06_decision_trees.ipynb

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    "colab": {
      "name": "06_decision_trees.ipynb",
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      "include_colab_link": true
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  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/aloiswirth/handson-ml2/blob/main/06_decision_trees.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "g3DFRKtITT5m"
      },
      "source": [
        "**Chapter 6 – Decision Trees**"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "iLV0yhSfTT5q"
      },
      "source": [
        "_This notebook contains all the sample code and solutions to the exercises in chapter 6._"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "DIlARjreTT5q"
      },
      "source": [
        "<table align=\"left\">\n",
        "  <td>\n",
        "    <a target=\"_blank\" href=\"https://colab.research.google.com/github/ageron/handson-ml2/blob/master/06_decision_trees.ipynb\"><img src=\"https://www.tensorflow.org/images/colab_logo_32px.png\" />Run in Google Colab</a>\n",
        "  </td>\n",
        "</table>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "9hbh4U6nTT5r"
      },
      "source": [
        "# Setup"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "4e27K5mzTT5r"
      },
      "source": [
        "First, let's import a few common modules, ensure MatplotLib plots figures inline and prepare a function to save the figures. We also check that Python 3.5 or later is installed (although Python 2.x may work, it is deprecated so we strongly recommend you use Python 3 instead), as well as Scikit-Learn ≥0.20."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "sZU4OQeOTT5r"
      },
      "source": [
        "# Python ≥3.5 is required\n",
        "import sys\n",
        "assert sys.version_info >= (3, 5)\n",
        "\n",
        "# Scikit-Learn ≥0.20 is required\n",
        "import sklearn\n",
        "assert sklearn.__version__ >= \"0.20\"\n",
        "\n",
        "# Common imports\n",
        "import numpy as np\n",
        "import os\n",
        "\n",
        "# to make this notebook's output stable across runs\n",
        "np.random.seed(42)\n",
        "\n",
        "# To plot pretty figures\n",
        "%matplotlib inline\n",
        "import matplotlib as mpl\n",
        "import matplotlib.pyplot as plt\n",
        "mpl.rc('axes', labelsize=14)\n",
        "mpl.rc('xtick', labelsize=12)\n",
        "mpl.rc('ytick', labelsize=12)\n",
        "\n",
        "# Where to save the figures\n",
        "PROJECT_ROOT_DIR = \".\"\n",
        "CHAPTER_ID = \"decision_trees\"\n",
        "IMAGES_PATH = os.path.join(PROJECT_ROOT_DIR, \"images\", CHAPTER_ID)\n",
        "os.makedirs(IMAGES_PATH, exist_ok=True)\n",
        "\n",
        "def save_fig(fig_id, tight_layout=True, fig_extension=\"png\", resolution=300):\n",
        "    path = os.path.join(IMAGES_PATH, fig_id + \".\" + fig_extension)\n",
        "    print(\"Saving figure\", fig_id)\n",
        "    if tight_layout:\n",
        "        plt.tight_layout()\n",
        "    plt.savefig(path, format=fig_extension, dpi=resolution)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "-SIz0WmoTT5s"
      },
      "source": [
        "# Training and visualizing"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "VL4MqfaTTT5t",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "57c30e09-3fca-4c7d-fbc8-852371d54f27"
      },
      "source": [
        "from sklearn.datasets import load_iris\n",
        "from sklearn.tree import DecisionTreeClassifier\n",
        "\n",
        "iris = load_iris()\n",
        "X = iris.data[:, 2:] # petal length and width\n",
        "y = iris.target\n",
        "\n",
        "tree_clf = DecisionTreeClassifier(max_depth=2, random_state=42)\n",
        "tree_clf.fit(X, y)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "DecisionTreeClassifier(ccp_alpha=0.0, class_weight=None, criterion='gini',\n",
              "                       max_depth=2, max_features=None, max_leaf_nodes=None,\n",
              "                       min_impurity_decrease=0.0, min_impurity_split=None,\n",
              "                       min_samples_leaf=1, min_samples_split=2,\n",
              "                       min_weight_fraction_leaf=0.0, presort='deprecated',\n",
              "                       random_state=42, splitter='best')"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 2
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "icY4H57-TT5u",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 440
        },
        "outputId": "e169004a-f095-431e-c6c2-d2689f786319"
      },
      "source": [
        "from graphviz import Source\n",
        "from sklearn.tree import export_graphviz\n",
        "\n",
        "export_graphviz(\n",
        "        tree_clf,\n",
        "        out_file=os.path.join(IMAGES_PATH, \"iris_tree.dot\"),\n",
        "        feature_names=iris.feature_names[2:],\n",
        "        class_names=iris.target_names,\n",
        "        rounded=True,\n",
        "        filled=True\n",
        "    )\n",
        "\n",
        "Source.from_file(os.path.join(IMAGES_PATH, \"iris_tree.dot\"))"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
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              "<graphviz.files.Source at 0x7f66ada31d90>"
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          },
          "metadata": {
            "tags": []
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          "execution_count": 3
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "SxDFU4qDTT5v",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 405
        },
        "outputId": "90b64fdb-9b83-4218-90ba-6f5089262cc3"
      },
      "source": [
        "from matplotlib.colors import ListedColormap\n",
        "\n",
        "def plot_decision_boundary(clf, X, y, axes=[0, 7.5, 0, 3], iris=True, legend=False, plot_training=True):\n",
        "    x1s = np.linspace(axes[0], axes[1], 100)\n",
        "    x2s = np.linspace(axes[2], axes[3], 100)\n",
        "    x1, x2 = np.meshgrid(x1s, x2s)\n",
        "    X_new = np.c_[x1.ravel(), x2.ravel()]\n",
        "    print(X_new[:5])\n",
        "    y_pred = clf.predict(X_new).reshape(x1.shape)\n",
        "    custom_cmap = ListedColormap(['#fafab0','#9898ff','#a0faa0'])\n",
        "    plt.contourf(x1, x2, y_pred, alpha=0.3, cmap=custom_cmap)\n",
        "    if not iris:\n",
        "        custom_cmap2 = ListedColormap(['#7d7d58','#4c4c7f','#507d50'])\n",
        "        plt.contour(x1, x2, y_pred, cmap=custom_cmap2, alpha=0.8)\n",
        "    if plot_training:\n",
        "        plt.plot(X[:, 0][y==0], X[:, 1][y==0], \"yo\", label=\"Iris setosa\")\n",
        "        plt.plot(X[:, 0][y==1], X[:, 1][y==1], \"bs\", label=\"Iris versicolor\")\n",
        "        plt.plot(X[:, 0][y==2], X[:, 1][y==2], \"g^\", label=\"Iris virginica\")\n",
        "        plt.axis(axes)\n",
        "    if iris:\n",
        "        plt.xlabel(\"Petal length\", fontsize=14)\n",
        "        plt.ylabel(\"Petal width\", fontsize=14)\n",
        "    else:\n",
        "        plt.xlabel(r\"$x_1$\", fontsize=18)\n",
        "        plt.ylabel(r\"$x_2$\", fontsize=18, rotation=0)\n",
        "    if legend:\n",
        "        plt.legend(loc=\"lower right\", fontsize=14)\n",
        "\n",
        "plt.figure(figsize=(8, 4))\n",
        "plot_decision_boundary(tree_clf, X, y)\n",
        "plt.plot([2.45, 2.45], [0, 3], \"k-\", linewidth=2)\n",
        "plt.plot([2.45, 7.5], [1.75, 1.75], \"k--\", linewidth=2)\n",
        "plt.plot([4.95, 4.95], [0, 1.75], \"k:\", linewidth=2)\n",
        "plt.plot([4.85, 4.85], [1.75, 3], \"k:\", linewidth=2)\n",
        "plt.text(1.40, 1.0, \"Depth=0\", fontsize=15)\n",
        "plt.text(3.2, 1.80, \"Depth=1\", fontsize=13)\n",
        "plt.text(4.05, 0.5, \"(Depth=2)\", fontsize=11)\n",
        "\n",
        "save_fig(\"decision_tree_decision_boundaries_plot\")\n",
        "plt.show()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[[0.         0.        ]\n",
            " [0.07575758 0.        ]\n",
            " [0.15151515 0.        ]\n",
            " [0.22727273 0.        ]\n",
            " [0.3030303  0.        ]]\n",
            "Saving figure decision_tree_decision_boundaries_plot\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
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\n",
            "text/plain": [
              "<Figure size 576x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "7WCP5fkgTT5w"
      },
      "source": [
        "# Predicting classes and class probabilities"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "6bUjapxzTT5w",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "1076f786-61f2-489b-a739-00316de9b77c"
      },
      "source": [
        "tree_clf.predict_proba([[5, 1.5]])"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[0.        , 0.90740741, 0.09259259]])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 5
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ebBZz-8ITT5x",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "2138ae1f-48f7-41c7-a289-ecd8a386e531"
      },
      "source": [
        "tree_clf.predict([[5, 1.5]])"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([1])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 6
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "-BCcM9fFTT5x"
      },
      "source": [
        "# Sensitivity to training set details"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "8BS2cs-3TT5y",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "b0d66052-d23f-47ea-a9da-900ae82b5781"
      },
      "source": [
        "X[(X[:, 1]==X[:, 1][y==1].max()) & (y==1)] # widest Iris versicolor flower"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[4.8, 1.8]])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 7
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Ou3AyoWSTT5z",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "93467a94-4212-4f30-9896-8eae1a3abee7"
      },
      "source": [
        "not_widest_versicolor = (X[:, 1]!=1.8) | (y==2)\n",
        "X_tweaked = X[not_widest_versicolor]\n",
        "y_tweaked = y[not_widest_versicolor]\n",
        "\n",
        "tree_clf_tweaked = DecisionTreeClassifier(max_depth=2, random_state=40)\n",
        "tree_clf_tweaked.fit(X_tweaked, y_tweaked)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "DecisionTreeClassifier(ccp_alpha=0.0, class_weight=None, criterion='gini',\n",
              "                       max_depth=2, max_features=None, max_leaf_nodes=None,\n",
              "                       min_impurity_decrease=0.0, min_impurity_split=None,\n",
              "                       min_samples_leaf=1, min_samples_split=2,\n",
              "                       min_weight_fraction_leaf=0.0, presort='deprecated',\n",
              "                       random_state=40, splitter='best')"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 8
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "tvb5Jo5DTT5z",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 405
        },
        "outputId": "e2ee9ad2-01b5-4fb8-9f5d-f5491b02c71f"
      },
      "source": [
        "plt.figure(figsize=(8, 4))\n",
        "plot_decision_boundary(tree_clf_tweaked, X_tweaked, y_tweaked, legend=False)\n",
        "plt.plot([0, 7.5], [0.8, 0.8], \"k-\", linewidth=2)\n",
        "plt.plot([0, 7.5], [1.75, 1.75], \"k--\", linewidth=2)\n",
        "plt.text(1.0, 0.9, \"Depth=0\", fontsize=15)\n",
        "plt.text(1.0, 1.80, \"Depth=1\", fontsize=13)\n",
        "\n",
        "save_fig(\"decision_tree_instability_plot\")\n",
        "plt.show()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[[0.         0.        ]\n",
            " [0.07575758 0.        ]\n",
            " [0.15151515 0.        ]\n",
            " [0.22727273 0.        ]\n",
            " [0.3030303  0.        ]]\n",
            "Saving figure decision_tree_instability_plot\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 576x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "AERyJLMjTT50",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 495
        },
        "outputId": "6be74c45-cfc2-4c64-9e2a-351ed4e1ae42"
      },
      "source": [
        "from sklearn.datasets import make_moons\n",
        "Xm, ym = make_moons(n_samples=100, noise=0.25, random_state=53)\n",
        "\n",
        "deep_tree_clf1 = DecisionTreeClassifier(random_state=42)\n",
        "deep_tree_clf2 = DecisionTreeClassifier(min_samples_leaf=4, random_state=42)\n",
        "deep_tree_clf1.fit(Xm, ym)\n",
        "deep_tree_clf2.fit(Xm, ym)\n",
        "\n",
        "fig, axes = plt.subplots(ncols=2, figsize=(10, 4), sharey=True)\n",
        "plt.sca(axes[0])\n",
        "plot_decision_boundary(deep_tree_clf1, Xm, ym, axes=[-1.5, 2.4, -1, 1.5], iris=False)\n",
        "plt.title(\"No restrictions\", fontsize=16)\n",
        "plt.sca(axes[1])\n",
        "plot_decision_boundary(deep_tree_clf2, Xm, ym, axes=[-1.5, 2.4, -1, 1.5], iris=False)\n",
        "plt.title(\"min_samples_leaf = {}\".format(deep_tree_clf2.min_samples_leaf), fontsize=14)\n",
        "plt.ylabel(\"\")\n",
        "\n",
        "save_fig(\"min_samples_leaf_plot\")\n",
        "plt.show()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[[-1.5        -1.        ]\n",
            " [-1.46060606 -1.        ]\n",
            " [-1.42121212 -1.        ]\n",
            " [-1.38181818 -1.        ]\n",
            " [-1.34242424 -1.        ]]\n",
            "[[-1.5        -1.        ]\n",
            " [-1.46060606 -1.        ]\n",
            " [-1.42121212 -1.        ]\n",
            " [-1.38181818 -1.        ]\n",
            " [-1.34242424 -1.        ]]\n",
            "Saving figure min_samples_leaf_plot\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 720x288 with 2 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ejdYhqTpTT50",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 331
        },
        "outputId": "9039b680-6e34-41b4-a60a-ce905b67b822"
      },
      "source": [
        "angle = np.pi / 180 * 20\n",
        "rotation_matrix = np.array([[np.cos(angle), -np.sin(angle)], [np.sin(angle), np.cos(angle)]])\n",
        "Xr = X.dot(rotation_matrix)\n",
        "\n",
        "tree_clf_r = DecisionTreeClassifier(random_state=42)\n",
        "tree_clf_r.fit(Xr, y)\n",
        "\n",
        "plt.figure(figsize=(8, 3))\n",
        "plot_decision_boundary(tree_clf_r, Xr, y, axes=[0.5, 7.5, -1.0, 1], iris=False)\n",
        "\n",
        "plt.show()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[[ 0.5        -1.        ]\n",
            " [ 0.57070707 -1.        ]\n",
            " [ 0.64141414 -1.        ]\n",
            " [ 0.71212121 -1.        ]\n",
            " [ 0.78282828 -1.        ]]\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 576x216 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "6QV_G3dbTT51",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 495
        },
        "outputId": "997bdbfd-3d35-4d3f-bf7d-f9fbaf829c7b"
      },
      "source": [
        "np.random.seed(6)\n",
        "Xs = np.random.rand(100, 2) - 0.5\n",
        "ys = (Xs[:, 0] > 0).astype(np.float32) * 2\n",
        "\n",
        "angle = np.pi / 4\n",
        "rotation_matrix = np.array([[np.cos(angle), -np.sin(angle)], [np.sin(angle), np.cos(angle)]])\n",
        "Xsr = Xs.dot(rotation_matrix)\n",
        "\n",
        "tree_clf_s = DecisionTreeClassifier(random_state=42)\n",
        "tree_clf_s.fit(Xs, ys)\n",
        "tree_clf_sr = DecisionTreeClassifier(random_state=42)\n",
        "tree_clf_sr.fit(Xsr, ys)\n",
        "\n",
        "fig, axes = plt.subplots(ncols=2, figsize=(10, 4), sharey=True)\n",
        "plt.sca(axes[0])\n",
        "plot_decision_boundary(tree_clf_s, Xs, ys, axes=[-0.7, 0.7, -0.7, 0.7], iris=False)\n",
        "plt.sca(axes[1])\n",
        "plot_decision_boundary(tree_clf_sr, Xsr, ys, axes=[-0.7, 0.7, -0.7, 0.7], iris=False)\n",
        "plt.ylabel(\"\")\n",
        "\n",
        "save_fig(\"sensitivity_to_rotation_plot\")\n",
        "plt.show()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[[-0.7        -0.7       ]\n",
            " [-0.68585859 -0.7       ]\n",
            " [-0.67171717 -0.7       ]\n",
            " [-0.65757576 -0.7       ]\n",
            " [-0.64343434 -0.7       ]]\n",
            "[[-0.7        -0.7       ]\n",
            " [-0.68585859 -0.7       ]\n",
            " [-0.67171717 -0.7       ]\n",
            " [-0.65757576 -0.7       ]\n",
            " [-0.64343434 -0.7       ]]\n",
            "Saving figure sensitivity_to_rotation_plot\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 720x288 with 2 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "dru9DUURTT51"
      },
      "source": [
        "# Regression trees"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "LzZpUM5sTT52"
      },
      "source": [
        "# Quadratic training set + noise\n",
        "np.random.seed(42)\n",
        "m = 200\n",
        "X = np.random.rand(m, 1)\n",
        "y = 4 * (X - 0.5) ** 2\n",
        "y = y + np.random.randn(m, 1) / 10"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "JAlVQ2SoTT52",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "96f416ef-be94-43af-a8fd-b13c5561c1cd"
      },
      "source": [
        "from sklearn.tree import DecisionTreeRegressor\n",
        "\n",
        "tree_reg = DecisionTreeRegressor(max_depth=2, random_state=42)\n",
        "tree_reg.fit(X, y)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "DecisionTreeRegressor(ccp_alpha=0.0, criterion='mse', max_depth=2,\n",
              "                      max_features=None, max_leaf_nodes=None,\n",
              "                      min_impurity_decrease=0.0, min_impurity_split=None,\n",
              "                      min_samples_leaf=1, min_samples_split=2,\n",
              "                      min_weight_fraction_leaf=0.0, presort='deprecated',\n",
              "                      random_state=42, splitter='best')"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 16
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "aYxAGEkqTT52",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 315
        },
        "outputId": "0e234218-f708-4ac3-ddb3-17eb67cb6913"
      },
      "source": [
        "from sklearn.tree import DecisionTreeRegressor\n",
        "\n",
        "tree_reg1 = DecisionTreeRegressor(random_state=42, max_depth=2)\n",
        "tree_reg2 = DecisionTreeRegressor(random_state=42, max_depth=3)\n",
        "tree_reg1.fit(X, y)\n",
        "tree_reg2.fit(X, y)\n",
        "\n",
        "def plot_regression_predictions(tree_reg, X, y, axes=[0, 1, -0.2, 1], ylabel=\"$y$\"):\n",
        "    x1 = np.linspace(axes[0], axes[1], 500).reshape(-1, 1)\n",
        "    y_pred = tree_reg.predict(x1)\n",
        "    plt.axis(axes)\n",
        "    plt.xlabel(\"$x_1$\", fontsize=18)\n",
        "    if ylabel:\n",
        "        plt.ylabel(ylabel, fontsize=18, rotation=0)\n",
        "    plt.plot(X, y, \"b.\")\n",
        "    plt.plot(x1, y_pred, \"r.-\", linewidth=2, label=r\"$\\hat{y}$\")\n",
        "\n",
        "fig, axes = plt.subplots(ncols=2, figsize=(10, 4), sharey=True)\n",
        "plt.sca(axes[0])\n",
        "plot_regression_predictions(tree_reg1, X, y)\n",
        "for split, style in ((0.1973, \"k-\"), (0.0917, \"k--\"), (0.7718, \"k--\")):\n",
        "    plt.plot([split, split], [-0.2, 1], style, linewidth=2)\n",
        "plt.text(0.21, 0.65, \"Depth=0\", fontsize=15)\n",
        "plt.text(0.01, 0.2, \"Depth=1\", fontsize=13)\n",
        "plt.text(0.65, 0.8, \"Depth=1\", fontsize=13)\n",
        "plt.legend(loc=\"upper center\", fontsize=18)\n",
        "plt.title(\"max_depth=2\", fontsize=14)\n",
        "\n",
        "plt.sca(axes[1])\n",
        "plot_regression_predictions(tree_reg2, X, y, ylabel=None)\n",
        "for split, style in ((0.1973, \"k-\"), (0.0917, \"k--\"), (0.7718, \"k--\")):\n",
        "    plt.plot([split, split], [-0.2, 1], style, linewidth=2)\n",
        "for split in (0.0458, 0.1298, 0.2873, 0.9040):\n",
        "    plt.plot([split, split], [-0.2, 1], \"k:\", linewidth=1)\n",
        "plt.text(0.3, 0.5, \"Depth=2\", fontsize=13)\n",
        "plt.title(\"max_depth=3\", fontsize=14)\n",
        "\n",
        "save_fig(\"tree_regression_plot\")\n",
        "plt.show()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Saving figure tree_regression_plot\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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            "text/plain": [
              "<Figure size 720x288 with 2 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "e1RQ-c4tTT53"
      },
      "source": [
        "export_graphviz(\n",
        "        tree_reg1,\n",
        "        out_file=os.path.join(IMAGES_PATH, \"regression_tree.dot\"),\n",
        "        feature_names=[\"x1\"],\n",
        "        rounded=True,\n",
        "        filled=True\n",
        "    )"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "HTWcmK1uTT53",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 380
        },
        "outputId": "b44c9065-a49c-446e-e119-8635d44818b3"
      },
      "source": [
        "Source.from_file(os.path.join(IMAGES_PATH, \"regression_tree.dot\"))"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<graphviz.files.Source at 0x7f669bfd4f10>"
            ],
            "image/svg+xml": "<?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\"?>\n<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n<!-- Generated by graphviz version 2.40.1 (20161225.0304)\n -->\n<!-- Title: Tree Pages: 1 -->\n<svg width=\"486pt\" height=\"269pt\"\n viewBox=\"0.00 0.00 486.00 269.00\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n<g id=\"graph0\" class=\"graph\" transform=\"scale(1 1) rotate(0) translate(4 265)\">\n<title>Tree</title>\n<polygon fill=\"#ffffff\" stroke=\"transparent\" points=\"-4,4 -4,-265 482,-265 482,4 -4,4\"/>\n<!-- 0 -->\n<g id=\"node1\" class=\"node\">\n<title>0</title>\n<path fill=\"#f6d6be\" stroke=\"#000000\" d=\"M281,-261C281,-261 193,-261 193,-261 187,-261 181,-255 181,-249 181,-249 181,-205 181,-205 181,-199 187,-193 193,-193 193,-193 281,-193 281,-193 287,-193 293,-199 293,-205 293,-205 293,-249 293,-249 293,-255 287,-261 281,-261\"/>\n<text text-anchor=\"middle\" x=\"237\" y=\"-245.8\" font-family=\"Helvetica,sans-Serif\" font-size=\"14.00\" fill=\"#000000\">x1 &lt;= 0.197</text>\n<text text-anchor=\"middle\" x=\"237\" y=\"-230.8\" font-family=\"Helvetica,sans-Serif\" font-size=\"14.00\" fill=\"#000000\">mse = 0.098</text>\n<text text-anchor=\"middle\" x=\"237\" y=\"-215.8\" font-family=\"Helvetica,sans-Serif\" font-size=\"14.00\" fill=\"#000000\">samples = 200</text>\n<text text-anchor=\"middle\" x=\"237\" y=\"-200.8\" font-family=\"Helvetica,sans-Serif\" font-size=\"14.00\" fill=\"#000000\">value = 0.354</text>\n</g>\n<!-- 1 -->\n<g id=\"node2\" class=\"node\">\n<title>1</title>\n<path fill=\"#eb9d65\" stroke=\"#000000\" d=\"M214,-157C214,-157 134,-157 134,-157 128,-157 122,-151 122,-145 122,-145 122,-101 122,-101 122,-95 128,-89 134,-89 134,-89 214,-89 214,-89 220,-89 226,-95 226,-101 226,-101 226,-145 226,-145 226,-151 220,-157 214,-157\"/>\n<text text-anchor=\"middle\" x=\"174\" y=\"-141.8\" font-family=\"Helvetica,sans-Serif\" font-size=\"14.00\" fill=\"#000000\">x1 &lt;= 0.092</text>\n<text text-anchor=\"middle\" x=\"174\" y=\"-126.8\" font-family=\"Helvetica,sans-Serif\" font-size=\"14.00\" fill=\"#000000\">mse = 0.038</text>\n<text text-anchor=\"middle\" x=\"174\" y=\"-111.8\" font-family=\"Helvetica,sans-Serif\" font-size=\"14.00\" fill=\"#000000\">samples = 44</text>\n<text text-anchor=\"middle\" x=\"174\" y=\"-96.8\" font-family=\"Helvetica,sans-Serif\" font-size=\"14.00\" fill=\"#000000\">value = 0.689</text>\n</g>\n<!-- 0&#45;&gt;1 -->\n<g id=\"edge1\" class=\"edge\">\n<title>0&#45;&gt;1</title>\n<path fill=\"none\" stroke=\"#000000\" d=\"M216.3714,-192.9465C211.1501,-184.3271 205.4745,-174.9579 200.0245,-165.9611\"/>\n<polygon fill=\"#000000\" stroke=\"#000000\" points=\"202.8497,-163.8697 194.6749,-157.13 196.8626,-167.4965 202.8497,-163.8697\"/>\n<text text-anchor=\"middle\" x=\"188.7142\" y=\"-177.709\" font-family=\"Helvetica,sans-Serif\" font-size=\"14.00\" fill=\"#000000\">True</text>\n</g>\n<!-- 4 -->\n<g id=\"node5\" class=\"node\">\n<title>4</title>\n<path fill=\"#fae6d7\" stroke=\"#000000\" d=\"M344,-157C344,-157 256,-157 256,-157 250,-157 244,-151 244,-145 244,-145 244,-101 244,-101 244,-95 250,-89 256,-89 256,-89 344,-89 344,-89 350,-89 356,-95 356,-101 356,-101 356,-145 356,-145 356,-151 350,-157 344,-157\"/>\n<text text-anchor=\"middle\" x=\"300\" y=\"-141.8\" font-family=\"Helvetica,sans-Serif\" font-size=\"14.00\" fill=\"#000000\">x1 &lt;= 0.772</text>\n<text text-anchor=\"middle\" x=\"300\" y=\"-126.8\" font-family=\"Helvetica,sans-Serif\" font-size=\"14.00\" fill=\"#000000\">mse = 0.074</text>\n<text text-anchor=\"middle\" x=\"300\" y=\"-111.8\" font-family=\"Helvetica,sans-Serif\" font-size=\"14.00\" fill=\"#000000\">samples = 156</text>\n<text text-anchor=\"middle\" x=\"300\" y=\"-96.8\" font-family=\"Helvetica,sans-Serif\" font-size=\"14.00\" fill=\"#000000\">value = 0.259</text>\n</g>\n<!-- 0&#45;&gt;4 -->\n<g 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          },
          "metadata": {
            "tags": []
          },
          "execution_count": 19
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "mUUfniCmTT54",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 315
        },
        "outputId": "20991b8c-c4f3-441e-d6d7-e81efba02824"
      },
      "source": [
        "tree_reg1 = DecisionTreeRegressor(random_state=42)\n",
        "tree_reg2 = DecisionTreeRegressor(random_state=42, min_samples_leaf=10)\n",
        "tree_reg1.fit(X, y)\n",
        "tree_reg2.fit(X, y)\n",
        "\n",
        "x1 = np.linspace(0, 1, 500).reshape(-1, 1)\n",
        "y_pred1 = tree_reg1.predict(x1)\n",
        "y_pred2 = tree_reg2.predict(x1)\n",
        "\n",
        "fig, axes = plt.subplots(ncols=2, figsize=(10, 4), sharey=True)\n",
        "\n",
        "plt.sca(axes[0])\n",
        "plt.plot(X, y, \"b.\")\n",
        "plt.plot(x1, y_pred1, \"r.-\", linewidth=2, label=r\"$\\hat{y}$\")\n",
        "plt.axis([0, 1, -0.2, 1.1])\n",
        "plt.xlabel(\"$x_1$\", fontsize=18)\n",
        "plt.ylabel(\"$y$\", fontsize=18, rotation=0)\n",
        "plt.legend(loc=\"upper center\", fontsize=18)\n",
        "plt.title(\"No restrictions\", fontsize=14)\n",
        "\n",
        "plt.sca(axes[1])\n",
        "plt.plot(X, y, \"b.\")\n",
        "plt.plot(x1, y_pred2, \"r.-\", linewidth=2, label=r\"$\\hat{y}$\")\n",
        "plt.axis([0, 1, -0.2, 1.1])\n",
        "plt.xlabel(\"$x_1$\", fontsize=18)\n",
        "plt.title(\"min_samples_leaf={}\".format(tree_reg2.min_samples_leaf), fontsize=14)\n",
        "\n",
        "save_fig(\"tree_regression_regularization_plot\")\n",
        "plt.show()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Saving figure tree_regression_regularization_plot\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 720x288 with 2 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "2ha5L6UpTT54"
      },
      "source": [
        "# Exercise solutions"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "94VlhBSqTT55"
      },
      "source": [
        "## 1. to 6."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "sRusI9qVTT55"
      },
      "source": [
        "See appendix A."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "HALRLeGwTT56"
      },
      "source": [
        "## 7."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "BMwtL1g3TT57"
      },
      "source": [
        "_Exercise: train and fine-tune a Decision Tree for the moons dataset._"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "I3D7HLVbTT58"
      },
      "source": [
        "a. Generate a moons dataset using `make_moons(n_samples=10000, noise=0.4)`."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "8soC7HIcTT5-"
      },
      "source": [
        "Adding `random_state=42` to make this notebook's output constant:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ojSGEM9ZTT6A"
      },
      "source": [
        "from sklearn.datasets import make_moons\n",
        "\n",
        "X, y = make_moons(n_samples=10000, noise=0.4, random_state=42)"
      ],
      "execution_count": 1,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ESvQE9GgTT6B"
      },
      "source": [
        "b. Split it into a training set and a test set using `train_test_split()`."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "SNaLdvbBTT6B"
      },
      "source": [
        "from sklearn.model_selection import train_test_split\n",
        "\n",
        "X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2, random_state=42)"
      ],
      "execution_count": 2,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "b_jXGRuoTT6B"
      },
      "source": [
        "c. Use grid search with cross-validation (with the help of the `GridSearchCV` class) to find good hyperparameter values for a `DecisionTreeClassifier`. Hint: try various values for `max_leaf_nodes`."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "2KvCBsN-TT6C",
        "outputId": "9fd5e5ee-4d31-42c6-9051-96749ec73565",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "source": [
        "from sklearn.model_selection import GridSearchCV\n",
        "from sklearn.tree import DecisionTreeClassifier\n",
        "\n",
        "params = {'max_leaf_nodes': list(range(2, 100)), 'min_samples_split': [2, 3, 4]}\n",
        "grid_search_cv = GridSearchCV(DecisionTreeClassifier(random_state=42), params, verbose=1, cv=3)\n",
        "\n",
        "grid_search_cv.fit(X_train, y_train)"
      ],
      "execution_count": 5,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Fitting 3 folds for each of 294 candidates, totalling 882 fits\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "stream",
          "text": [
            "[Parallel(n_jobs=1)]: Using backend SequentialBackend with 1 concurrent workers.\n",
            "[Parallel(n_jobs=1)]: Done 882 out of 882 | elapsed:    8.9s finished\n"
          ],
          "name": "stderr"
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "GridSearchCV(cv=3, error_score=nan,\n",
              "             estimator=DecisionTreeClassifier(ccp_alpha=0.0, class_weight=None,\n",
              "                                              criterion='gini', max_depth=None,\n",
              "                                              max_features=None,\n",
              "                                              max_leaf_nodes=None,\n",
              "                                              min_impurity_decrease=0.0,\n",
              "                                              min_impurity_split=None,\n",
              "                                              min_samples_leaf=1,\n",
              "                                              min_samples_split=2,\n",
              "                                              min_weight_fraction_leaf=0.0,\n",
              "                                              presort='deprecated',\n",
              "                                              random_state=42,\n",
              "                                              splitter='best'),\n",
              "             iid='deprecated', n_jobs=None,\n",
              "             param_grid={'max_leaf_nodes': [2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12,\n",
              "                                            13, 14, 15, 16, 17, 18, 19, 20, 21,\n",
              "                                            22, 23, 24, 25, 26, 27, 28, 29, 30,\n",
              "                                            31, ...],\n",
              "                         'min_samples_split': [2, 3, 4]},\n",
              "             pre_dispatch='2*n_jobs', refit=True, return_train_score=False,\n",
              "             scoring=None, verbose=1)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 5
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ka60qQ2nTT6C",
        "outputId": "d4697607-ffa6-4a69-9595-66bdc70a0006",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "source": [
        "grid_search_cv.best_estimator_"
      ],
      "execution_count": 6,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "DecisionTreeClassifier(ccp_alpha=0.0, class_weight=None, criterion='gini',\n",
              "                       max_depth=None, max_features=None, max_leaf_nodes=17,\n",
              "                       min_impurity_decrease=0.0, min_impurity_split=None,\n",
              "                       min_samples_leaf=1, min_samples_split=2,\n",
              "                       min_weight_fraction_leaf=0.0, presort='deprecated',\n",
              "                       random_state=42, splitter='best')"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 6
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "GsaDx3PNTT6C"
      },
      "source": [
        "d. Train it on the full training set using these hyperparameters, and measure your model's performance on the test set. You should get roughly 85% to 87% accuracy."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Flmv2z2ATT6D"
      },
      "source": [
        "By default, `GridSearchCV` trains the best model found on the whole training set (you can change this by setting `refit=False`), so we don't need to do it again. We can simply evaluate the model's accuracy:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "nKZpq3FwTT6E",
        "outputId": "c1fee736-3f73-4418-f94c-f22981813dce",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "source": [
        "from sklearn.metrics import accuracy_score\n",
        "\n",
        "y_pred = grid_search_cv.predict(X_test)\n",
        "accuracy_score(y_test, y_pred)"
      ],
      "execution_count": 7,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.8695"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 7
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "OX-AQDw5TT6E"
      },
      "source": [
        "## 8."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "dEAiBYkzTT6E"
      },
      "source": [
        "_Exercise: Grow a forest._"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "EfTPVelaTT6E"
      },
      "source": [
        "a. Continuing the previous exercise, generate 1,000 subsets of the training set, each containing 100 instances selected randomly. Hint: you can use Scikit-Learn's `ShuffleSplit` class for this."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "S_zgoz9cTT6F"
      },
      "source": [
        "from sklearn.model_selection import ShuffleSplit\n",
        "\n",
        "n_trees = 1000\n",
        "n_instances = 100\n",
        "\n",
        "mini_sets = []\n",
        "\n",
        "rs = ShuffleSplit(n_splits=n_trees, test_size=len(X_train) - n_instances, random_state=42)\n",
        "for mini_train_index, mini_test_index in rs.split(X_train):\n",
        "    X_mini_train = X_train[mini_train_index]\n",
        "    y_mini_train = y_train[mini_train_index]\n",
        "    mini_sets.append((X_mini_train, y_mini_train))"
      ],
      "execution_count": 8,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "IMqB3CwETT6F"
      },
      "source": [
        "b. Train one Decision Tree on each subset, using the best hyperparameter values found above. Evaluate these 1,000 Decision Trees on the test set. Since they were trained on smaller sets, these Decision Trees will likely perform worse than the first Decision Tree, achieving only about 80% accuracy."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Aa1CtBiVTT6F",
        "outputId": "209f7526-59a1-4db7-abce-f92e06417fd4",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "source": [
        "from sklearn.base import clone\n",
        "import numpy as np\n",
        "\n",
        "\n",
        "forest = [clone(grid_search_cv.best_estimator_) for _ in range(n_trees)]\n",
        "\n",
        "accuracy_scores = []\n",
        "\n",
        "for tree, (X_mini_train, y_mini_train) in zip(forest, mini_sets):\n",
        "    tree.fit(X_mini_train, y_mini_train)\n",
        "    \n",
        "    y_pred = tree.predict(X_test)\n",
        "    accuracy_scores.append(accuracy_score(y_test, y_pred))\n",
        "\n",
        "np.mean(accuracy_scores)"
      ],
      "execution_count": 10,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.8054499999999999"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 10
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "weV-AV7NXbbE"
      },
      "source": [
        "forest"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "69uGoRsITT6F"
      },
      "source": [
        "c. Now comes the magic. For each test set instance, generate the predictions of the 1,000 Decision Trees, and keep only the most frequent prediction (you can use SciPy's `mode()` function for this). This gives you _majority-vote predictions_ over the test set."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "vdF-o26iTT6F"
      },
      "source": [
        "Y_pred = np.empty([n_trees, len(X_test)], dtype=np.uint8)\n",
        "\n",
        "for tree_index, tree in enumerate(forest):\n",
        "    Y_pred[tree_index] = tree.predict(X_test)"
      ],
      "execution_count": 12,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "9hYuPtI9YEmf",
        "outputId": "c69e601a-342c-474e-f2f9-71dda493867c",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "source": [
        "Y_pred"
      ],
      "execution_count": 14,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[0, 1, 0, ..., 0, 0, 1],\n",
              "       [1, 1, 1, ..., 0, 0, 0],\n",
              "       [1, 1, 0, ..., 0, 0, 1],\n",
              "       ...,\n",
              "       [1, 1, 0, ..., 0, 0, 0],\n",
              "       [1, 1, 0, ..., 0, 0, 1],\n",
              "       [1, 1, 0, ..., 0, 0, 0]], dtype=uint8)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 14
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "k6VLMrdDTT6F"
      },
      "source": [
        "from scipy.stats import mode\n",
        "\n",
        "y_pred_majority_votes, n_votes = mode(Y_pred, axis=0)"
      ],
      "execution_count": 15,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "IMat-Xm5TT6G"
      },
      "source": [
        "d. Evaluate these predictions on the test set: you should obtain a slightly higher accuracy than your first model (about 0.5 to 1.5% higher). Congratulations, you have trained a Random Forest classifier!"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "X_bFy7boTT6G",
        "outputId": "61ee45bc-827d-4ebf-a43b-c68e254a3a16",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "source": [
        "accuracy_score(y_test, y_pred_majority_votes.reshape([-1]))"
      ],
      "execution_count": 16,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.872"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 16
        }
      ]
    }
  ]
}