6_decision_trees.ipynb

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      "source": [
        "# Decision Trees\n",
        "\n",
        "Decision Trees are machine learning algorithms that can be used for both classification and regression tasks. They serve as the foundational building blocks for Random Forests.\n",
        "\n",
        "Various tree algorithms exist, and our attention is directed towards the CART algorithm implemented in `scikit-learn`. The CART algorithm generates binary trees, ensuring that each node, upon splitting, results in precisely two children denoted as True/False."
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        "# code to set things up\n",
        "\n",
        "# importing common libraries\n",
        "import numpy as np\n",
        "import pandas as pd\n",
        "\n",
        "# Things related to figures and plots\n",
        "# make figures look nicer\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "plt.rc('font', size=14)\n",
        "plt.rc('axes', labelsize=14, titlesize=14)\n",
        "plt.rc('legend', fontsize=14)\n",
        "plt.rc('xtick', labelsize=10)\n",
        "plt.rc('ytick', labelsize=10)\n"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Training and Visualizing a Decision Tree\n",
        "\n",
        "To illustrate how decision trees work, we will train a decision tree classifier on the Iris dataset, visualize the model, and use it for making predictions.\n",
        "\n",
        "Note: Decision trees do not require much data preparation (i.e. no need to scale the data or center it)"
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    {
      "cell_type": "code",
      "source": [
        "# Load the Iris dataset\n",
        "from sklearn import datasets\n",
        "\n",
        "iris = datasets.load_iris(as_frame=True)\n",
        "X_iris = iris.data[[\"petal length (cm)\", \"petal width (cm)\"]].values\n",
        "y_iris = iris.target"
      ],
      "metadata": {
        "id": "lZffcI6eUwBE"
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      "execution_count": 2,
      "outputs": []
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      "source": [
        "# Train a tree Decision Tree Classifier\n",
        "\n",
        "from sklearn.tree import DecisionTreeClassifier\n",
        "\n",
        "max_depth = 2\n",
        "#max_depth = None\n",
        "\n",
        "random_state = 42\n",
        "#random_state = 40 # generates a completly different decision boundary\n",
        "\n",
        "tree_clf = DecisionTreeClassifier(max_depth=max_depth, random_state=random_state)\n",
        "tree_clf.fit(X_iris, y_iris)\n",
        "\n"
      ],
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          "base_uri": "https://localhost:8080/",
          "height": 80
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        "outputId": "11e2d068-e039-4b31-ba16-21897e129e94"
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              "DecisionTreeClassifier(max_depth=2, random_state=42)"
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              "div.sk-label-container:hover .sk-estimator-doc-link.fitted:hover,\n",
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              "  color: var(--sklearn-color-background);\n",
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              "  position: relative;\n",
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              "  padding: .5ex;\n",
              "  margin: .5ex;\n",
              "  width: min-content;\n",
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              "  height: 1rem;\n",
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              "  background-color: var(--sklearn-color-fitted-level-3);\n",
              "}\n",
              "</style><div id=\"sk-container-id-1\" class=\"sk-top-container\"><div class=\"sk-text-repr-fallback\"><pre>DecisionTreeClassifier(max_depth=2, random_state=42)</pre><b>In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook. <br />On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.</b></div><div class=\"sk-container\" hidden><div class=\"sk-item\"><div class=\"sk-estimator fitted sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-1\" type=\"checkbox\" checked><label for=\"sk-estimator-id-1\" class=\"sk-toggleable__label fitted sk-toggleable__label-arrow fitted\">&nbsp;&nbsp;DecisionTreeClassifier<a class=\"sk-estimator-doc-link fitted\" rel=\"noreferrer\" target=\"_blank\" href=\"https://scikit-learn.org/1.5/modules/generated/sklearn.tree.DecisionTreeClassifier.html\">?<span>Documentation for DecisionTreeClassifier</span></a><span class=\"sk-estimator-doc-link fitted\">i<span>Fitted</span></span></label><div class=\"sk-toggleable__content fitted\"><pre>DecisionTreeClassifier(max_depth=2, random_state=42)</pre></div> </div></div></div></div>"
            ]
          },
          "metadata": {},
          "execution_count": 3
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "We can use [Graphviz](https://graphviz.org/) to visualize the tree."
      ],
      "metadata": {
        "id": "QmPK8BX2VJDW"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Visualize the tree\n",
        "from sklearn.tree import export_graphviz\n",
        "from graphviz import Source\n",
        "\n",
        "# Export the tree as graphvis\n",
        "export_graphviz(\n",
        "    tree_clf,\n",
        "    out_file=\"iris_tree.dot\",\n",
        "    feature_names=[\"petal length (cm)\", \"petal width (cm)\"],\n",
        "    class_names=iris.target_names,\n",
        "    rounded=True,\n",
        "    filled=True\n",
        ")\n",
        "\n",
        "Source.from_file(\"iris_tree.dot\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 440
        },
        "id": "UaUdTNBMU-fk",
        "outputId": "38ca5f62-0dda-41d5-b000-e49f1279a988"
      },
      "execution_count": 4,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "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 2.43.0 (0)\n -->\n<!-- Title: Tree Pages: 1 -->\n<svg width=\"351pt\" height=\"314pt\"\n viewBox=\"0.00 0.00 351.00 314.00\" 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(4 310)\">\n<title>Tree</title>\n<polygon fill=\"white\" stroke=\"transparent\" points=\"-4,4 -4,-310 347,-310 347,4 -4,4\"/>\n<!-- 0 -->\n<g id=\"node1\" class=\"node\">\n<title>0</title>\n<path fill=\"#ffffff\" stroke=\"black\" d=\"M209.5,-306C209.5,-306 65.5,-306 65.5,-306 59.5,-306 53.5,-300 53.5,-294 53.5,-294 53.5,-235 53.5,-235 53.5,-229 59.5,-223 65.5,-223 65.5,-223 209.5,-223 209.5,-223 215.5,-223 221.5,-229 221.5,-235 221.5,-235 221.5,-294 221.5,-294 221.5,-300 215.5,-306 209.5,-306\"/>\n<text text-anchor=\"middle\" x=\"137.5\" y=\"-290.8\" font-family=\"Helvetica,sans-Serif\" font-size=\"14.00\">petal length (cm) &lt;= 2.45</text>\n<text text-anchor=\"middle\" x=\"137.5\" y=\"-275.8\" font-family=\"Helvetica,sans-Serif\" font-size=\"14.00\">gini = 0.667</text>\n<text text-anchor=\"middle\" x=\"137.5\" y=\"-260.8\" font-family=\"Helvetica,sans-Serif\" font-size=\"14.00\">samples = 150</text>\n<text text-anchor=\"middle\" x=\"137.5\" y=\"-245.8\" font-family=\"Helvetica,sans-Serif\" font-size=\"14.00\">value = [50, 50, 50]</text>\n<text text-anchor=\"middle\" x=\"137.5\" y=\"-230.8\" font-family=\"Helvetica,sans-Serif\" font-size=\"14.00\">class = setosa</text>\n</g>\n<!-- 1 -->\n<g id=\"node2\" class=\"node\">\n<title>1</title>\n<path fill=\"#e58139\" stroke=\"black\" d=\"M105,-179.5C105,-179.5 12,-179.5 12,-179.5 6,-179.5 0,-173.5 0,-167.5 0,-167.5 0,-123.5 0,-123.5 0,-117.5 6,-111.5 12,-111.5 12,-111.5 105,-111.5 105,-111.5 111,-111.5 117,-117.5 117,-123.5 117,-123.5 117,-167.5 117,-167.5 117,-173.5 111,-179.5 105,-179.5\"/>\n<text text-anchor=\"middle\" x=\"58.5\" y=\"-164.3\" font-family=\"Helvetica,sans-Serif\" font-size=\"14.00\">gini = 0.0</text>\n<text text-anchor=\"middle\" x=\"58.5\" y=\"-149.3\" font-family=\"Helvetica,sans-Serif\" font-size=\"14.00\">samples = 50</text>\n<text text-anchor=\"middle\" x=\"58.5\" y=\"-134.3\" font-family=\"Helvetica,sans-Serif\" font-size=\"14.00\">value = [50, 0, 0]</text>\n<text text-anchor=\"middle\" x=\"58.5\" y=\"-119.3\" font-family=\"Helvetica,sans-Serif\" font-size=\"14.00\">class = setosa</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=\"black\" d=\"M110.09,-222.91C102.49,-211.65 94.23,-199.42 86.59,-188.11\"/>\n<polygon fill=\"black\" stroke=\"black\" points=\"89.39,-186 80.89,-179.67 83.59,-189.91 89.39,-186\"/>\n<text text-anchor=\"middle\" x=\"76.14\" y=\"-200.51\" font-family=\"Helvetica,sans-Serif\" font-size=\"14.00\">True</text>\n</g>\n<!-- 2 -->\n<g id=\"node3\" class=\"node\">\n<title>2</title>\n<path fill=\"#ffffff\" stroke=\"black\" d=\"M286,-187C286,-187 147,-187 147,-187 141,-187 135,-181 135,-175 135,-175 135,-116 135,-116 135,-110 141,-104 147,-104 147,-104 286,-104 286,-104 292,-104 298,-110 298,-116 298,-116 298,-175 298,-175 298,-181 292,-187 286,-187\"/>\n<text text-anchor=\"middle\" x=\"216.5\" y=\"-171.8\" font-family=\"Helvetica,sans-Serif\" font-size=\"14.00\">petal width (cm) &lt;= 1.75</text>\n<text text-anchor=\"middle\" x=\"216.5\" y=\"-156.8\" font-family=\"Helvetica,sans-Serif\" font-size=\"14.00\">gini = 0.5</text>\n<text text-anchor=\"middle\" x=\"216.5\" y=\"-141.8\" font-family=\"Helvetica,sans-Serif\" font-size=\"14.00\">samples = 100</text>\n<text text-anchor=\"middle\" x=\"216.5\" y=\"-126.8\" font-family=\"Helvetica,sans-Serif\" font-size=\"14.00\">value = [0, 50, 50]</text>\n<text text-anchor=\"middle\" x=\"216.5\" y=\"-111.8\" font-family=\"Helvetica,sans-Serif\" font-size=\"14.00\">class = versicolor</text>\n</g>\n<!-- 0&#45;&gt;2 -->\n<g id=\"edge2\" class=\"edge\">\n<title>0&#45;&gt;2</title>\n<path fill=\"none\" stroke=\"black\" d=\"M164.91,-222.91C170.91,-214.01 177.33,-204.51 183.53,-195.33\"/>\n<polygon fill=\"black\" stroke=\"black\" points=\"186.44,-197.27 189.14,-187.02 180.64,-193.35 186.44,-197.27\"/>\n<text text-anchor=\"middle\" x=\"193.9\" y=\"-207.86\" font-family=\"Helvetica,sans-Serif\" font-size=\"14.00\">False</text>\n</g>\n<!-- 3 -->\n<g id=\"node4\" class=\"node\">\n<title>3</title>\n<path fill=\"#4de88e\" stroke=\"black\" d=\"M196,-68C196,-68 99,-68 99,-68 93,-68 87,-62 87,-56 87,-56 87,-12 87,-12 87,-6 93,0 99,0 99,0 196,0 196,0 202,0 208,-6 208,-12 208,-12 208,-56 208,-56 208,-62 202,-68 196,-68\"/>\n<text text-anchor=\"middle\" x=\"147.5\" y=\"-52.8\" font-family=\"Helvetica,sans-Serif\" font-size=\"14.00\">gini = 0.168</text>\n<text text-anchor=\"middle\" x=\"147.5\" y=\"-37.8\" font-family=\"Helvetica,sans-Serif\" font-size=\"14.00\">samples = 54</text>\n<text text-anchor=\"middle\" x=\"147.5\" y=\"-22.8\" font-family=\"Helvetica,sans-Serif\" font-size=\"14.00\">value = [0, 49, 5]</text>\n<text text-anchor=\"middle\" x=\"147.5\" y=\"-7.8\" font-family=\"Helvetica,sans-Serif\" font-size=\"14.00\">class = versicolor</text>\n</g>\n<!-- 2&#45;&gt;3 -->\n<g id=\"edge3\" class=\"edge\">\n<title>2&#45;&gt;3</title>\n<path fill=\"none\" stroke=\"black\" d=\"M190.81,-103.73C185.29,-94.97 179.45,-85.7 173.91,-76.91\"/>\n<polygon fill=\"black\" stroke=\"black\" points=\"176.78,-74.89 168.48,-68.3 170.85,-78.63 176.78,-74.89\"/>\n</g>\n<!-- 4 -->\n<g id=\"node5\" class=\"node\">\n<title>4</title>\n<path fill=\"#843de6\" stroke=\"black\" d=\"M331,-68C331,-68 238,-68 238,-68 232,-68 226,-62 226,-56 226,-56 226,-12 226,-12 226,-6 232,0 238,0 238,0 331,0 331,0 337,0 343,-6 343,-12 343,-12 343,-56 343,-56 343,-62 337,-68 331,-68\"/>\n<text text-anchor=\"middle\" x=\"284.5\" y=\"-52.8\" font-family=\"Helvetica,sans-Serif\" font-size=\"14.00\">gini = 0.043</text>\n<text text-anchor=\"middle\" x=\"284.5\" y=\"-37.8\" font-family=\"Helvetica,sans-Serif\" font-size=\"14.00\">samples = 46</text>\n<text text-anchor=\"middle\" x=\"284.5\" y=\"-22.8\" font-family=\"Helvetica,sans-Serif\" font-size=\"14.00\">value = [0, 1, 45]</text>\n<text text-anchor=\"middle\" x=\"284.5\" y=\"-7.8\" font-family=\"Helvetica,sans-Serif\" font-size=\"14.00\">class = virginica</text>\n</g>\n<!-- 2&#45;&gt;4 -->\n<g id=\"edge4\" class=\"edge\">\n<title>2&#45;&gt;4</title>\n<path fill=\"none\" stroke=\"black\" d=\"M241.82,-103.73C247.26,-94.97 253.01,-85.7 258.48,-76.91\"/>\n<polygon fill=\"black\" stroke=\"black\" points=\"261.52,-78.64 263.82,-68.3 255.57,-74.95 261.52,-78.64\"/>\n</g>\n</g>\n</svg>\n",
            "text/plain": [
              "<graphviz.sources.Source at 0x7bc051d09480>"
            ]
          },
          "metadata": {},
          "execution_count": 4
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Making Predictions\n",
        "\n",
        "Predictions are simple to make once you have a trained tree. Let's use the graphviz output above to make predictions and learn how to read the graph.\n",
        "\n",
        "* The top of the graph shows the root node (depth 0)\n",
        "* The middle nodes are depth 1, and the last nodes are depth 2\n",
        "* Nodes without children are leaf nodes\n",
        "* Nodes with children are split nodes\n",
        "* The tree is binary (left=True, right=False) because we use the CART algorithm to fit the tree\n",
        "\n",
        "Let's predict the class for a new iris flower with petal length = 2.1 and petal width = 5.2. The root node asks if the petal length <= 2.45, in this case it is so you end up in the leaf node at depth 1, which indicate the class is setosa\n",
        "\n",
        "Let's predict the class for another iris flower with petal length = 5.5 and petal width = 1.5. The root node (petal length <= 2.45) leads us to the split node on depth 1. This in turn asks if the petal width <= 1.75, which it is so we end up in the green leaf node indicating the class is versicolor"
      ],
      "metadata": {
        "id": "aNCDAVY8Ws20"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "X_test = [\n",
        "    [2.1, 5.2],\n",
        "    [5.5, 1.5]\n",
        "]\n",
        "\n",
        "tree_clf.predict(X_test)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "U3HMi21uVKgD",
        "outputId": "5725bd47-b3e9-4101-8f7b-6faee8d12dd6"
      },
      "execution_count": 5,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([0, 1])"
            ]
          },
          "metadata": {},
          "execution_count": 5
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "iris.target_names"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "gre4Cv2hX5Ot",
        "outputId": "1a134b6d-1003-4f9e-951b-86bf938272e3"
      },
      "execution_count": 6,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array(['setosa', 'versicolor', 'virginica'], dtype='<U10')"
            ]
          },
          "metadata": {},
          "execution_count": 6
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "The nodes of the tree show additional info:\n",
        "\n",
        "* `samples`: Counts how many training instances it applies to. There are 150 instances at the root node, 50 have petal length <= 2.45. Out of the 100 instances left, 54 have petal width <= 1.75 and 46 have petal width >1.75\n",
        "* `value`: How many training instances of each class this node applies to. For exmple, the green leaf node applies to 0 Setosa, 49 versicolor and 5 virginica\n",
        "* `gini`: Measures the **Gini impurity**. The node is \"pure\" (`gini=0`) if all training instances it applies to belong to the same class. Orange leaf (right node/depth 1) applies to setosa flower only."
      ],
      "metadata": {
        "id": "nNRhrwKjX-uN"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Computing the Gini Impurity\n",
        "The _Gini impurity_ $G_i$ for a node $i$ can be calculated as:\n",
        "$$\n",
        "G_i = 1 - \\sum_{k=1}^{n} p_{i, k}^2\n",
        "$$\n",
        "\n",
        "Where $p_{i, k}$ is the ratio of instances belonging to class $k$ among all training instances in the $i$ node\n",
        "\n",
        "* For the orange node (left node/depth 1):\n",
        "$$\n",
        "G_1 = 1 - (\\frac{50}{50})^2 - (\\frac{0}{50})^2 - (\\frac{0}{50})^2 = 0\n",
        "$$\n",
        "\n",
        "* For green node (left node/depth 2)\n",
        "$$\n",
        "G_3 = 1 - (\\frac{0}{54})^2 - (\\frac{49}{54})^2 - (\\frac{5}{54})^2 = 0.1680384087791\n",
        "$$\n",
        "\n",
        "* For purple node (right node/depth 2)\n",
        "$$\n",
        "G_4 = 1 - (\\frac{0}{46})^2 - (\\frac{1}{46})^2 - (\\frac{45}{46})^2 = 0.04253308129\n",
        "$$"
      ],
      "metadata": {
        "id": "Zg9GTzjIYTYd"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Estimating Class Probabilities\n",
        "\n",
        "For a specific instance, traverse the tree and find the leaf node for the instance. The probabilities for each class can be computed using the ratio of training instances in that leaf node to its number of samples.\n",
        "\n",
        "Examples:\n",
        "* Instance `[1.2, 5.2]` will end up in (left node/depth 1). The prbabilities are:\n",
        "   * $p(k=0) = \\frac{50}{50} = 1$ (PREDICTED CLASS)\n",
        "   * $p(k=1) = \\frac{0}{50} = 0$\n",
        "   * $p(k=2) = \\frac{0}{50} = 0$\n",
        "\n",
        "\n",
        "* Instance `[5.5, 1.5]` will end up in (left node/depth 2). The prbabilities are:\n",
        "   * $p(k=0) = \\frac{0}{54} = 0$\n",
        "   * $p(k=1) = \\frac{49}{54} = 0.90740741$ (PREDICTED CLASS)\n",
        "   * $p(k=2) = \\frac{5}{54} = 0.09259259$"
      ],
      "metadata": {
        "id": "AU39-MFgYkqr"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "X_test"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "MpG52C5bX7HO",
        "outputId": "d53ab444-6a7a-4f3f-fd9a-9ca617b3ba45"
      },
      "execution_count": 7,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[[2.1, 5.2], [5.5, 1.5]]"
            ]
          },
          "metadata": {},
          "execution_count": 7
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "tree_clf.predict_proba(X_test)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "klwO9imeYuHE",
        "outputId": "cb2709c3-aa5a-4833-c40c-4e103fd5a2ef"
      },
      "execution_count": 8,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[1.        , 0.        , 0.        ],\n",
              "       [0.        , 0.90740741, 0.09259259]])"
            ]
          },
          "metadata": {},
          "execution_count": 8
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "tree_clf.predict(X_test)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "DK0j9gt3YxtH",
        "outputId": "d8ac08ca-232f-4bd0-d115-5cf09ba6da74"
      },
      "execution_count": 9,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([0, 1])"
            ]
          },
          "metadata": {},
          "execution_count": 9
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Ploting the Decision Boundaries"
      ],
      "metadata": {
        "id": "CMpRIErsZcv2"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "plt.figure(figsize=(8, 4))\n",
        "\n",
        "lengths, widths = np.meshgrid(np.linspace(0, 7.1, 500), np.linspace(0, 2.7, 500))\n",
        "X_iris_all = np.c_[lengths.ravel(), widths.ravel()]\n",
        "y_pred = tree_clf.predict(X_iris_all).reshape(lengths.shape)\n",
        "plt.contourf(lengths, widths, y_pred, alpha=0.3)\n",
        "\n",
        "# Plot the raw data\n",
        "for idx, (name, style) in enumerate(zip(iris.target_names, (\"mo\", \"bs\", \"g^\"))):\n",
        "  plt.plot(X_iris[:, 0][y_iris==idx], X_iris[:, 1][y_iris==idx],\n",
        "           style, label=f\"{name}\")\n",
        "\n",
        "\n",
        "plt.xlabel(\"Petal length (cm)\")\n",
        "plt.ylabel(\"Petal width (cm)\")\n",
        "plt.legend()\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 393
        },
        "id": "uerf9e15Yzm_",
        "outputId": "fd17c755-293b-4d43-edf8-e329415b1edf"
      },
      "execution_count": 10,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 800x400 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Accessing the tree Structure\n",
        "\n",
        "The tree structure and all its information, including the details displayed using Graphviz, can be directly accessed using the classifier's `tree_` attribute, as demonstrated in the following code cells."
      ],
      "metadata": {
        "id": "x7eUDkEAeKWj"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "tree = tree_clf.tree_"
      ],
      "metadata": {
        "id": "N5Bp0sSiZdri"
      },
      "execution_count": 11,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "type(tree)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "ZtFmnQzHen8I",
        "outputId": "4ed95581-4432-4609-db42-7db1a2674b5c"
      },
      "execution_count": 12,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "sklearn.tree._tree.Tree"
            ]
          },
          "metadata": {},
          "execution_count": 12
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "tree.node_count"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "5IMy8g70erwq",
        "outputId": "0be8c8a7-8517-4fde-cacd-4f3d2dcac2e2"
      },
      "execution_count": 13,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "5"
            ]
          },
          "metadata": {},
          "execution_count": 13
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "tree.max_depth"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "gFQ0XM75etjj",
        "outputId": "09ec3e6f-e34c-4214-dec0-969faa588eb0"
      },
      "execution_count": 14,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "2"
            ]
          },
          "metadata": {},
          "execution_count": 14
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "tree.max_n_classes"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "8Wb5c0Oiewu6",
        "outputId": "0dd61840-4935-4e8a-98eb-eb873785ed18"
      },
      "execution_count": 15,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "3"
            ]
          },
          "metadata": {},
          "execution_count": 15
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "tree.n_leaves"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "kqlYMekRexsg",
        "outputId": "c1f4cf40-d832-4ee8-b394-bd5255e31a43"
      },
      "execution_count": 16,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "3"
            ]
          },
          "metadata": {},
          "execution_count": 16
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Gini impurities for all nodes\n",
        "tree.impurity"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "C9i3PdLLeyqj",
        "outputId": "b67d6f10-6540-4d07-86fb-213ccd8bed3d"
      },
      "execution_count": 17,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([0.66666667, 0.        , 0.5       , 0.16803841, 0.04253308])"
            ]
          },
          "metadata": {},
          "execution_count": 17
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "The root node has index 0. The left and right children nodes of node `i` can be accessed using `tree.children_left[i]` and `tree.children_right[i]`. For example, the children of the root node are:"
      ],
      "metadata": {
        "id": "KRgN_UxnhnJa"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "print(tree.children_left[0]) # index of root's left child\n",
        "print(tree.children_right[0]) # index of root's right child"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Po4mig4Ye0ET",
        "outputId": "610b4f8b-1f0d-4d41-834f-dcc7a918ea51"
      },
      "execution_count": 18,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "1\n",
            "2\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# when the left and right children index are equal, you are at a leaf node\n",
        "# children of the node with index 1\n",
        "tree.children_left[1], tree.children_right[1]"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Z6H-CkXXe2IU",
        "outputId": "93d1e237-a69d-4b01-b0db-a4e4237ede95"
      },
      "execution_count": 19,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(-1, -1)"
            ]
          },
          "metadata": {},
          "execution_count": 19
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "tree.children_left"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "vvTkkdHn-bXI",
        "outputId": "f2114d6e-76df-4245-a0f4-5fab680cd0c0"
      },
      "execution_count": 20,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([ 1, -1,  3, -1, -1], dtype=int64)"
            ]
          },
          "metadata": {},
          "execution_count": 20
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "tree.children_right"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "_lj0_0zK-eAT",
        "outputId": "558ccf63-b5cb-49e5-cb01-209f9b3acb65"
      },
      "execution_count": 21,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([ 2, -1,  4, -1, -1], dtype=int64)"
            ]
          },
          "metadata": {},
          "execution_count": 21
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# indecies of leaf nodes\n",
        "is_leaf = (tree.children_left == tree.children_right)\n",
        "np.arange(tree.node_count)[is_leaf]"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "i7L3W10Je6hm",
        "outputId": "d2bebd53-d622-45fd-8815-69debb7d4197"
      },
      "execution_count": 22,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([1, 3, 4])"
            ]
          },
          "metadata": {},
          "execution_count": 22
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# split nodes use a feature to peform a split. The features are available\n",
        "tree.feature\n",
        "\n",
        "# values for leaf nodes should be ignored"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "eXdmRppWfVSU",
        "outputId": "f70fda56-a57e-4ad8-95dd-15b85f2dcaea"
      },
      "execution_count": 23,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([ 0, -2,  1, -2, -2], dtype=int64)"
            ]
          },
          "metadata": {},
          "execution_count": 23
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# threshold used for each feature\n",
        "# threshold for leaf nodes should be ignored\n",
        "tree.threshold"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "CekUF3nTfWCh",
        "outputId": "e6438795-7ec9-4643-f9f9-c3dda6afdade"
      },
      "execution_count": 24,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([ 2.44999999, -2.        ,  1.75      , -2.        , -2.        ])"
            ]
          },
          "metadata": {},
          "execution_count": 24
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# values/probabilities: the proportion of samples reaching a node for each class and for each output\n",
        "tree.value"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "-D8NbsSHfW73",
        "outputId": "4b3219c9-30e2-49e1-bb0c-a2d32b2edd02"
      },
      "execution_count": 25,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[[0.33333333, 0.33333333, 0.33333333]],\n",
              "\n",
              "       [[1.        , 0.        , 0.        ]],\n",
              "\n",
              "       [[0.        , 0.5       , 0.5       ]],\n",
              "\n",
              "       [[0.        , 0.90740741, 0.09259259]],\n",
              "\n",
              "       [[0.        , 0.02173913, 0.97826087]]])"
            ]
          },
          "metadata": {},
          "execution_count": 25
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "tree.n_node_samples"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "qvvEL_JPfX9A",
        "outputId": "9053d0ed-2819-4ab8-8245-18b324a933d1"
      },
      "execution_count": 26,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([150,  50, 100,  54,  46], dtype=int64)"
            ]
          },
          "metadata": {},
          "execution_count": 26
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# you can compute the depth of each node as follows:\n",
        "\n",
        "def compute_depth(tree_clf):\n",
        "    tree = tree_clf.tree_\n",
        "    depth = np.zeros(tree.node_count)\n",
        "    stack = [(0, 0)]\n",
        "    while stack:\n",
        "        node, node_depth = stack.pop()\n",
        "        depth[node] = node_depth\n",
        "        if tree.children_left[node] != tree.children_right[node]:\n",
        "            stack.append((tree.children_left[node], node_depth + 1))\n",
        "            stack.append((tree.children_right[node], node_depth + 1))\n",
        "    return depth\n",
        "\n",
        "depth = compute_depth(tree_clf)\n",
        "depth"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "psoQlKGgfY24",
        "outputId": "9e421d94-d055-4eed-a4b6-ca593b879b26"
      },
      "execution_count": 27,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([0., 1., 1., 2., 2.])"
            ]
          },
          "metadata": {},
          "execution_count": 27
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# get the feature and threshold of all split nodes at depth 1\n",
        "\n",
        "print(tree.feature[(depth == 1) & (~is_leaf)])\n",
        "print(tree.threshold[(depth == 1) & (~is_leaf)])"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Qmt6hKPkfZ2K",
        "outputId": "8a510436-df66-4d00-8646-e7bd3f88ab20"
      },
      "execution_count": 28,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[1]\n",
            "[1.75]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "# The CART Training Algorithm\n",
        "\n",
        "`sklearn` uses the ***Classification and Regression Tree (CART)*** algorithm to train (or grow) trees. The logic behind the algorithm is simple, use a single feature $k$ (i.e. petal length) and a threshold $t_k$ (i.e. <= 2.45) to split the training data into two subsets. $k$ and $t_k$ are chosen to produce the purest subsets, weighted by their size. The associated cost function:\n",
        "$$\n",
        "J(k, t_k) = \\frac{m_{left}}{m}G_{left} + \\frac{m_{right}}{m}G_{right}\n",
        "$$\n",
        "Where:\n",
        "$$\n",
        "\\begin{cases}\n",
        "G_{left/right} & \\text{measures the impurity of the left/right subset} \\\\\n",
        "m_{left/right} & \\text{is the number of instances in the left/right subset}\n",
        "\\end{cases}\n",
        "$$\n",
        "\n",
        "Once a split is completed, the subsets are split using the same logic, then the sub-subsets, and so on (recursively). The splitting should stop once a maximum depth (`max_depth`) is reached or if there is no split that will reduce impurity. Other regularization hyperparameters can also be used for stopping.\n",
        "\n",
        "The CART algorithm is a _greedy_ algorithm which finds a reasonably good but not necessarily optimum solution."
      ],
      "metadata": {
        "id": "XsPK25U5j3z8"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Regularization Hyperparameters\n",
        "\n",
        "Decision trees are **nonparametric** models, which does not imply that they have no parameters. On the contrary, they may have many parameters; however, unlike models with predefined assumptions (and predetermined number of parameters such as linear models), the number of parameters in decision trees is not fixed. When growing a decision tree, it dynamically adjusts to the training set. This is why decision trees should be regularized because, if left unconstrained, they are susceptible to overfitting.\n",
        "\n",
        "`DecisionTreeClassifier` has the following hyperparameters that can be used for regularization:\n",
        "* `max_depth`: Maximum depth of the tree (`None` = unlimited)\n",
        "* `max_features`: Maximum number of features that are evaluated for splitting at each node\n",
        "* `max_leaf_nodes`: Maximum number of leaf nodes\n",
        "------------\n",
        "* `min_samples_split`: Minimum number of samples required to split a node\n",
        "* `min_samples_leaf`: Minimum number of samples required for a leaf node to be created\n",
        "* `min_weight_fraction_leaf`: Same as `min_samples_leaf` but expressed as a fraction of the total number of weighted instances\n",
        "\n",
        "***Increasing `min_` or decreasing `max_` hyperparameters will regularize the model***"
      ],
      "metadata": {
        "id": "DgRnInUjkAPP"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# helper functions\n",
        "\n",
        "def plot_dataset(X, y, axes):\n",
        "  plt.plot(X[:, 0][y==0], X[:, 1][y==0], \"bs\")\n",
        "  plt.plot(X[:, 0][y==1], X[:, 1][y==1], \"g^\")\n",
        "  plt.axis(axes)\n",
        "  plt.grid(True)\n",
        "  plt.xlabel(\"$x_1$\")\n",
        "  plt.ylabel(\"$x_2$\", rotation=0)\n",
        "\n",
        "def plot_predictions(clf, axes):\n",
        "  x1s = np.linspace(axes[0], axes[1], 500)\n",
        "  x2s = np.linspace(axes[2], axes[3], 500)\n",
        "  x1, x2 = np.meshgrid(x1s, x2s)\n",
        "  X = np.c_[x1.ravel(), x2.ravel()]\n",
        "  y_pred = clf.predict(X).reshape(x1.shape)\n",
        "  plt.contourf(x1, x2, y_pred, cmap=plt.cm.brg, alpha=0.2)\n",
        "  plt.contour(x1, x2, y_pred, cmap=\"Greys\", alpha=0.8)\n"
      ],
      "metadata": {
        "id": "fdAB-3j-fa1x"
      },
      "execution_count": 29,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# Make two interleaving half circles\n",
        "\n",
        "from sklearn.datasets import make_moons\n",
        "\n",
        "X_moons, y_moons = make_moons(n_samples=150, noise=0.2, random_state=42)\n",
        "\n",
        "plt.figure(figsize=(6, 4))\n",
        "plot_dataset(X_moons, y_moons, [-1.5, 2.5, -1, 1.5])\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 398
        },
        "id": "XiuP3ybJoRHs",
        "outputId": "fe5dac4d-67ca-4f6c-ae71-d359f677f8cf"
      },
      "execution_count": 30,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 600x400 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "tree_clf1 = DecisionTreeClassifier(random_state=42) # no restrictions\n",
        "tree_clf1.fit(X_moons, y_moons)\n",
        "\n",
        "tree_clf2 = DecisionTreeClassifier(min_samples_leaf=5, random_state=42)\n",
        "tree_clf2.fit(X_moons, y_moons)\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 80
        },
        "id": "nl-CpP5roSS6",
        "outputId": "6d07e3c3-3e22-4616-a48a-ebe84b16ead6"
      },
      "execution_count": 31,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "DecisionTreeClassifier(min_samples_leaf=5, random_state=42)"
            ],
            "text/html": [
              "<style>#sk-container-id-2 {\n",
              "  /* Definition of color scheme common for light and dark mode */\n",
              "  --sklearn-color-text: black;\n",
              "  --sklearn-color-line: gray;\n",
              "  /* Definition of color scheme for unfitted estimators */\n",
              "  --sklearn-color-unfitted-level-0: #fff5e6;\n",
              "  --sklearn-color-unfitted-level-1: #f6e4d2;\n",
              "  --sklearn-color-unfitted-level-2: #ffe0b3;\n",
              "  --sklearn-color-unfitted-level-3: chocolate;\n",
              "  /* Definition of color scheme for fitted estimators */\n",
              "  --sklearn-color-fitted-level-0: #f0f8ff;\n",
              "  --sklearn-color-fitted-level-1: #d4ebff;\n",
              "  --sklearn-color-fitted-level-2: #b3dbfd;\n",
              "  --sklearn-color-fitted-level-3: cornflowerblue;\n",
              "\n",
              "  /* Specific color for light theme */\n",
              "  --sklearn-color-text-on-default-background: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, black)));\n",
              "  --sklearn-color-background: var(--sg-background-color, var(--theme-background, var(--jp-layout-color0, white)));\n",
              "  --sklearn-color-border-box: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, black)));\n",
              "  --sklearn-color-icon: #696969;\n",
              "\n",
              "  @media (prefers-color-scheme: dark) {\n",
              "    /* Redefinition of color scheme for dark theme */\n",
              "    --sklearn-color-text-on-default-background: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, white)));\n",
              "    --sklearn-color-background: var(--sg-background-color, var(--theme-background, var(--jp-layout-color0, #111)));\n",
              "    --sklearn-color-border-box: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, white)));\n",
              "    --sklearn-color-icon: #878787;\n",
              "  }\n",
              "}\n",
              "\n",
              "#sk-container-id-2 {\n",
              "  color: var(--sklearn-color-text);\n",
              "}\n",
              "\n",
              "#sk-container-id-2 pre {\n",
              "  padding: 0;\n",
              "}\n",
              "\n",
              "#sk-container-id-2 input.sk-hidden--visually {\n",
              "  border: 0;\n",
              "  clip: rect(1px 1px 1px 1px);\n",
              "  clip: rect(1px, 1px, 1px, 1px);\n",
              "  height: 1px;\n",
              "  margin: -1px;\n",
              "  overflow: hidden;\n",
              "  padding: 0;\n",
              "  position: absolute;\n",
              "  width: 1px;\n",
              "}\n",
              "\n",
              "#sk-container-id-2 div.sk-dashed-wrapped {\n",
              "  border: 1px dashed var(--sklearn-color-line);\n",
              "  margin: 0 0.4em 0.5em 0.4em;\n",
              "  box-sizing: border-box;\n",
              "  padding-bottom: 0.4em;\n",
              "  background-color: var(--sklearn-color-background);\n",
              "}\n",
              "\n",
              "#sk-container-id-2 div.sk-container {\n",
              "  /* jupyter's `normalize.less` sets `[hidden] { display: none; }`\n",
              "     but bootstrap.min.css set `[hidden] { display: none !important; }`\n",
              "     so we also need the `!important` here to be able to override the\n",
              "     default hidden behavior on the sphinx rendered scikit-learn.org.\n",
              "     See: https://github.com/scikit-learn/scikit-learn/issues/21755 */\n",
              "  display: inline-block !important;\n",
              "  position: relative;\n",
              "}\n",
              "\n",
              "#sk-container-id-2 div.sk-text-repr-fallback {\n",
              "  display: none;\n",
              "}\n",
              "\n",
              "div.sk-parallel-item,\n",
              "div.sk-serial,\n",
              "div.sk-item {\n",
              "  /* draw centered vertical line to link estimators */\n",
              "  background-image: linear-gradient(var(--sklearn-color-text-on-default-background), var(--sklearn-color-text-on-default-background));\n",
              "  background-size: 2px 100%;\n",
              "  background-repeat: no-repeat;\n",
              "  background-position: center center;\n",
              "}\n",
              "\n",
              "/* Parallel-specific style estimator block */\n",
              "\n",
              "#sk-container-id-2 div.sk-parallel-item::after {\n",
              "  content: \"\";\n",
              "  width: 100%;\n",
              "  border-bottom: 2px solid var(--sklearn-color-text-on-default-background);\n",
              "  flex-grow: 1;\n",
              "}\n",
              "\n",
              "#sk-container-id-2 div.sk-parallel {\n",
              "  display: flex;\n",
              "  align-items: stretch;\n",
              "  justify-content: center;\n",
              "  background-color: var(--sklearn-color-background);\n",
              "  position: relative;\n",
              "}\n",
              "\n",
              "#sk-container-id-2 div.sk-parallel-item {\n",
              "  display: flex;\n",
              "  flex-direction: column;\n",
              "}\n",
              "\n",
              "#sk-container-id-2 div.sk-parallel-item:first-child::after {\n",
              "  align-self: flex-end;\n",
              "  width: 50%;\n",
              "}\n",
              "\n",
              "#sk-container-id-2 div.sk-parallel-item:last-child::after {\n",
              "  align-self: flex-start;\n",
              "  width: 50%;\n",
              "}\n",
              "\n",
              "#sk-container-id-2 div.sk-parallel-item:only-child::after {\n",
              "  width: 0;\n",
              "}\n",
              "\n",
              "/* Serial-specific style estimator block */\n",
              "\n",
              "#sk-container-id-2 div.sk-serial {\n",
              "  display: flex;\n",
              "  flex-direction: column;\n",
              "  align-items: center;\n",
              "  background-color: var(--sklearn-color-background);\n",
              "  padding-right: 1em;\n",
              "  padding-left: 1em;\n",
              "}\n",
              "\n",
              "\n",
              "/* Toggleable style: style used for estimator/Pipeline/ColumnTransformer box that is\n",
              "clickable and can be expanded/collapsed.\n",
              "- Pipeline and ColumnTransformer use this feature and define the default style\n",
              "- Estimators will overwrite some part of the style using the `sk-estimator` class\n",
              "*/\n",
              "\n",
              "/* Pipeline and ColumnTransformer style (default) */\n",
              "\n",
              "#sk-container-id-2 div.sk-toggleable {\n",
              "  /* Default theme specific background. It is overwritten whether we have a\n",
              "  specific estimator or a Pipeline/ColumnTransformer */\n",
              "  background-color: var(--sklearn-color-background);\n",
              "}\n",
              "\n",
              "/* Toggleable label */\n",
              "#sk-container-id-2 label.sk-toggleable__label {\n",
              "  cursor: pointer;\n",
              "  display: block;\n",
              "  width: 100%;\n",
              "  margin-bottom: 0;\n",
              "  padding: 0.5em;\n",
              "  box-sizing: border-box;\n",
              "  text-align: center;\n",
              "}\n",
              "\n",
              "#sk-container-id-2 label.sk-toggleable__label-arrow:before {\n",
              "  /* Arrow on the left of the label */\n",
              "  content: \"▸\";\n",
              "  float: left;\n",
              "  margin-right: 0.25em;\n",
              "  color: var(--sklearn-color-icon);\n",
              "}\n",
              "\n",
              "#sk-container-id-2 label.sk-toggleable__label-arrow:hover:before {\n",
              "  color: var(--sklearn-color-text);\n",
              "}\n",
              "\n",
              "/* Toggleable content - dropdown */\n",
              "\n",
              "#sk-container-id-2 div.sk-toggleable__content {\n",
              "  max-height: 0;\n",
              "  max-width: 0;\n",
              "  overflow: hidden;\n",
              "  text-align: left;\n",
              "  /* unfitted */\n",
              "  background-color: var(--sklearn-color-unfitted-level-0);\n",
              "}\n",
              "\n",
              "#sk-container-id-2 div.sk-toggleable__content.fitted {\n",
              "  /* fitted */\n",
              "  background-color: var(--sklearn-color-fitted-level-0);\n",
              "}\n",
              "\n",
              "#sk-container-id-2 div.sk-toggleable__content pre {\n",
              "  margin: 0.2em;\n",
              "  border-radius: 0.25em;\n",
              "  color: var(--sklearn-color-text);\n",
              "  /* unfitted */\n",
              "  background-color: var(--sklearn-color-unfitted-level-0);\n",
              "}\n",
              "\n",
              "#sk-container-id-2 div.sk-toggleable__content.fitted pre {\n",
              "  /* unfitted */\n",
              "  background-color: var(--sklearn-color-fitted-level-0);\n",
              "}\n",
              "\n",
              "#sk-container-id-2 input.sk-toggleable__control:checked~div.sk-toggleable__content {\n",
              "  /* Expand drop-down */\n",
              "  max-height: 200px;\n",
              "  max-width: 100%;\n",
              "  overflow: auto;\n",
              "}\n",
              "\n",
              "#sk-container-id-2 input.sk-toggleable__control:checked~label.sk-toggleable__label-arrow:before {\n",
              "  content: \"▾\";\n",
              "}\n",
              "\n",
              "/* Pipeline/ColumnTransformer-specific style */\n",
              "\n",
              "#sk-container-id-2 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
              "  color: var(--sklearn-color-text);\n",
              "  background-color: var(--sklearn-color-unfitted-level-2);\n",
              "}\n",
              "\n",
              "#sk-container-id-2 div.sk-label.fitted input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
              "  background-color: var(--sklearn-color-fitted-level-2);\n",
              "}\n",
              "\n",
              "/* Estimator-specific style */\n",
              "\n",
              "/* Colorize estimator box */\n",
              "#sk-container-id-2 div.sk-estimator input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
              "  /* unfitted */\n",
              "  background-color: var(--sklearn-color-unfitted-level-2);\n",
              "}\n",
              "\n",
              "#sk-container-id-2 div.sk-estimator.fitted input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
              "  /* fitted */\n",
              "  background-color: var(--sklearn-color-fitted-level-2);\n",
              "}\n",
              "\n",
              "#sk-container-id-2 div.sk-label label.sk-toggleable__label,\n",
              "#sk-container-id-2 div.sk-label label {\n",
              "  /* The background is the default theme color */\n",
              "  color: var(--sklearn-color-text-on-default-background);\n",
              "}\n",
              "\n",
              "/* On hover, darken the color of the background */\n",
              "#sk-container-id-2 div.sk-label:hover label.sk-toggleable__label {\n",
              "  color: var(--sklearn-color-text);\n",
              "  background-color: var(--sklearn-color-unfitted-level-2);\n",
              "}\n",
              "\n",
              "/* Label box, darken color on hover, fitted */\n",
              "#sk-container-id-2 div.sk-label.fitted:hover label.sk-toggleable__label.fitted {\n",
              "  color: var(--sklearn-color-text);\n",
              "  background-color: var(--sklearn-color-fitted-level-2);\n",
              "}\n",
              "\n",
              "/* Estimator label */\n",
              "\n",
              "#sk-container-id-2 div.sk-label label {\n",
              "  font-family: monospace;\n",
              "  font-weight: bold;\n",
              "  display: inline-block;\n",
              "  line-height: 1.2em;\n",
              "}\n",
              "\n",
              "#sk-container-id-2 div.sk-label-container {\n",
              "  text-align: center;\n",
              "}\n",
              "\n",
              "/* Estimator-specific */\n",
              "#sk-container-id-2 div.sk-estimator {\n",
              "  font-family: monospace;\n",
              "  border: 1px dotted var(--sklearn-color-border-box);\n",
              "  border-radius: 0.25em;\n",
              "  box-sizing: border-box;\n",
              "  margin-bottom: 0.5em;\n",
              "  /* unfitted */\n",
              "  background-color: var(--sklearn-color-unfitted-level-0);\n",
              "}\n",
              "\n",
              "#sk-container-id-2 div.sk-estimator.fitted {\n",
              "  /* fitted */\n",
              "  background-color: var(--sklearn-color-fitted-level-0);\n",
              "}\n",
              "\n",
              "/* on hover */\n",
              "#sk-container-id-2 div.sk-estimator:hover {\n",
              "  /* unfitted */\n",
              "  background-color: var(--sklearn-color-unfitted-level-2);\n",
              "}\n",
              "\n",
              "#sk-container-id-2 div.sk-estimator.fitted:hover {\n",
              "  /* fitted */\n",
              "  background-color: var(--sklearn-color-fitted-level-2);\n",
              "}\n",
              "\n",
              "/* Specification for estimator info (e.g. \"i\" and \"?\") */\n",
              "\n",
              "/* Common style for \"i\" and \"?\" */\n",
              "\n",
              ".sk-estimator-doc-link,\n",
              "a:link.sk-estimator-doc-link,\n",
              "a:visited.sk-estimator-doc-link {\n",
              "  float: right;\n",
              "  font-size: smaller;\n",
              "  line-height: 1em;\n",
              "  font-family: monospace;\n",
              "  background-color: var(--sklearn-color-background);\n",
              "  border-radius: 1em;\n",
              "  height: 1em;\n",
              "  width: 1em;\n",
              "  text-decoration: none !important;\n",
              "  margin-left: 1ex;\n",
              "  /* unfitted */\n",
              "  border: var(--sklearn-color-unfitted-level-1) 1pt solid;\n",
              "  color: var(--sklearn-color-unfitted-level-1);\n",
              "}\n",
              "\n",
              ".sk-estimator-doc-link.fitted,\n",
              "a:link.sk-estimator-doc-link.fitted,\n",
              "a:visited.sk-estimator-doc-link.fitted {\n",
              "  /* fitted */\n",
              "  border: var(--sklearn-color-fitted-level-1) 1pt solid;\n",
              "  color: var(--sklearn-color-fitted-level-1);\n",
              "}\n",
              "\n",
              "/* On hover */\n",
              "div.sk-estimator:hover .sk-estimator-doc-link:hover,\n",
              ".sk-estimator-doc-link:hover,\n",
              "div.sk-label-container:hover .sk-estimator-doc-link:hover,\n",
              ".sk-estimator-doc-link:hover {\n",
              "  /* unfitted */\n",
              "  background-color: var(--sklearn-color-unfitted-level-3);\n",
              "  color: var(--sklearn-color-background);\n",
              "  text-decoration: none;\n",
              "}\n",
              "\n",
              "div.sk-estimator.fitted:hover .sk-estimator-doc-link.fitted:hover,\n",
              ".sk-estimator-doc-link.fitted:hover,\n",
              "div.sk-label-container:hover .sk-estimator-doc-link.fitted:hover,\n",
              ".sk-estimator-doc-link.fitted:hover {\n",
              "  /* fitted */\n",
              "  background-color: var(--sklearn-color-fitted-level-3);\n",
              "  color: var(--sklearn-color-background);\n",
              "  text-decoration: none;\n",
              "}\n",
              "\n",
              "/* Span, style for the box shown on hovering the info icon */\n",
              ".sk-estimator-doc-link span {\n",
              "  display: none;\n",
              "  z-index: 9999;\n",
              "  position: relative;\n",
              "  font-weight: normal;\n",
              "  right: .2ex;\n",
              "  padding: .5ex;\n",
              "  margin: .5ex;\n",
              "  width: min-content;\n",
              "  min-width: 20ex;\n",
              "  max-width: 50ex;\n",
              "  color: var(--sklearn-color-text);\n",
              "  box-shadow: 2pt 2pt 4pt #999;\n",
              "  /* unfitted */\n",
              "  background: var(--sklearn-color-unfitted-level-0);\n",
              "  border: .5pt solid var(--sklearn-color-unfitted-level-3);\n",
              "}\n",
              "\n",
              ".sk-estimator-doc-link.fitted span {\n",
              "  /* fitted */\n",
              "  background: var(--sklearn-color-fitted-level-0);\n",
              "  border: var(--sklearn-color-fitted-level-3);\n",
              "}\n",
              "\n",
              ".sk-estimator-doc-link:hover span {\n",
              "  display: block;\n",
              "}\n",
              "\n",
              "/* \"?\"-specific style due to the `<a>` HTML tag */\n",
              "\n",
              "#sk-container-id-2 a.estimator_doc_link {\n",
              "  float: right;\n",
              "  font-size: 1rem;\n",
              "  line-height: 1em;\n",
              "  font-family: monospace;\n",
              "  background-color: var(--sklearn-color-background);\n",
              "  border-radius: 1rem;\n",
              "  height: 1rem;\n",
              "  width: 1rem;\n",
              "  text-decoration: none;\n",
              "  /* unfitted */\n",
              "  color: var(--sklearn-color-unfitted-level-1);\n",
              "  border: var(--sklearn-color-unfitted-level-1) 1pt solid;\n",
              "}\n",
              "\n",
              "#sk-container-id-2 a.estimator_doc_link.fitted {\n",
              "  /* fitted */\n",
              "  border: var(--sklearn-color-fitted-level-1) 1pt solid;\n",
              "  color: var(--sklearn-color-fitted-level-1);\n",
              "}\n",
              "\n",
              "/* On hover */\n",
              "#sk-container-id-2 a.estimator_doc_link:hover {\n",
              "  /* unfitted */\n",
              "  background-color: var(--sklearn-color-unfitted-level-3);\n",
              "  color: var(--sklearn-color-background);\n",
              "  text-decoration: none;\n",
              "}\n",
              "\n",
              "#sk-container-id-2 a.estimator_doc_link.fitted:hover {\n",
              "  /* fitted */\n",
              "  background-color: var(--sklearn-color-fitted-level-3);\n",
              "}\n",
              "</style><div id=\"sk-container-id-2\" class=\"sk-top-container\"><div class=\"sk-text-repr-fallback\"><pre>DecisionTreeClassifier(min_samples_leaf=5, random_state=42)</pre><b>In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook. <br />On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.</b></div><div class=\"sk-container\" hidden><div class=\"sk-item\"><div class=\"sk-estimator fitted sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-2\" type=\"checkbox\" checked><label for=\"sk-estimator-id-2\" class=\"sk-toggleable__label fitted sk-toggleable__label-arrow fitted\">&nbsp;&nbsp;DecisionTreeClassifier<a class=\"sk-estimator-doc-link fitted\" rel=\"noreferrer\" target=\"_blank\" href=\"https://scikit-learn.org/1.5/modules/generated/sklearn.tree.DecisionTreeClassifier.html\">?<span>Documentation for DecisionTreeClassifier</span></a><span class=\"sk-estimator-doc-link fitted\">i<span>Fitted</span></span></label><div class=\"sk-toggleable__content fitted\"><pre>DecisionTreeClassifier(min_samples_leaf=5, random_state=42)</pre></div> </div></div></div></div>"
            ]
          },
          "metadata": {},
          "execution_count": 31
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "fig, axes = plt.subplots(ncols=2, figsize=(15, 4), sharey=True)\n",
        "\n",
        "plt.sca(axes[0])\n",
        "plot_predictions(tree_clf1, [-1.5, 2.5, -1, 1.5])\n",
        "plot_dataset(X_moons, y_moons, [-1.5, 2.5, -1, 1.5])\n",
        "plt.title(\"No restrictions\")\n",
        "\n",
        "plt.sca(axes[1])\n",
        "plot_predictions(tree_clf2, [-1.5, 2.5, -1, 1.5])\n",
        "plot_dataset(X_moons, y_moons, [-1.5, 2.5, -1, 1.5])\n",
        "plt.title(f\"min_samples_leaf = {tree_clf2.min_samples_leaf}\")\n",
        "plt.ylabel(\"\")\n",
        "\n",
        "plt.show()\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 382
        },
        "id": "hfWaBWZgoVU0",
        "outputId": "178a4c9c-2a22-434e-af75-11c988b2fc79"
      },
      "execution_count": 32,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1500x400 with 2 Axes>"
            ],
            "image/png": 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          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# generate a moons test set (with a different random seed)\n",
        "X_moons_test, y_moons_test = make_moons(n_samples=1000, noise=0.2, random_state=43)"
      ],
      "metadata": {
        "id": "izL0qFA9oWTc"
      },
      "execution_count": 33,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "tree_clf1.score(X_moons_test, y_moons_test)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "c5BBVsxJoYG9",
        "outputId": "1749a6e2-d477-4ef9-de6a-b74bb380bda5"
      },
      "execution_count": 34,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.898"
            ]
          },
          "metadata": {},
          "execution_count": 34
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "tree_clf2.score(X_moons_test, y_moons_test)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "JrE8FePpoZDb",
        "outputId": "ae20ea45-2ae8-4106-ae55-fae7af2120c4"
      },
      "execution_count": 35,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.92"
            ]
          },
          "metadata": {},
          "execution_count": 35
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "It appears that the regularized model outperforms the non-regularized one."
      ],
      "metadata": {
        "id": "FYzJrEbeocIy"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Regression\n",
        "\n",
        "Decision Trees can be used for regression. Let's test them on a noisy quadratic dataset"
      ],
      "metadata": {
        "id": "HTwI5GVfsNVo"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# generate non-linear quadratic regression data\n",
        "\n",
        "np.random.seed(42)\n",
        "X_quad = np.random.rand(200, 1) - 0.5\n",
        "y_quad = X_quad[:, 0] ** 2 + 0.025 * np.random.randn(200)\n",
        "\n",
        "plt.figure(figsize=(7, 5))\n",
        "plt.plot(X_quad, y_quad, \"bo\", markersize=4)\n",
        "plt.xlabel(\"$x_1$\")\n",
        "plt.ylabel(\"$y$\", rotation=0)\n",
        "plt.axis([-0.5, 0.5, -0.05, 0.25])\n",
        "plt.grid()\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 475
        },
        "id": "Uw7kIAFCoaT-",
        "outputId": "ced253cb-b90e-4ddd-f498-6e37785e067f"
      },
      "execution_count": 36,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 700x500 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Train a Decision tree regressor\n",
        "from sklearn.tree import DecisionTreeRegressor\n",
        "\n",
        "max_depth = 2\n",
        "#max_depth = 3\n",
        "#max_depth = None\n",
        "\n",
        "tree_reg = DecisionTreeRegressor(max_depth = max_depth, random_state=42)\n",
        "tree_reg.fit(X_quad, y_quad)\n",
        "\n",
        "export_graphviz(\n",
        "    tree_reg,\n",
        "    out_file=\"regression_tree.dot\",\n",
        "    feature_names=[\"x1\"],\n",
        "    rounded=True,\n",
        "    filled=True\n",
        ")\n",
        "\n",
        "Source.from_file(\"regression_tree.dot\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 380
        },
        "id": "fAKZxsAWsQ2N",
        "outputId": "b7ce7eb9-0527-4757-e4fa-b46105565dc7"
      },
      "execution_count": 37,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
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            "text/plain": [
              "<graphviz.sources.Source at 0x7bc012043730>"
            ]
          },
          "metadata": {},
          "execution_count": 37
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Predicting a value\n",
        "\n",
        "Similar to classification, predicting a value for a new instance is simple once you have a trained regression tree.\n",
        "\n",
        "Say you want to predict the value for $x_1 = 0.2$:\n",
        "* Root node: Tests $x_1 \\leq -0.303$ (False, move to the right child on depth 1)\n",
        "* Right split node on depth 1 test $x1 \\leq 0.272$ (True, move to the left child on depth 2)\n",
        "* Leaf node predicts a value of $0.028$ which is the average for all 110 samples in that leaf and the average MSE (for all 110 samples) is 0.001"
      ],
      "metadata": {
        "id": "YJThO4oouXCo"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Plot the regressor\n",
        "\n",
        "def plot_regression_predictions(tree_reg, X, y, axes=[-0.5, 0.5, -0.05, 0.25]):\n",
        "  x1 = np.linspace(axes[0], axes[1], 500).reshape(-1, 1)\n",
        "  y_pred = tree_reg.predict(x1)\n",
        "  plt.plot(X, y, \"b.\")\n",
        "  plt.plot(x1, y_pred, \"r.-\", linewidth=2, label=r\"$\\hat{y}$\")\n",
        "  plt.axis(axes)\n",
        "  plt.xlabel(\"$x_1$\")\n",
        "\n",
        "plot_regression_predictions(tree_reg, X_quad, y_quad)\n",
        "plt.title(f\"max_depth={tree_reg.tree_.max_depth}\")\n",
        "plt.legend(loc=\"upper center\")\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 478
        },
        "id": "9exptvCssSC_",
        "outputId": "4de082f4-cf5f-4fc7-d75a-c0c4c7959065"
      },
      "execution_count": 38,
      "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": [
        "Each segment of the prediction line is the average of all points within its region. In other words, the training algorithms tries to create regions where the training instances are as close as possible to the predicted value."
      ],
      "metadata": {
        "id": "ZG7WfLFBuwrH"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## The CART Training Algorithm\n",
        "\n",
        "The CART for regression works in the same way it works for classification; however, instead of spliting the trainin set so the impurity is minimized, it now splits the training set so that the weighted MSE is minimized for the different subsets. The cost function is:\n",
        "\n",
        "$$\n",
        "J(k, t_k) = \\frac{m_{left}}{m}\\text{MSE}_{left} + \\frac{m_{right}}{m}\\text{MSE}_{right}\n",
        "$$\n",
        "Where: $$\n",
        "\\begin{cases}\n",
        "\\text{MSE}_{\\text{node}} = \\frac{\\sum_{i \\in \\text{node}} (\\hat{y}_{\\text{node}} - y^{(i)})^2}{m_{\\text{node}}} \\\\\n",
        "\\hat{y}_{\\text{node}} = \\frac{\\sum_{i \\in \\text{node}} y^{(i)}}{m_{\\text{node}}} \\\\\n",
        "\\end{cases}\n",
        "$$"
      ],
      "metadata": {
        "id": "3EC44RNou9jk"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Regularization Hyperparameters\n",
        "\n",
        "Similar to classification, decision trees for regression are also prone to overfitting and should be regularized."
      ],
      "metadata": {
        "id": "ANSDQeteu_k4"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# no regularization\n",
        "tree_reg1 = DecisionTreeRegressor(random_state=42)\n",
        "tree_reg1.fit(X_quad, y_quad)\n",
        "\n",
        "# Some regularization\n",
        "min_samples_leaf = 10\n",
        "\n",
        "tree_reg2 = DecisionTreeRegressor(random_state=42, min_samples_leaf=min_samples_leaf)\n",
        "tree_reg2.fit(X_quad, y_quad)\n",
        "\n",
        "# plot\n",
        "fig, axes = plt.subplots(ncols=2, figsize=(15, 4), sharey=True)\n",
        "\n",
        "plt.sca(axes[0])\n",
        "plot_regression_predictions(tree_reg1, X_quad, y_quad)\n",
        "plt.legend(loc=\"upper center\")\n",
        "plt.title(\"No regularization\")\n",
        "plt.ylabel(\"$y$\", rotation=0)\n",
        "plt.sca(axes[1])\n",
        "plot_regression_predictions(tree_reg2, X_quad, y_quad)\n",
        "plt.legend(loc=\"upper center\")\n",
        "plt.title(f\"min_samples_leaf={tree_reg2.min_samples_leaf}\")\n",
        "\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 383
        },
        "id": "EsMjZ368uqXy",
        "outputId": "3de70e6e-51fa-47a6-a81b-b4a2a911de0a"
      },
      "execution_count": 39,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1500x400 with 2 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "The left figure is obviously overfitting the training data; whereas, the right figure shows that setting the minimum number of instances in a leaf to 10 (moderate regularization) produces a more reasonable model."
      ],
      "metadata": {
        "id": "a86WF4IAvGe8"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Sensitivity to Axis Orientation\n",
        "\n",
        "Decision trees generate orthogonal decision boundaries (all perpendicular to an axis). This makes them senesitive to data orientation.\n",
        "\n",
        "The following shows an example of a dataset and a rotated version of it (by 45 degrees) both fitted with trees of the same hyperparameters. The tree model fitted with the rotated data can sepearte all points successfully; however, the decision boundary is more convoluted and will probably not generalize as well."
      ],
      "metadata": {
        "id": "IRG-2ZaLxCvS"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Generate some linearly separable data\n",
        "np.random.seed(6)\n",
        "X_square = np.random.rand(100, 2) - 0.5\n",
        "y_square = (X_square[:, 0] > 0).astype(np.int64)\n",
        "\n",
        "# Generate a rotated version of the same data\n",
        "angle = np.pi / 4 # rotation angle = 45 degrees\n",
        "rotation_matrix = np.array([\n",
        "    [np.cos(angle), -np.sin(angle)],\n",
        "    [np.sin(angle), np.cos(angle)]\n",
        "])\n",
        "\n",
        "X_rotated_square = X_square @ rotation_matrix\n",
        "\n",
        "# Fit classification trees\n",
        "tree_clf_square = DecisionTreeClassifier(random_state=42)\n",
        "tree_clf_square.fit(X_square, y_square)\n",
        "\n",
        "tree_clf_rotate_square = DecisionTreeClassifier(random_state=42)\n",
        "tree_clf_rotate_square.fit(X_rotated_square, y_square)\n",
        "\n",
        "# Plot the decision boundaries\n",
        "fig, axes = plt.subplots(ncols=2, figsize=(15, 4), sharey=True)\n",
        "\n",
        "plt.sca(axes[0])\n",
        "plot_predictions(tree_clf_square, [-0.7, 0.7, -0.7, 0.7])\n",
        "plot_dataset(X_square, y_square, [-0.7, 0.7, -0.7, 0.7])\n",
        "plt.grid(False)\n",
        "\n",
        "plt.sca(axes[1])\n",
        "plot_predictions(tree_clf_rotate_square, [-0.7, 0.7, -0.7, 0.7])\n",
        "plot_dataset(X_rotated_square, y_square, [-0.7, 0.7, -0.7, 0.7])\n",
        "plt.grid(False)\n",
        "\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 363
        },
        "id": "bpI__YRkvEoU",
        "outputId": "a3d4dfde-57d2-401d-93e2-4f81df2c6d99"
      },
      "execution_count": 40,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1500x400 with 2 Axes>"
            ],
            "image/png": 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          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "One approach to reduce this limitation is to scale the data then transform it using principal component analysis (PCA). PCA decorrelate the data and transform it to a space where the eigen vector are the axes.\n",
        "\n",
        "**NOTE**: this approach might make things easier for trees (but not always)"
      ],
      "metadata": {
        "id": "be_JSkd5xHHr"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "from sklearn.pipeline import make_pipeline\n",
        "from sklearn.preprocessing import StandardScaler\n",
        "from sklearn.decomposition import PCA\n",
        "\n",
        "pca_pipeline = make_pipeline(\n",
        "    StandardScaler(),\n",
        "    PCA()\n",
        ")\n",
        "\n",
        "X_rotated_square_pca = pca_pipeline.fit_transform(X_rotated_square)\n",
        "\n",
        "pca_pipeline #to display the pca pipeline\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 143
        },
        "id": "PdHqTGNBxJpg",
        "outputId": "e07716b2-f655-49f3-a357-e4a13398ecf2"
      },
      "execution_count": 41,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Pipeline(steps=[('standardscaler', StandardScaler()), ('pca', PCA())])"
            ],
            "text/html": [
              "<style>#sk-container-id-3 {\n",
              "  /* Definition of color scheme common for light and dark mode */\n",
              "  --sklearn-color-text: black;\n",
              "  --sklearn-color-line: gray;\n",
              "  /* Definition of color scheme for unfitted estimators */\n",
              "  --sklearn-color-unfitted-level-0: #fff5e6;\n",
              "  --sklearn-color-unfitted-level-1: #f6e4d2;\n",
              "  --sklearn-color-unfitted-level-2: #ffe0b3;\n",
              "  --sklearn-color-unfitted-level-3: chocolate;\n",
              "  /* Definition of color scheme for fitted estimators */\n",
              "  --sklearn-color-fitted-level-0: #f0f8ff;\n",
              "  --sklearn-color-fitted-level-1: #d4ebff;\n",
              "  --sklearn-color-fitted-level-2: #b3dbfd;\n",
              "  --sklearn-color-fitted-level-3: cornflowerblue;\n",
              "\n",
              "  /* Specific color for light theme */\n",
              "  --sklearn-color-text-on-default-background: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, black)));\n",
              "  --sklearn-color-background: var(--sg-background-color, var(--theme-background, var(--jp-layout-color0, white)));\n",
              "  --sklearn-color-border-box: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, black)));\n",
              "  --sklearn-color-icon: #696969;\n",
              "\n",
              "  @media (prefers-color-scheme: dark) {\n",
              "    /* Redefinition of color scheme for dark theme */\n",
              "    --sklearn-color-text-on-default-background: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, white)));\n",
              "    --sklearn-color-background: var(--sg-background-color, var(--theme-background, var(--jp-layout-color0, #111)));\n",
              "    --sklearn-color-border-box: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, white)));\n",
              "    --sklearn-color-icon: #878787;\n",
              "  }\n",
              "}\n",
              "\n",
              "#sk-container-id-3 {\n",
              "  color: var(--sklearn-color-text);\n",
              "}\n",
              "\n",
              "#sk-container-id-3 pre {\n",
              "  padding: 0;\n",
              "}\n",
              "\n",
              "#sk-container-id-3 input.sk-hidden--visually {\n",
              "  border: 0;\n",
              "  clip: rect(1px 1px 1px 1px);\n",
              "  clip: rect(1px, 1px, 1px, 1px);\n",
              "  height: 1px;\n",
              "  margin: -1px;\n",
              "  overflow: hidden;\n",
              "  padding: 0;\n",
              "  position: absolute;\n",
              "  width: 1px;\n",
              "}\n",
              "\n",
              "#sk-container-id-3 div.sk-dashed-wrapped {\n",
              "  border: 1px dashed var(--sklearn-color-line);\n",
              "  margin: 0 0.4em 0.5em 0.4em;\n",
              "  box-sizing: border-box;\n",
              "  padding-bottom: 0.4em;\n",
              "  background-color: var(--sklearn-color-background);\n",
              "}\n",
              "\n",
              "#sk-container-id-3 div.sk-container {\n",
              "  /* jupyter's `normalize.less` sets `[hidden] { display: none; }`\n",
              "     but bootstrap.min.css set `[hidden] { display: none !important; }`\n",
              "     so we also need the `!important` here to be able to override the\n",
              "     default hidden behavior on the sphinx rendered scikit-learn.org.\n",
              "     See: https://github.com/scikit-learn/scikit-learn/issues/21755 */\n",
              "  display: inline-block !important;\n",
              "  position: relative;\n",
              "}\n",
              "\n",
              "#sk-container-id-3 div.sk-text-repr-fallback {\n",
              "  display: none;\n",
              "}\n",
              "\n",
              "div.sk-parallel-item,\n",
              "div.sk-serial,\n",
              "div.sk-item {\n",
              "  /* draw centered vertical line to link estimators */\n",
              "  background-image: linear-gradient(var(--sklearn-color-text-on-default-background), var(--sklearn-color-text-on-default-background));\n",
              "  background-size: 2px 100%;\n",
              "  background-repeat: no-repeat;\n",
              "  background-position: center center;\n",
              "}\n",
              "\n",
              "/* Parallel-specific style estimator block */\n",
              "\n",
              "#sk-container-id-3 div.sk-parallel-item::after {\n",
              "  content: \"\";\n",
              "  width: 100%;\n",
              "  border-bottom: 2px solid var(--sklearn-color-text-on-default-background);\n",
              "  flex-grow: 1;\n",
              "}\n",
              "\n",
              "#sk-container-id-3 div.sk-parallel {\n",
              "  display: flex;\n",
              "  align-items: stretch;\n",
              "  justify-content: center;\n",
              "  background-color: var(--sklearn-color-background);\n",
              "  position: relative;\n",
              "}\n",
              "\n",
              "#sk-container-id-3 div.sk-parallel-item {\n",
              "  display: flex;\n",
              "  flex-direction: column;\n",
              "}\n",
              "\n",
              "#sk-container-id-3 div.sk-parallel-item:first-child::after {\n",
              "  align-self: flex-end;\n",
              "  width: 50%;\n",
              "}\n",
              "\n",
              "#sk-container-id-3 div.sk-parallel-item:last-child::after {\n",
              "  align-self: flex-start;\n",
              "  width: 50%;\n",
              "}\n",
              "\n",
              "#sk-container-id-3 div.sk-parallel-item:only-child::after {\n",
              "  width: 0;\n",
              "}\n",
              "\n",
              "/* Serial-specific style estimator block */\n",
              "\n",
              "#sk-container-id-3 div.sk-serial {\n",
              "  display: flex;\n",
              "  flex-direction: column;\n",
              "  align-items: center;\n",
              "  background-color: var(--sklearn-color-background);\n",
              "  padding-right: 1em;\n",
              "  padding-left: 1em;\n",
              "}\n",
              "\n",
              "\n",
              "/* Toggleable style: style used for estimator/Pipeline/ColumnTransformer box that is\n",
              "clickable and can be expanded/collapsed.\n",
              "- Pipeline and ColumnTransformer use this feature and define the default style\n",
              "- Estimators will overwrite some part of the style using the `sk-estimator` class\n",
              "*/\n",
              "\n",
              "/* Pipeline and ColumnTransformer style (default) */\n",
              "\n",
              "#sk-container-id-3 div.sk-toggleable {\n",
              "  /* Default theme specific background. It is overwritten whether we have a\n",
              "  specific estimator or a Pipeline/ColumnTransformer */\n",
              "  background-color: var(--sklearn-color-background);\n",
              "}\n",
              "\n",
              "/* Toggleable label */\n",
              "#sk-container-id-3 label.sk-toggleable__label {\n",
              "  cursor: pointer;\n",
              "  display: block;\n",
              "  width: 100%;\n",
              "  margin-bottom: 0;\n",
              "  padding: 0.5em;\n",
              "  box-sizing: border-box;\n",
              "  text-align: center;\n",
              "}\n",
              "\n",
              "#sk-container-id-3 label.sk-toggleable__label-arrow:before {\n",
              "  /* Arrow on the left of the label */\n",
              "  content: \"▸\";\n",
              "  float: left;\n",
              "  margin-right: 0.25em;\n",
              "  color: var(--sklearn-color-icon);\n",
              "}\n",
              "\n",
              "#sk-container-id-3 label.sk-toggleable__label-arrow:hover:before {\n",
              "  color: var(--sklearn-color-text);\n",
              "}\n",
              "\n",
              "/* Toggleable content - dropdown */\n",
              "\n",
              "#sk-container-id-3 div.sk-toggleable__content {\n",
              "  max-height: 0;\n",
              "  max-width: 0;\n",
              "  overflow: hidden;\n",
              "  text-align: left;\n",
              "  /* unfitted */\n",
              "  background-color: var(--sklearn-color-unfitted-level-0);\n",
              "}\n",
              "\n",
              "#sk-container-id-3 div.sk-toggleable__content.fitted {\n",
              "  /* fitted */\n",
              "  background-color: var(--sklearn-color-fitted-level-0);\n",
              "}\n",
              "\n",
              "#sk-container-id-3 div.sk-toggleable__content pre {\n",
              "  margin: 0.2em;\n",
              "  border-radius: 0.25em;\n",
              "  color: var(--sklearn-color-text);\n",
              "  /* unfitted */\n",
              "  background-color: var(--sklearn-color-unfitted-level-0);\n",
              "}\n",
              "\n",
              "#sk-container-id-3 div.sk-toggleable__content.fitted pre {\n",
              "  /* unfitted */\n",
              "  background-color: var(--sklearn-color-fitted-level-0);\n",
              "}\n",
              "\n",
              "#sk-container-id-3 input.sk-toggleable__control:checked~div.sk-toggleable__content {\n",
              "  /* Expand drop-down */\n",
              "  max-height: 200px;\n",
              "  max-width: 100%;\n",
              "  overflow: auto;\n",
              "}\n",
              "\n",
              "#sk-container-id-3 input.sk-toggleable__control:checked~label.sk-toggleable__label-arrow:before {\n",
              "  content: \"▾\";\n",
              "}\n",
              "\n",
              "/* Pipeline/ColumnTransformer-specific style */\n",
              "\n",
              "#sk-container-id-3 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
              "  color: var(--sklearn-color-text);\n",
              "  background-color: var(--sklearn-color-unfitted-level-2);\n",
              "}\n",
              "\n",
              "#sk-container-id-3 div.sk-label.fitted input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
              "  background-color: var(--sklearn-color-fitted-level-2);\n",
              "}\n",
              "\n",
              "/* Estimator-specific style */\n",
              "\n",
              "/* Colorize estimator box */\n",
              "#sk-container-id-3 div.sk-estimator input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
              "  /* unfitted */\n",
              "  background-color: var(--sklearn-color-unfitted-level-2);\n",
              "}\n",
              "\n",
              "#sk-container-id-3 div.sk-estimator.fitted input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
              "  /* fitted */\n",
              "  background-color: var(--sklearn-color-fitted-level-2);\n",
              "}\n",
              "\n",
              "#sk-container-id-3 div.sk-label label.sk-toggleable__label,\n",
              "#sk-container-id-3 div.sk-label label {\n",
              "  /* The background is the default theme color */\n",
              "  color: var(--sklearn-color-text-on-default-background);\n",
              "}\n",
              "\n",
              "/* On hover, darken the color of the background */\n",
              "#sk-container-id-3 div.sk-label:hover label.sk-toggleable__label {\n",
              "  color: var(--sklearn-color-text);\n",
              "  background-color: var(--sklearn-color-unfitted-level-2);\n",
              "}\n",
              "\n",
              "/* Label box, darken color on hover, fitted */\n",
              "#sk-container-id-3 div.sk-label.fitted:hover label.sk-toggleable__label.fitted {\n",
              "  color: var(--sklearn-color-text);\n",
              "  background-color: var(--sklearn-color-fitted-level-2);\n",
              "}\n",
              "\n",
              "/* Estimator label */\n",
              "\n",
              "#sk-container-id-3 div.sk-label label {\n",
              "  font-family: monospace;\n",
              "  font-weight: bold;\n",
              "  display: inline-block;\n",
              "  line-height: 1.2em;\n",
              "}\n",
              "\n",
              "#sk-container-id-3 div.sk-label-container {\n",
              "  text-align: center;\n",
              "}\n",
              "\n",
              "/* Estimator-specific */\n",
              "#sk-container-id-3 div.sk-estimator {\n",
              "  font-family: monospace;\n",
              "  border: 1px dotted var(--sklearn-color-border-box);\n",
              "  border-radius: 0.25em;\n",
              "  box-sizing: border-box;\n",
              "  margin-bottom: 0.5em;\n",
              "  /* unfitted */\n",
              "  background-color: var(--sklearn-color-unfitted-level-0);\n",
              "}\n",
              "\n",
              "#sk-container-id-3 div.sk-estimator.fitted {\n",
              "  /* fitted */\n",
              "  background-color: var(--sklearn-color-fitted-level-0);\n",
              "}\n",
              "\n",
              "/* on hover */\n",
              "#sk-container-id-3 div.sk-estimator:hover {\n",
              "  /* unfitted */\n",
              "  background-color: var(--sklearn-color-unfitted-level-2);\n",
              "}\n",
              "\n",
              "#sk-container-id-3 div.sk-estimator.fitted:hover {\n",
              "  /* fitted */\n",
              "  background-color: var(--sklearn-color-fitted-level-2);\n",
              "}\n",
              "\n",
              "/* Specification for estimator info (e.g. \"i\" and \"?\") */\n",
              "\n",
              "/* Common style for \"i\" and \"?\" */\n",
              "\n",
              ".sk-estimator-doc-link,\n",
              "a:link.sk-estimator-doc-link,\n",
              "a:visited.sk-estimator-doc-link {\n",
              "  float: right;\n",
              "  font-size: smaller;\n",
              "  line-height: 1em;\n",
              "  font-family: monospace;\n",
              "  background-color: var(--sklearn-color-background);\n",
              "  border-radius: 1em;\n",
              "  height: 1em;\n",
              "  width: 1em;\n",
              "  text-decoration: none !important;\n",
              "  margin-left: 1ex;\n",
              "  /* unfitted */\n",
              "  border: var(--sklearn-color-unfitted-level-1) 1pt solid;\n",
              "  color: var(--sklearn-color-unfitted-level-1);\n",
              "}\n",
              "\n",
              ".sk-estimator-doc-link.fitted,\n",
              "a:link.sk-estimator-doc-link.fitted,\n",
              "a:visited.sk-estimator-doc-link.fitted {\n",
              "  /* fitted */\n",
              "  border: var(--sklearn-color-fitted-level-1) 1pt solid;\n",
              "  color: var(--sklearn-color-fitted-level-1);\n",
              "}\n",
              "\n",
              "/* On hover */\n",
              "div.sk-estimator:hover .sk-estimator-doc-link:hover,\n",
              ".sk-estimator-doc-link:hover,\n",
              "div.sk-label-container:hover .sk-estimator-doc-link:hover,\n",
              ".sk-estimator-doc-link:hover {\n",
              "  /* unfitted */\n",
              "  background-color: var(--sklearn-color-unfitted-level-3);\n",
              "  color: var(--sklearn-color-background);\n",
              "  text-decoration: none;\n",
              "}\n",
              "\n",
              "div.sk-estimator.fitted:hover .sk-estimator-doc-link.fitted:hover,\n",
              ".sk-estimator-doc-link.fitted:hover,\n",
              "div.sk-label-container:hover .sk-estimator-doc-link.fitted:hover,\n",
              ".sk-estimator-doc-link.fitted:hover {\n",
              "  /* fitted */\n",
              "  background-color: var(--sklearn-color-fitted-level-3);\n",
              "  color: var(--sklearn-color-background);\n",
              "  text-decoration: none;\n",
              "}\n",
              "\n",
              "/* Span, style for the box shown on hovering the info icon */\n",
              ".sk-estimator-doc-link span {\n",
              "  display: none;\n",
              "  z-index: 9999;\n",
              "  position: relative;\n",
              "  font-weight: normal;\n",
              "  right: .2ex;\n",
              "  padding: .5ex;\n",
              "  margin: .5ex;\n",
              "  width: min-content;\n",
              "  min-width: 20ex;\n",
              "  max-width: 50ex;\n",
              "  color: var(--sklearn-color-text);\n",
              "  box-shadow: 2pt 2pt 4pt #999;\n",
              "  /* unfitted */\n",
              "  background: var(--sklearn-color-unfitted-level-0);\n",
              "  border: .5pt solid var(--sklearn-color-unfitted-level-3);\n",
              "}\n",
              "\n",
              ".sk-estimator-doc-link.fitted span {\n",
              "  /* fitted */\n",
              "  background: var(--sklearn-color-fitted-level-0);\n",
              "  border: var(--sklearn-color-fitted-level-3);\n",
              "}\n",
              "\n",
              ".sk-estimator-doc-link:hover span {\n",
              "  display: block;\n",
              "}\n",
              "\n",
              "/* \"?\"-specific style due to the `<a>` HTML tag */\n",
              "\n",
              "#sk-container-id-3 a.estimator_doc_link {\n",
              "  float: right;\n",
              "  font-size: 1rem;\n",
              "  line-height: 1em;\n",
              "  font-family: monospace;\n",
              "  background-color: var(--sklearn-color-background);\n",
              "  border-radius: 1rem;\n",
              "  height: 1rem;\n",
              "  width: 1rem;\n",
              "  text-decoration: none;\n",
              "  /* unfitted */\n",
              "  color: var(--sklearn-color-unfitted-level-1);\n",
              "  border: var(--sklearn-color-unfitted-level-1) 1pt solid;\n",
              "}\n",
              "\n",
              "#sk-container-id-3 a.estimator_doc_link.fitted {\n",
              "  /* fitted */\n",
              "  border: var(--sklearn-color-fitted-level-1) 1pt solid;\n",
              "  color: var(--sklearn-color-fitted-level-1);\n",
              "}\n",
              "\n",
              "/* On hover */\n",
              "#sk-container-id-3 a.estimator_doc_link:hover {\n",
              "  /* unfitted */\n",
              "  background-color: var(--sklearn-color-unfitted-level-3);\n",
              "  color: var(--sklearn-color-background);\n",
              "  text-decoration: none;\n",
              "}\n",
              "\n",
              "#sk-container-id-3 a.estimator_doc_link.fitted:hover {\n",
              "  /* fitted */\n",
              "  background-color: var(--sklearn-color-fitted-level-3);\n",
              "}\n",
              "</style><div id=\"sk-container-id-3\" class=\"sk-top-container\"><div class=\"sk-text-repr-fallback\"><pre>Pipeline(steps=[(&#x27;standardscaler&#x27;, StandardScaler()), (&#x27;pca&#x27;, PCA())])</pre><b>In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook. <br />On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.</b></div><div class=\"sk-container\" hidden><div class=\"sk-item sk-dashed-wrapped\"><div class=\"sk-label-container\"><div class=\"sk-label fitted sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-3\" type=\"checkbox\" ><label for=\"sk-estimator-id-3\" class=\"sk-toggleable__label fitted sk-toggleable__label-arrow fitted\">&nbsp;&nbsp;Pipeline<a class=\"sk-estimator-doc-link fitted\" rel=\"noreferrer\" target=\"_blank\" href=\"https://scikit-learn.org/1.5/modules/generated/sklearn.pipeline.Pipeline.html\">?<span>Documentation for Pipeline</span></a><span class=\"sk-estimator-doc-link fitted\">i<span>Fitted</span></span></label><div class=\"sk-toggleable__content fitted\"><pre>Pipeline(steps=[(&#x27;standardscaler&#x27;, StandardScaler()), (&#x27;pca&#x27;, PCA())])</pre></div> </div></div><div class=\"sk-serial\"><div class=\"sk-item\"><div class=\"sk-estimator fitted sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-4\" type=\"checkbox\" ><label for=\"sk-estimator-id-4\" class=\"sk-toggleable__label fitted sk-toggleable__label-arrow fitted\">&nbsp;StandardScaler<a class=\"sk-estimator-doc-link fitted\" rel=\"noreferrer\" target=\"_blank\" href=\"https://scikit-learn.org/1.5/modules/generated/sklearn.preprocessing.StandardScaler.html\">?<span>Documentation for StandardScaler</span></a></label><div class=\"sk-toggleable__content fitted\"><pre>StandardScaler()</pre></div> </div></div><div class=\"sk-item\"><div class=\"sk-estimator fitted sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-5\" type=\"checkbox\" ><label for=\"sk-estimator-id-5\" class=\"sk-toggleable__label fitted sk-toggleable__label-arrow fitted\">&nbsp;PCA<a class=\"sk-estimator-doc-link fitted\" rel=\"noreferrer\" target=\"_blank\" href=\"https://scikit-learn.org/1.5/modules/generated/sklearn.decomposition.PCA.html\">?<span>Documentation for PCA</span></a></label><div class=\"sk-toggleable__content fitted\"><pre>PCA()</pre></div> </div></div></div></div></div></div>"
            ]
          },
          "metadata": {},
          "execution_count": 41
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Fit classification trees\n",
        "tree_clf_pca = DecisionTreeClassifier(random_state=42)\n",
        "tree_clf_pca.fit(X_rotated_square_pca, y_square)\n",
        "\n",
        "# Plot the decision boundary\n",
        "plt.figure(figsize=(7, 4))\n",
        "plot_predictions(tree_clf_pca, [-2, 2, -2, 2])\n",
        "plot_dataset(X_rotated_square_pca, y_square, [-2, 2, -2, 2])\n",
        "plt.grid(False)\n",
        "plt.xlabel(\"$z_1$\")\n",
        "plt.ylabel(\"$z_2$\", rotation=0)\n",
        "\n",
        "\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 398
        },
        "id": "8yWcFBbRxJ7G",
        "outputId": "9aca4f95-31c6-4948-9c86-d56876ebc52f"
      },
      "execution_count": 42,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 700x400 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "The decision boundary is much simpler after scaling and PCA transformation."
      ],
      "metadata": {
        "id": "g2JXc_RdxMxH"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Scale/PCA the iris dataset\n",
        "\n",
        "X_iris_pca = pca_pipeline.fit_transform(X_iris)\n",
        "tree_clf_iris_pca = DecisionTreeClassifier(random_state=42, max_depth=2)\n",
        "tree_clf_iris_pca.fit(X_iris_pca, y_iris)\n",
        "\n",
        "# Plot the decision boundary\n",
        "plt.figure(figsize=(8, 4))\n",
        "axes = [-2.2, 2.4, -0.6, 0.7]\n",
        "plot_predictions(tree_clf_iris_pca, axes)\n",
        "for idx, (name, style) in enumerate(zip(iris.target_names, (\"yo\", \"bs\", \"g^\"))):\n",
        "    plt.plot(X_iris_pca[:, 0][y_iris == idx],\n",
        "             X_iris_pca[:, 1][y_iris == idx],\n",
        "             style, label=f\"{name}\")\n",
        "plt.xlabel(\"$z_1$\")\n",
        "plt.ylabel(\"$z_2$\", rotation=2)\n",
        "plt.legend(loc=\"upper center\")\n",
        "plt.show()\n",
        "\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 393
        },
        "id": "B_WEuujWxLKX",
        "outputId": "76697b29-4e9b-41b2-b530-024fb846a3ed"
      },
      "execution_count": 43,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 800x400 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    }
  ]
}