n",
        "for epoch in range(n_epochs):\n",
        "  for iteration in range(m):\n",
        "    random_index = np.random.randint(m)\n",
        "    xi = X_b[random_index : random_index + 1]\n",
        "    yi = y[random_index : random_index + 1]\n",
        "    gradients = 2 * xi.T @ (xi @ theta - yi) # For SGD do not divide by m!\n",
        "    eta = learning_schedule(epoch * m + iteration)\n",
        "    theta = theta - eta * gradients\n",
        "\n",
        "print(f\"Learned Parameters:\\n{theta}\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "zSR2kPFIG5X-",
        "outputId": "86375c83-aa9b-46fd-9ea7-16316fb11c8a"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Learned Parameters:\n",
            "[[0.97923723]\n",
            " [2.48630954]]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "from sklearn.linear_model import SGDRegressor\n",
        "\n",
        "sgd_reg = SGDRegressor(max_iter=1000,\n",
        "                       tol=1e-5,\n",
        "                       penalty=None,\n",
        "                       eta0=0.01,\n",
        "                       n_iter_no_change=100)\n",
        "sgd_reg.fit(X, y.ravel())"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 74
        },
        "id": "XHkHJhjoG5bT",
        "outputId": "1d921f80-be8c-482d-8633-9b409f8590dc"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "SGDRegressor(n_iter_no_change=100, penalty=None, tol=1e-05)"
            ],
            "text/html": [
              "<style>#sk-container-id-3 {color: black;background-color: white;}#sk-container-id-3 pre{padding: 0;}#sk-container-id-3 div.sk-toggleable {background-color: white;}#sk-container-id-3 label.sk-toggleable__label {cursor: pointer;display: block;width: 100%;margin-bottom: 0;padding: 0.3em;box-sizing: border-box;text-align: center;}#sk-container-id-3 label.sk-toggleable__label-arrow:before {content: \"▸\";float: left;margin-right: 0.25em;color: #696969;}#sk-container-id-3 label.sk-toggleable__label-arrow:hover:before {color: black;}#sk-container-id-3 div.sk-estimator:hover label.sk-toggleable__label-arrow:before {color: black;}#sk-container-id-3 div.sk-toggleable__content {max-height: 0;max-width: 0;overflow: hidden;text-align: left;background-color: #f0f8ff;}#sk-container-id-3 div.sk-toggleable__content pre {margin: 0.2em;color: black;border-radius: 0.25em;background-color: #f0f8ff;}#sk-container-id-3 input.sk-toggleable__control:checked~div.sk-toggleable__content {max-height: 200px;max-width: 100%;overflow: auto;}#sk-container-id-3 input.sk-toggleable__control:checked~label.sk-toggleable__label-arrow:before {content: \"▾\";}#sk-container-id-3 div.sk-estimator input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-3 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-3 input.sk-hidden--visually {border: 0;clip: rect(1px 1px 1px 1px);clip: rect(1px, 1px, 1px, 1px);height: 1px;margin: -1px;overflow: hidden;padding: 0;position: absolute;width: 1px;}#sk-container-id-3 div.sk-estimator {font-family: monospace;background-color: #f0f8ff;border: 1px dotted black;border-radius: 0.25em;box-sizing: border-box;margin-bottom: 0.5em;}#sk-container-id-3 div.sk-estimator:hover {background-color: #d4ebff;}#sk-container-id-3 div.sk-parallel-item::after {content: \"\";width: 100%;border-bottom: 1px solid gray;flex-grow: 1;}#sk-container-id-3 div.sk-label:hover label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-3 div.sk-serial::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: 0;}#sk-container-id-3 div.sk-serial {display: flex;flex-direction: column;align-items: center;background-color: white;padding-right: 0.2em;padding-left: 0.2em;position: relative;}#sk-container-id-3 div.sk-item {position: relative;z-index: 1;}#sk-container-id-3 div.sk-parallel {display: flex;align-items: stretch;justify-content: center;background-color: white;position: relative;}#sk-container-id-3 div.sk-item::before, #sk-container-id-3 div.sk-parallel-item::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: -1;}#sk-container-id-3 div.sk-parallel-item {display: flex;flex-direction: column;z-index: 1;position: relative;background-color: white;}#sk-container-id-3 div.sk-parallel-item:first-child::after {align-self: flex-end;width: 50%;}#sk-container-id-3 div.sk-parallel-item:last-child::after {align-self: flex-start;width: 50%;}#sk-container-id-3 div.sk-parallel-item:only-child::after {width: 0;}#sk-container-id-3 div.sk-dashed-wrapped {border: 1px dashed gray;margin: 0 0.4em 0.5em 0.4em;box-sizing: border-box;padding-bottom: 0.4em;background-color: white;}#sk-container-id-3 div.sk-label label {font-family: monospace;font-weight: bold;display: inline-block;line-height: 1.2em;}#sk-container-id-3 div.sk-label-container {text-align: center;}#sk-container-id-3 div.sk-container {/* jupyter's `normalize.less` sets `[hidden] { display: none; }` but bootstrap.min.css set `[hidden] { display: none !important; }` so we also need the `!important` here to be able to override the default hidden behavior on the sphinx rendered scikit-learn.org. See: https://github.com/scikit-learn/scikit-learn/issues/21755 */display: inline-block !important;position: relative;}#sk-container-id-3 div.sk-text-repr-fallback {display: none;}</style><div id=\"sk-container-id-3\" class=\"sk-top-container\"><div class=\"sk-text-repr-fallback\"><pre>SGDRegressor(n_iter_no_change=100, penalty=None, tol=1e-05)</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-3\" type=\"checkbox\" checked><label for=\"sk-estimator-id-3\" class=\"sk-toggleable__label sk-toggleable__label-arrow\">SGDRegressor</label><div class=\"sk-toggleable__content\"><pre>SGDRegressor(n_iter_no_change=100, penalty=None, tol=1e-05)</pre></div></div></div></div></div>"
            ]
          },
          "metadata": {},
          "execution_count": 66
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "sgd_reg.coef_, sgd_reg.intercept_"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "DNFCYDygG5el",
        "outputId": "d1da0b31-34ef-4a66-ac5c-a1b2f644bd1a"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(array([0.84394957]), array([3.56579101]))"
            ]
          },
          "metadata": {},
          "execution_count": 67
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Polynomial Regression"
      ],
      "metadata": {
        "id": "cX_jFpyxFlzF"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "X.ravel()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "fHf7K9SOJBdd",
        "outputId": "234dc673-e6f9-40d7-ab99-0598dd52a819"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([-0.75275929,  2.70428584,  1.39196365,  0.59195091, -2.06388816,\n",
              "       -2.06403288, -2.65149833,  2.19705687,  0.60669007,  1.24843547,\n",
              "       -2.87649303,  2.81945911,  1.99465584, -1.72596534, -1.9090502 ,\n",
              "       -1.89957294, -1.17454654,  0.14853859, -0.40832989, -1.25262516,\n",
              "        0.67111737, -2.16303684, -1.24713211, -0.80182894, -0.26358009,\n",
              "        1.71105577, -1.80195731,  0.08540663,  0.55448741, -2.72129752,\n",
              "        0.64526911, -1.97685526, -2.60969044,  2.69331322,  2.7937922 ,\n",
              "        1.85038409, -1.17231738, -2.41396732,  1.10539816, -0.35908504,\n",
              "       -2.26777059, -0.02893854, -2.79366887,  2.45592241, -1.44732011,\n",
              "        0.97513371, -1.12973354,  0.12040813,  0.28026168, -1.89087327,\n",
              "        2.81750777,  1.65079694,  2.63699365,  2.3689641 ,  0.58739987,\n",
              "        2.53124541, -2.46904499, -1.82410283, -2.72863627, -1.04801802,\n",
              "       -0.66793626, -1.37190581,  1.97242505, -0.85948004, -1.31439294,\n",
              "        0.2561765 , -2.15445465,  1.81318188, -2.55269614,  2.92132162,\n",
              "        1.63346862, -1.80770591, -2.9668673 ,  1.89276857,  1.24114406,\n",
              "        1.37404301,  1.62762208, -2.55573209, -0.84920563, -2.30478564,\n",
              "        2.17862056,  0.73978876, -1.01461185, -2.6186499 , -1.13410607,\n",
              "       -1.04890007,  1.37763707,  0.82534483,  2.32327646, -0.16671045,\n",
              "       -2.28243452,  1.27946872,  1.56471029,  0.36766319,  1.62580308,\n",
              "       -0.03722642,  0.13639698, -0.43475389, -2.84748524, -2.35265144])"
            ]
          },
          "metadata": {},
          "execution_count": 68
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "np.random.seed(42)\n",
        "m = 100\n",
        "X = 6 * np.random.rand(m, 1) - 3\n",
        "y = 0.5 * X ** 2 + X + 2 + np.random.randn(m, 1)\n",
        "plt.plot(X.ravel(), y.ravel(), 'b.');"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 430
        },
        "id": "yPf-y0KHIx1T",
        "outputId": "f6bdf2ec-c97f-4994-df67-11ac7940d7d9"
      },
      "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": "code",
      "source": [
        "from sklearn.preprocessing import PolynomialFeatures\n",
        "\n",
        "poly_features = PolynomialFeatures(degree=2, include_bias=False)\n",
        "X_poly = poly_features.fit_transform(X)\n",
        "X[0]"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "qrhCYJ76Fl1v",
        "outputId": "89e5293d-8ba3-40e4-808b-ff440b9f7b23"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([-0.75275929])"
            ]
          },
          "metadata": {},
          "execution_count": 70
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "X_poly[0]"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "XClw4HLHFl3o",
        "outputId": "ccaad816-e30b-4000-b9c5-6e381e32ebfa"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([-0.75275929,  0.56664654])"
            ]
          },
          "metadata": {},
          "execution_count": 71
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "lin_reg = LinearRegression()\n",
        "lin_reg.fit(X_poly, y)\n",
        "lin_reg.coef_, lin_reg.intercept_"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "YZWDPDMlJc2s",
        "outputId": "f11f93fc-0bb2-4cbe-be0b-c63e01d7dcbd"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(array([[0.93366893, 0.56456263]]), array([1.78134581]))"
            ]
          },
          "metadata": {},
          "execution_count": 72
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "X[:10]"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "IhsbjeeOKcHg",
        "outputId": "45bafa1a-df8e-4b24-8a61-520a331986b5"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[-0.75275929],\n",
              "       [ 2.70428584],\n",
              "       [ 1.39196365],\n",
              "       [ 0.59195091],\n",
              "       [-2.06388816],\n",
              "       [-2.06403288],\n",
              "       [-2.65149833],\n",
              "       [ 2.19705687],\n",
              "       [ 0.60669007],\n",
              "       [ 1.24843547]])"
            ]
          },
          "metadata": {},
          "execution_count": 73
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "x_predict = np.linspace(-3, 3, 100).reshape(-1, 1)\n",
        "x_predict = poly_features.fit_transform(x_predict)\n",
        "predictions = lin_reg.predict(x_predict)\n",
        "\n",
        "np.random.seed(42)\n",
        "plt.plot(X.ravel(), y.ravel(), 'b.', label=\"Data Points\")\n",
        "plt.plot(x_predict[:, 0], predictions, \"r.\", label=\"Predictions\")\n",
        "plt.legend()\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 430
        },
        "id": "XhS1md5cJyYS",
        "outputId": "f37ea35a-65ef-4ede-f421-c68538b54c32"
      },
      "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": [
        "## Learning Curves"
      ],
      "metadata": {
        "id": "BLlocZO_KA2B"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "from sklearn.model_selection import learning_curve\n",
        "\n",
        "train_sizes, train_scores, valid_scores = learning_curve(estimator=LinearRegression(),\n",
        "                                                         X=X,\n",
        "                                                         y=y,\n",
        "                                                         train_sizes=np.linspace(0.1, 1.0, 100),\n",
        "                                                         cv=5,\n",
        "                                                         scoring=\"neg_root_mean_squared_error\")\n",
        "# Calculate means for every fold\n",
        "train_error_mean = -train_scores.mean(axis=1)\n",
        "valid_error_mean = -valid_scores.mean(axis=1)\n",
        "\n",
        "plt.figure(figsize=(12, 5))\n",
        "# Plot Learning Curves\n",
        "plt.plot(train_sizes, train_error_mean, label=\"Train Scores\")\n",
        "plt.plot(train_sizes, valid_error_mean, label=\"Valid Scores\")\n",
        "plt.grid()\n",
        "plt.legend()\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 501
        },
        "id": "rA6mE9xHK6dH",
        "outputId": "1a46caed-5f75-4d74-e719-3e5c81d92a42"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "/usr/local/lib/python3.10/dist-packages/sklearn/model_selection/_validation.py:1690: RuntimeWarning: Removed duplicate entries from 'train_sizes'. Number of ticks will be less than the size of 'train_sizes': 73 instead of 100.\n",
            "  warnings.warn(\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1200x500 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "from sklearn.pipeline import make_pipeline\n",
        "\n",
        "polynomial_regression = make_pipeline(PolynomialFeatures(degree=10, include_bias=False),\n",
        "                                      LinearRegression())\n",
        "\n",
        "train_sizes, train_scores, valid_scores = learning_curve(estimator=polynomial_regression,\n",
        "                                                         X=X,\n",
        "                                                         y=y,\n",
        "                                                         train_sizes=np.linspace(0.1, 1.0, 100),\n",
        "                                                         cv=5,\n",
        "                                                         scoring=\"neg_root_mean_squared_error\")\n",
        "# Calculate means for every fold\n",
        "train_error_mean = -train_scores.mean(axis=1)\n",
        "valid_error_mean = -valid_scores.mean(axis=1)\n",
        "\n",
        "plt.figure(figsize=(12, 5))\n",
        "ax = plt.gca()\n",
        "# Plot Learning Curves\n",
        "plt.plot(train_sizes, train_error_mean, label=\"Train Scores\")\n",
        "plt.plot(train_sizes, valid_error_mean, label=\"Valid Scores\")\n",
        "plt.grid()\n",
        "ax.set_ylim(0, 3)\n",
        "plt.legend()\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 507
        },
        "id": "H5r144zDK6kX",
        "outputId": "129980d8-c5ef-4b6a-aea9-a3770a4908ed"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "/usr/local/lib/python3.10/dist-packages/sklearn/model_selection/_validation.py:1690: RuntimeWarning: Removed duplicate entries from 'train_sizes'. Number of ticks will be less than the size of 'train_sizes': 73 instead of 100.\n",
            "  warnings.warn(\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1200x500 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Regularized Linear Models"
      ],
      "metadata": {
        "id": "_NsHCQmuSc03"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Ridge"
      ],
      "metadata": {
        "id": "7MATBwoKT5UT"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "from sklearn.linear_model import Ridge\n",
        "\n",
        "ridge_reg = Ridge(alpha=0.1,\n",
        "                  solver=\"cholesky\")\n",
        "ridge_reg.fit(X, y)\n",
        "ridge_reg.predict([[1.5]])"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Pst4ZAr2TD0C",
        "outputId": "9813f48f-594a-45a0-80e7-e10570ebb172"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[4.82899748]])"
            ]
          },
          "metadata": {},
          "execution_count": 90
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Using SGD\n",
        "sgd_reg = SGDRegressor(penalty=\"l2\", alpha = 0.1 / m, tol=None,\n",
        "                       max_iter=1000, eta0=0.01, random_state=42)\n",
        "sgd_reg.fit(X, y.ravel())\n",
        "sgd_reg.predict([[1.5]])"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "pyKv7iHnTD2l",
        "outputId": "4aa29f4c-2e8d-494f-861b-081919c70c6f"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([4.82830117])"
            ]
          },
          "metadata": {},
          "execution_count": 91
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Lasso"
      ],
      "metadata": {
        "id": "QZ0Ti7MITD5O"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "from sklearn.linear_model import Lasso\n",
        "\n",
        "lasso_reg = Lasso(alpha=0.1)\n",
        "lasso_reg.fit(X, y)\n",
        "lasso_reg.predict([[1.5]])"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "ucXw-VUoTD7b",
        "outputId": "3b8084e6-acae-4280-8296-966f75fde32b"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([4.77621741])"
            ]
          },
          "metadata": {},
          "execution_count": 92
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "### ElasticNet"
      ],
      "metadata": {
        "id": "L6KhzTroUHkF"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "from sklearn.linear_model import ElasticNet\n",
        "\n",
        "en_reg = ElasticNet(alpha=0.1)\n",
        "en_reg.fit(X, y)\n",
        "en_reg.predict([[1.5]])"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "LmK45FAxUMju",
        "outputId": "3396c452-ac2e-4ce4-d6e0-d7e6a1c79611"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([4.78114505])"
            ]
          },
          "metadata": {},
          "execution_count": 93
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## EarlyStopping"
      ],
      "metadata": {
        "id": "V03UciQPUMm8"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "from copy import deepcopy\n",
        "from sklearn.metrics import mean_squared_error\n",
        "from sklearn.preprocessing import StandardScaler\n",
        "from sklearn.model_selection import train_test_split\n",
        "\n",
        "X_train, X_valid, y_train, y_valid = train_test_split(X, y, test_size=0.2)"
      ],
      "metadata": {
        "id": "Jm6-BFOiUjGM"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "preprocessing = make_pipeline(PolynomialFeatures(degree=10),\n",
        "                              StandardScaler())\n",
        "X_train_prep = preprocessing.fit_transform(X_train)\n",
        "X_valid_prep = preprocessing.transform(X_valid)\n",
        "sgd_reg = SGDRegressor(penalty=None, eta0=0.002)\n",
        "n_epochs=500\n",
        "best_valid_rmse = float('inf')"
      ],
      "metadata": {
        "id": "5UCBcWNAUjJi"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "for epoch in range(n_epochs):\n",
        "  # Use Partial-fit here\n",
        "  sgd_reg.partial_fit(X_train_prep, y_train.ravel())\n",
        "  y_valid_predict = sgd_reg.predict(X_valid_prep)\n",
        "  val_error = mean_squared_error(y_valid, y_valid_predict, squared=False)\n",
        "  if val_error < best_valid_rmse:\n",
        "    best_valid_rmse = val_error\n",
        "    best_model = deepcopy(sgd_reg)\n",
        "\n",
        "best_model.predict(preprocessing.transform([[1.5]]))"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "gWQ80xIDUMpy",
        "outputId": "eb78a113-ed4c-4a98-c977-6612d119ca1b"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([4.01961387])"
            ]
          },
          "metadata": {},
          "execution_count": 113
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Logistic Regression"
      ],
      "metadata": {
        "id": "uDYXqmEYXCqD"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "from sklearn.datasets import load_iris\n",
        "\n",
        "iris = load_iris(as_frame=True)\n",
        "list(iris)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "7MnfA3vpYDz_",
        "outputId": "c47b9044-62c7-411d-b2f5-c4328426701c"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "['data',\n",
              " 'target',\n",
              " 'frame',\n",
              " 'target_names',\n",
              " 'DESCR',\n",
              " 'feature_names',\n",
              " 'filename',\n",
              " 'data_module']"
            ]
          },
          "metadata": {},
          "execution_count": 118
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "iris.target"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "1XR8CBVUYkQS",
        "outputId": "a33836c5-5689-4be4-8881-7e740e8dc912"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0      0\n",
              "1      0\n",
              "2      0\n",
              "3      0\n",
              "4      0\n",
              "      ..\n",
              "145    2\n",
              "146    2\n",
              "147    2\n",
              "148    2\n",
              "149    2\n",
              "Name: target, Length: 150, dtype: int64"
            ]
          },
          "metadata": {},
          "execution_count": 119
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "iris.data"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 423
        },
        "id": "I4cwPfDYYyzr",
        "outputId": "f5b1b711-f9c5-4f3f-81e8-c5395d83df78"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "     sepal length (cm)  sepal width (cm)  petal length (cm)  petal width (cm)\n",
              "0                  5.1               3.5                1.4               0.2\n",
              "1                  4.9               3.0                1.4               0.2\n",
              "2                  4.7               3.2                1.3               0.2\n",
              "3                  4.6               3.1                1.5               0.2\n",
              "4                  5.0               3.6                1.4               0.2\n",
              "..                 ...               ...                ...               ...\n",
              "145                6.7               3.0                5.2               2.3\n",
              "146                6.3               2.5                5.0               1.9\n",
              "147                6.5               3.0                5.2               2.0\n",
              "148                6.2               3.4                5.4               2.3\n",
              "149                5.9               3.0                5.1               1.8\n",
              "\n",
              "[150 rows x 4 columns]"
            ],
            "text/html": [
              "\n",
              "  <div id=\"df-c746d6e3-f775-4c39-969a-21078ec194bd\" 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>sepal length (cm)</th>\n",
              "      <th>sepal width (cm)</th>\n",
              "      <th>petal length (cm)</th>\n",
              "      <th>petal width (cm)</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>5.1</td>\n",
              "      <td>3.5</td>\n",
              "      <td>1.4</td>\n",
              "      <td>0.2</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>4.9</td>\n",
              "      <td>3.0</td>\n",
              "      <td>1.4</td>\n",
              "      <td>0.2</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>4.7</td>\n",
              "      <td>3.2</td>\n",
              "      <td>1.3</td>\n",
              "      <td>0.2</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>4.6</td>\n",
              "      <td>3.1</td>\n",
              "      <td>1.5</td>\n",
              "      <td>0.2</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>5.0</td>\n",
              "      <td>3.6</td>\n",
              "      <td>1.4</td>\n",
              "      <td>0.2</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>...</th>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>145</th>\n",
              "      <td>6.7</td>\n",
              "      <td>3.0</td>\n",
              "      <td>5.2</td>\n",
              "      <td>2.3</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>146</th>\n",
              "      <td>6.3</td>\n",
              "      <td>2.5</td>\n",
              "      <td>5.0</td>\n",
              "      <td>1.9</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>147</th>\n",
              "      <td>6.5</td>\n",
              "      <td>3.0</td>\n",
              "      <td>5.2</td>\n",
              "      <td>2.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>148</th>\n",
              "      <td>6.2</td>\n",
              "      <td>3.4</td>\n",
              "      <td>5.4</td>\n",
              "      <td>2.3</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>149</th>\n",
              "      <td>5.9</td>\n",
              "      <td>3.0</td>\n",
              "      <td>5.1</td>\n",
              "      <td>1.8</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "<p>150 rows × 4 columns</p>\n",
              "</div>\n",
              "    <div class=\"colab-df-buttons\">\n",
              "\n",
              "  <div class=\"colab-df-container\">\n",
              "    <button class=\"colab-df-convert\" onclick=\"convertToInteractive('df-c746d6e3-f775-4c39-969a-21078ec194bd')\"\n",
              "            title=\"Convert this dataframe to an interactive table.\"\n",
              "            style=\"display:none;\">\n",
              "\n",
              "  <svg xmlns=\"http://www.w3.org/2000/svg\" height=\"24px\" viewBox=\"0 -960 960 960\">\n",
              "    <path d=\"M120-120v-720h720v720H120Zm60-500h600v-160H180v160Zm220 220h160v-160H400v160Zm0 220h160v-160H400v160ZM180-400h160v-160H180v160Zm440 0h160v-160H620v160ZM180-180h160v-160H180v160Zm440 0h160v-160H620v160Z\"/>\n",
              "  </svg>\n",
              "    </button>\n",
              "\n",
              "  <style>\n",
              "    .colab-df-container {\n",
              "      display:flex;\n",
              "      gap: 12px;\n",
              "    }\n",
              "\n",
              "    .colab-df-convert {\n",
              "      background-color: #E8F0FE;\n",
              "      border: none;\n",
              "      border-radius: 50%;\n",
              "      cursor: pointer;\n",
              "      display: none;\n",
              "      fill: #1967D2;\n",
              "      height: 32px;\n",
              "      padding: 0 0 0 0;\n",
              "      width: 32px;\n",
              "    }\n",
              "\n",
              "    .colab-df-convert:hover {\n",
              "      background-color: #E2EBFA;\n",
              "      box-shadow: 0px 1px 2px rgba(60, 64, 67, 0.3), 0px 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
              "      fill: #174EA6;\n",
              "    }\n",
              "\n",
              "    .colab-df-buttons div {\n",
              "      margin-bottom: 4px;\n",
              "    }\n",
              "\n",
              "    [theme=dark] .colab-df-convert {\n",
              "      background-color: #3B4455;\n",
              "      fill: #D2E3FC;\n",
              "    }\n",
              "\n",
              "    [theme=dark] .colab-df-convert:hover {\n",
              "      background-color: #434B5C;\n",
              "      box-shadow: 0px 1px 3px 1px rgba(0, 0, 0, 0.15);\n",
              "      filter: drop-shadow(0px 1px 2px rgba(0, 0, 0, 0.3));\n",
              "      fill: #FFFFFF;\n",
              "    }\n",
              "  </style>\n",
              "\n",
              "    <script>\n",
              "      const buttonEl =\n",
              "        document.querySelector('#df-c746d6e3-f775-4c39-969a-21078ec194bd button.colab-df-convert');\n",
              "      buttonEl.style.display =\n",
              "        google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
              "\n",
              "      async function convertToInteractive(key) {\n",
              "        const element = document.querySelector('#df-c746d6e3-f775-4c39-969a-21078ec194bd');\n",
              "        const dataTable =\n",
              "          await google.colab.kernel.invokeFunction('convertToInteractive',\n",
              "                                                    [key], {});\n",
              "        if (!dataTable) return;\n",
              "\n",
              "        const docLinkHtml = 'Like what you see? Visit the ' +\n",
              "          '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
              "          + ' to learn more about interactive tables.';\n",
              "        element.innerHTML = '';\n",
              "        dataTable['output_type'] = 'display_data';\n",
              "        await google.colab.output.renderOutput(dataTable, element);\n",
              "        const docLink = document.createElement('div');\n",
              "        docLink.innerHTML = docLinkHtml;\n",
              "        element.appendChild(docLink);\n",
              "      }\n",
              "    </script>\n",
              "  </div>\n",
              "\n",
              "\n",
              "<div id=\"df-a25711a5-ce10-4840-8cec-57ab2fb63fa9\">\n",
              "  <button class=\"colab-df-quickchart\" onclick=\"quickchart('df-a25711a5-ce10-4840-8cec-57ab2fb63fa9')\"\n",
              "            title=\"Suggest charts\"\n",
              "            style=\"display:none;\">\n",
              "\n",
              "<svg xmlns=\"http://www.w3.org/2000/svg\" height=\"24px\"viewBox=\"0 0 24 24\"\n",
              "     width=\"24px\">\n",
              "    <g>\n",
              "        <path d=\"M19 3H5c-1.1 0-2 .9-2 2v14c0 1.1.9 2 2 2h14c1.1 0 2-.9 2-2V5c0-1.1-.9-2-2-2zM9 17H7v-7h2v7zm4 0h-2V7h2v10zm4 0h-2v-4h2v4z\"/>\n",
              "    </g>\n",
              "</svg>\n",
              "  </button>\n",
              "\n",
              "<style>\n",
              "  .colab-df-quickchart {\n",
              "      --bg-color: #E8F0FE;\n",
              "      --fill-color: #1967D2;\n",
              "      --hover-bg-color: #E2EBFA;\n",
              "      --hover-fill-color: #174EA6;\n",
              "      --disabled-fill-color: #AAA;\n",
              "      --disabled-bg-color: #DDD;\n",
              "  }\n",
              "\n",
              "  [theme=dark] .colab-df-quickchart {\n",
              "      --bg-color: #3B4455;\n",
              "      --fill-color: #D2E3FC;\n",
              "      --hover-bg-color: #434B5C;\n",
              "      --hover-fill-color: #FFFFFF;\n",
              "      --disabled-bg-color: #3B4455;\n",
              "      --disabled-fill-color: #666;\n",
              "  }\n",
              "\n",
              "  .colab-df-quickchart {\n",
              "    background-color: var(--bg-color);\n",
              "    border: none;\n",
              "    border-radius: 50%;\n",
              "    cursor: pointer;\n",
              "    display: none;\n",
              "    fill: var(--fill-color);\n",
              "    height: 32px;\n",
              "    padding: 0;\n",
              "    width: 32px;\n",
              "  }\n",
              "\n",
              "  .colab-df-quickchart:hover {\n",
              "    background-color: var(--hover-bg-color);\n",
              "    box-shadow: 0 1px 2px rgba(60, 64, 67, 0.3), 0 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
              "    fill: var(--button-hover-fill-color);\n",
              "  }\n",
              "\n",
              "  .colab-df-quickchart-complete:disabled,\n",
              "  .colab-df-quickchart-complete:disabled:hover {\n",
              "    background-color: var(--disabled-bg-color);\n",
              "    fill: var(--disabled-fill-color);\n",
              "    box-shadow: none;\n",
              "  }\n",
              "\n",
              "  .colab-df-spinner {\n",
              "    border: 2px solid var(--fill-color);\n",
              "    border-color: transparent;\n",
              "    border-bottom-color: var(--fill-color);\n",
              "    animation:\n",
              "      spin 1s steps(1) infinite;\n",
              "  }\n",
              "\n",
              "  @keyframes spin {\n",
              "    0% {\n",
              "      border-color: transparent;\n",
              "      border-bottom-color: var(--fill-color);\n",
              "      border-left-color: var(--fill-color);\n",
              "    }\n",
              "    20% {\n",
              "      border-color: transparent;\n",
              "      border-left-color: var(--fill-color);\n",
              "      border-top-color: var(--fill-color);\n",
              "    }\n",
              "    30% {\n",
              "      border-color: transparent;\n",
              "      border-left-color: var(--fill-color);\n",
              "      border-top-color: var(--fill-color);\n",
              "      border-right-color: var(--fill-color);\n",
              "    }\n",
              "    40% {\n",
              "      border-color: transparent;\n",
              "      border-right-color: var(--fill-color);\n",
              "      border-top-color: var(--fill-color);\n",
              "    }\n",
              "    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",
              "    }\n",
              "    90% {\n",
              "      border-color: transparent;\n",
              "      border-bottom-color: var(--fill-color);\n",
              "    }\n",
              "  }\n",
              "</style>\n",
              "\n",
              "  <script>\n",
              "    async function quickchart(key) {\n",
              "      const quickchartButtonEl =\n",
              "        document.querySelector('#' + key + ' button');\n",
              "      quickchartButtonEl.disabled = true;  // To prevent multiple clicks.\n",
              "      quickchartButtonEl.classList.add('colab-df-spinner');\n",
              "      try {\n",
              "        const charts = await google.colab.kernel.invokeFunction(\n",
              "            'suggestCharts', [key], {});\n",
              "      } catch (error) {\n",
              "        console.error('Error during call to suggestCharts:', error);\n",
              "      }\n",
              "      quickchartButtonEl.classList.remove('colab-df-spinner');\n",
              "      quickchartButtonEl.classList.add('colab-df-quickchart-complete');\n",
              "    }\n",
              "    (() => {\n",
              "      let quickchartButtonEl =\n",
              "        document.querySelector('#df-a25711a5-ce10-4840-8cec-57ab2fb63fa9 button');\n",
              "      quickchartButtonEl.style.display =\n",
              "        google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
              "    })();\n",
              "  </script>\n",
              "</div>\n",
              "\n",
              "    </div>\n",
              "  </div>\n"
            ],
            "application/vnd.google.colaboratory.intrinsic+json": {
              "type": "dataframe",
              "summary": "{\n  \"name\": \"iris\",\n  \"rows\": 150,\n  \"fields\": [\n    {\n      \"column\": \"sepal length (cm)\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 0.828066127977863,\n        \"min\": 4.3,\n        \"max\": 7.9,\n        \"num_unique_values\": 35,\n        \"samples\": [\n          6.2,\n          4.5,\n          5.6\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"sepal width (cm)\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 0.4358662849366982,\n        \"min\": 2.0,\n        \"max\": 4.4,\n        \"num_unique_values\": 23,\n        \"samples\": [\n          2.3,\n          4.0,\n          3.5\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"petal length (cm)\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 1.7652982332594662,\n        \"min\": 1.0,\n        \"max\": 6.9,\n        \"num_unique_values\": 43,\n        \"samples\": [\n          6.7,\n          3.8,\n          3.7\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"petal width (cm)\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 0.7622376689603465,\n        \"min\": 0.1,\n        \"max\": 2.5,\n        \"num_unique_values\": 22,\n        \"samples\": [\n          0.2,\n          1.2,\n          1.3\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    }\n  ]\n}"
            }
          },
          "metadata": {},
          "execution_count": 120
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "from sklearn.linear_model import LogisticRegression\n",
        "\n",
        "X = iris.data[[\"petal width (cm)\"]].values\n",
        "y = iris.target_names[iris.target] == \"virginica\"\n",
        "X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2)\n",
        "\n",
        "log_reg = LogisticRegression()\n",
        "log_reg.fit(X_train, y_train)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 74
        },
        "id": "1AeWPA1sYD3G",
        "outputId": "ece0e770-d61a-465a-92c0-7fb48e379cbf"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "LogisticRegression()"
            ],
            "text/html": [
              "<style>#sk-container-id-7 {color: black;background-color: white;}#sk-container-id-7 pre{padding: 0;}#sk-container-id-7 div.sk-toggleable {background-color: white;}#sk-container-id-7 label.sk-toggleable__label {cursor: pointer;display: block;width: 100%;margin-bottom: 0;padding: 0.3em;box-sizing: border-box;text-align: center;}#sk-container-id-7 label.sk-toggleable__label-arrow:before {content: \"▸\";float: left;margin-right: 0.25em;color: #696969;}#sk-container-id-7 label.sk-toggleable__label-arrow:hover:before {color: black;}#sk-container-id-7 div.sk-estimator:hover label.sk-toggleable__label-arrow:before {color: black;}#sk-container-id-7 div.sk-toggleable__content {max-height: 0;max-width: 0;overflow: hidden;text-align: left;background-color: #f0f8ff;}#sk-container-id-7 div.sk-toggleable__content pre {margin: 0.2em;color: black;border-radius: 0.25em;background-color: #f0f8ff;}#sk-container-id-7 input.sk-toggleable__control:checked~div.sk-toggleable__content {max-height: 200px;max-width: 100%;overflow: auto;}#sk-container-id-7 input.sk-toggleable__control:checked~label.sk-toggleable__label-arrow:before {content: \"▾\";}#sk-container-id-7 div.sk-estimator input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-7 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-7 input.sk-hidden--visually {border: 0;clip: rect(1px 1px 1px 1px);clip: rect(1px, 1px, 1px, 1px);height: 1px;margin: -1px;overflow: hidden;padding: 0;position: absolute;width: 1px;}#sk-container-id-7 div.sk-estimator {font-family: monospace;background-color: #f0f8ff;border: 1px dotted black;border-radius: 0.25em;box-sizing: border-box;margin-bottom: 0.5em;}#sk-container-id-7 div.sk-estimator:hover {background-color: #d4ebff;}#sk-container-id-7 div.sk-parallel-item::after {content: \"\";width: 100%;border-bottom: 1px solid gray;flex-grow: 1;}#sk-container-id-7 div.sk-label:hover label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-7 div.sk-serial::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: 0;}#sk-container-id-7 div.sk-serial {display: flex;flex-direction: column;align-items: center;background-color: white;padding-right: 0.2em;padding-left: 0.2em;position: relative;}#sk-container-id-7 div.sk-item {position: relative;z-index: 1;}#sk-container-id-7 div.sk-parallel {display: flex;align-items: stretch;justify-content: center;background-color: white;position: relative;}#sk-container-id-7 div.sk-item::before, #sk-container-id-7 div.sk-parallel-item::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: -1;}#sk-container-id-7 div.sk-parallel-item {display: flex;flex-direction: column;z-index: 1;position: relative;background-color: white;}#sk-container-id-7 div.sk-parallel-item:first-child::after {align-self: flex-end;width: 50%;}#sk-container-id-7 div.sk-parallel-item:last-child::after {align-self: flex-start;width: 50%;}#sk-container-id-7 div.sk-parallel-item:only-child::after {width: 0;}#sk-container-id-7 div.sk-dashed-wrapped {border: 1px dashed gray;margin: 0 0.4em 0.5em 0.4em;box-sizing: border-box;padding-bottom: 0.4em;background-color: white;}#sk-container-id-7 div.sk-label label {font-family: monospace;font-weight: bold;display: inline-block;line-height: 1.2em;}#sk-container-id-7 div.sk-label-container {text-align: center;}#sk-container-id-7 div.sk-container {/* jupyter's `normalize.less` sets `[hidden] { display: none; }` but bootstrap.min.css set `[hidden] { display: none !important; }` so we also need the `!important` here to be able to override the default hidden behavior on the sphinx rendered scikit-learn.org. See: https://github.com/scikit-learn/scikit-learn/issues/21755 */display: inline-block !important;position: relative;}#sk-container-id-7 div.sk-text-repr-fallback {display: none;}</style><div id=\"sk-container-id-7\" class=\"sk-top-container\"><div class=\"sk-text-repr-fallback\"><pre>LogisticRegression()</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-7\" type=\"checkbox\" checked><label for=\"sk-estimator-id-7\" class=\"sk-toggleable__label sk-toggleable__label-arrow\">LogisticRegression</label><div class=\"sk-toggleable__content\"><pre>LogisticRegression()</pre></div></div></div></div></div>"
            ]
          },
          "metadata": {},
          "execution_count": 131
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "y_test"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "-KejQyjjZoke",
        "outputId": "ba53b24e-229f-451f-914d-c978f685f5b0"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([False, False, False, False, False, False, False, False,  True,\n",
              "       False, False, False, False,  True,  True, False,  True, False,\n",
              "       False, False, False, False, False,  True,  True, False, False,\n",
              "       False, False, False])"
            ]
          },
          "metadata": {},
          "execution_count": 132
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "from sklearn.metrics import accuracy_score\n",
        "accuracy_score(y_test, log_reg.predict(X_test))"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "AZ5j4Ai6ZYLl",
        "outputId": "c7e5eb44-5bf1-42af-df3c-a419dacfce0a"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "1.0"
            ]
          },
          "metadata": {},
          "execution_count": 133
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "from sklearn.linear_model import LogisticRegression\n",
        "\n",
        "X = iris.data[[\"petal width (cm)\"]].values\n",
        "y = iris.target\n",
        "X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2)\n",
        "\n",
        "softmax_reg = LogisticRegression()\n",
        "softmax_reg.fit(X_train, y_train)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 74
        },
        "id": "GcTRTNsMYD6W",
        "outputId": "a9b3ca89-abff-4909-8cda-4897a6bde253"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "LogisticRegression()"
            ],
            "text/html": [
              "<style>#sk-container-id-8 {color: black;background-color: white;}#sk-container-id-8 pre{padding: 0;}#sk-container-id-8 div.sk-toggleable {background-color: white;}#sk-container-id-8 label.sk-toggleable__label {cursor: pointer;display: block;width: 100%;margin-bottom: 0;padding: 0.3em;box-sizing: border-box;text-align: center;}#sk-container-id-8 label.sk-toggleable__label-arrow:before {content: \"▸\";float: left;margin-right: 0.25em;color: #696969;}#sk-container-id-8 label.sk-toggleable__label-arrow:hover:before {color: black;}#sk-container-id-8 div.sk-estimator:hover label.sk-toggleable__label-arrow:before {color: black;}#sk-container-id-8 div.sk-toggleable__content {max-height: 0;max-width: 0;overflow: hidden;text-align: left;background-color: #f0f8ff;}#sk-container-id-8 div.sk-toggleable__content pre {margin: 0.2em;color: black;border-radius: 0.25em;background-color: #f0f8ff;}#sk-container-id-8 input.sk-toggleable__control:checked~div.sk-toggleable__content {max-height: 200px;max-width: 100%;overflow: auto;}#sk-container-id-8 input.sk-toggleable__control:checked~label.sk-toggleable__label-arrow:before {content: \"▾\";}#sk-container-id-8 div.sk-estimator input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-8 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-8 input.sk-hidden--visually {border: 0;clip: rect(1px 1px 1px 1px);clip: rect(1px, 1px, 1px, 1px);height: 1px;margin: -1px;overflow: hidden;padding: 0;position: absolute;width: 1px;}#sk-container-id-8 div.sk-estimator {font-family: monospace;background-color: #f0f8ff;border: 1px dotted black;border-radius: 0.25em;box-sizing: border-box;margin-bottom: 0.5em;}#sk-container-id-8 div.sk-estimator:hover {background-color: #d4ebff;}#sk-container-id-8 div.sk-parallel-item::after {content: \"\";width: 100%;border-bottom: 1px solid gray;flex-grow: 1;}#sk-container-id-8 div.sk-label:hover label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-8 div.sk-serial::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: 0;}#sk-container-id-8 div.sk-serial {display: flex;flex-direction: column;align-items: center;background-color: white;padding-right: 0.2em;padding-left: 0.2em;position: relative;}#sk-container-id-8 div.sk-item {position: relative;z-index: 1;}#sk-container-id-8 div.sk-parallel {display: flex;align-items: stretch;justify-content: center;background-color: white;position: relative;}#sk-container-id-8 div.sk-item::before, #sk-container-id-8 div.sk-parallel-item::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: -1;}#sk-container-id-8 div.sk-parallel-item {display: flex;flex-direction: column;z-index: 1;position: relative;background-color: white;}#sk-container-id-8 div.sk-parallel-item:first-child::after {align-self: flex-end;width: 50%;}#sk-container-id-8 div.sk-parallel-item:last-child::after {align-self: flex-start;width: 50%;}#sk-container-id-8 div.sk-parallel-item:only-child::after {width: 0;}#sk-container-id-8 div.sk-dashed-wrapped {border: 1px dashed gray;margin: 0 0.4em 0.5em 0.4em;box-sizing: border-box;padding-bottom: 0.4em;background-color: white;}#sk-container-id-8 div.sk-label label {font-family: monospace;font-weight: bold;display: inline-block;line-height: 1.2em;}#sk-container-id-8 div.sk-label-container {text-align: center;}#sk-container-id-8 div.sk-container {/* jupyter's `normalize.less` sets `[hidden] { display: none; }` but bootstrap.min.css set `[hidden] { display: none !important; }` so we also need the `!important` here to be able to override the default hidden behavior on the sphinx rendered scikit-learn.org. See: https://github.com/scikit-learn/scikit-learn/issues/21755 */display: inline-block !important;position: relative;}#sk-container-id-8 div.sk-text-repr-fallback {display: none;}</style><div id=\"sk-container-id-8\" class=\"sk-top-container\"><div class=\"sk-text-repr-fallback\"><pre>LogisticRegression()</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-8\" type=\"checkbox\" checked><label for=\"sk-estimator-id-8\" class=\"sk-toggleable__label sk-toggleable__label-arrow\">LogisticRegression</label><div class=\"sk-toggleable__content\"><pre>LogisticRegression()</pre></div></div></div></div></div>"
            ]
          },
          "metadata": {},
          "execution_count": 134
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "accuracy_score(y_test, softmax_reg.predict(X_test))"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "R9KY9RoQZdVI",
        "outputId": "bf1acc92-52f7-4ea0-9a77-4243bde4d9e6"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.9333333333333333"
            ]
          },
          "metadata": {},
          "execution_count": 137
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [],
      "metadata": {
        "id": "k1YlRhHEYD9K"
      },
      "execution_count": null,
      "outputs": []
    }
  ]
}