06-Decision_Trees.ipynb

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   "source": [
    "# Decision Trees"
   ]
  },
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Training and Visualizing Decision Trees"
   ]
  },
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To understand Decision Trees, let’s build one and take a look at how it makes predictions."
   ]
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       "DecisionTreeClassifier(max_depth=2)"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.datasets import load_iris\n",
    "from sklearn.tree import DecisionTreeClassifier\n",
    "\n",
    "iris = load_iris()\n",
    "X = iris.data[:,2:] # petal length and petal width\n",
    "y = iris.target\n",
    "\n",
    "tree_clf = DecisionTreeClassifier(max_depth=2)\n",
    "tree_clf.fit(X,y)"
   ]
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   "source": [
    "We can visualize the trained Decision Tree by first using the `export_graphviz()` method to ouput a graph definition file called *iris_tree.dot*:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.tree import export_graphviz\n",
    "\n",
    "export_graphviz(tree_clf,out_file=\"./decision_tree_images/iris_tree.dot\", feature_names=iris.feature_names[2:], class_names=iris.target_names, rounded=True, filled=True)"
   ]
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    "Then we can use the dot command-line tool from the Graphviz package to convert this *.dot*\n",
    "file to a variety of formats, such as PDF or PNG. This command line converts the *.dot* file\n",
    "to a *.png* image file:"
   ]
  },
  {
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   "source": [
    "```bash\n",
    "$ dot -Tpng iris_tree.dot -o iris_tree.png\n",
    "```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
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     "execution_count": 4,
     "metadata": {},
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    }
   ],
   "source": [
    "import os\n",
    "from graphviz import Source\n",
    "\n",
    "Source.from_file(os.path.join(\"decision_tree_images\", \"iris_tree.dot\"))\n",
    "\n",
    "# Our first decision tree looks like this"
   ]
  },
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   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Making Predictions"
   ]
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   "source": [
    "Let's see how the tree represented in above figure makes predictions. Suppose we find an iris flower and want to classify it. We start at the root node (depth 0, at the top): this node asks whether flower's petal length is less than 2.45 cm. If yes, we move down to the root's left child node (depth 1, left). In this case it is *leaf node* (i.e., it does not have any child nodes), so it does not ask any questions: simply look at the predicted class for that node, and the Decision Tree predicts that flower is an *Iris Setosa* (`class=setosa`)\n",
    "\n",
    "Now suppose we find another flower, and this time flower's petal length is greater than 2.45 cm. We must move down to root's right child node (depth 1, right), which is not leaf node, so the node asks the question: is the petal width smaller than 1.75 cm? If it is, then flower is most likely *Iris Versicolor* (depth 2, left). If not, it is likely it is likely an *Iris Virginica* (depth 2, right)."
   ]
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  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**NOTE:**\n",
    "\n",
    "One of the many qualities of Decision Trees is that they require very little data preparation. In fact, they don’t require feature scaling or centering at all."
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
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   "source": [
    "A node's `samples` attribute counts how many training instances it applies to. For example, 100 training instances have petal length greater than 2.45 cm (depth 1, right) , and those of 100, 54 have petal width smaller than 1.75 cm (depth 2, left).\n",
    "\n",
    "A nodes's `value` attribute tells us how many training instances of each class this node applies to: for example, the bottom-right node applies to 0 *Iris Setosa*, 1 *Iris Versicolor* and 45 *Iris Virginica*.\n",
    "\n",
    "Node's `gini` attribute measures its *impurity*: a node is \"pure\" (`gini = 0`) if all training instances it applies belong to the same class. For example: since the depth-1 left node node applies only to *Iris Setosa* training instances, it is pure and is `gini score` is 0."
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**NOTE:**\n",
    "\n",
    "Scikit-Learn uses the CART algorithm, which produces only *binary trees*: nonleaf nodes always have two children (i.e., questions only have yes/no answers). However, other algorithms such as ID3 can produce Decision Trees with nodes that have more than two children."
   ]
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   "cell_type": "markdown",
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   "source": [
    "Code to generate decision boundaries"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from matplotlib.colors import ListedColormap\n",
    "\n",
    "def plot_decision_boundary(clf, X, y, axes=[0, 7.5, 0, 3], iris=True, legend=False, plot_training=True):\n",
    "    x1s = np.linspace(axes[0], axes[1], 100)\n",
    "    x2s = np.linspace(axes[2], axes[3], 100)\n",
    "    x1, x2 = np.meshgrid(x1s, x2s)\n",
    "    X_new = np.c_[x1.ravel(), x2.ravel()]\n",
    "    y_pred = clf.predict(X_new).reshape(x1.shape)\n",
    "    custom_cmap = ListedColormap(['#fafab0','#9898ff','#a0faa0'])\n",
    "    plt.contourf(x1, x2, y_pred, alpha=0.3, cmap=custom_cmap)\n",
    "    if not iris:\n",
    "        custom_cmap2 = ListedColormap(['#7d7d58','#4c4c7f','#507d50'])\n",
    "        plt.contour(x1, x2, y_pred, cmap=custom_cmap2, alpha=0.8)\n",
    "    if plot_training:\n",
    "        plt.plot(X[:, 0][y==0], X[:, 1][y==0], \"yo\", label=\"Iris setosa\")\n",
    "        plt.plot(X[:, 0][y==1], X[:, 1][y==1], \"bs\", label=\"Iris versicolor\")\n",
    "        plt.plot(X[:, 0][y==2], X[:, 1][y==2], \"g^\", label=\"Iris virginica\")\n",
    "        plt.axis(axes)\n",
    "    if iris:\n",
    "        plt.xlabel(\"Petal length\", fontsize=14)\n",
    "        plt.ylabel(\"Petal width\", fontsize=14)\n",
    "    else:\n",
    "        plt.xlabel(r\"$x_1$\", fontsize=18)\n",
    "        plt.ylabel(r\"$x_2$\", fontsize=18, rotation=0)\n",
    "    if legend:\n",
    "        plt.legend(loc=\"lower right\", fontsize=14)\n",
    "\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
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",
      "text/plain": [
       "<Figure size 800x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(8,4))\n",
    "plot_decision_boundary(tree_clf, X, y)\n",
    "plt.plot([2.45, 2.45], [0,3], \"k-\", linewidth=2)\n",
    "plt.plot([2.45, 7.5], [1.75, 1.75], \"k--\", linewidth=2)\n",
    "plt.plot([4.95, 4.95], [0,1.75], \"k:\", linewidth=2)\n",
    "plt.plot([4.85, 4.85], [1.75, 3], \"k:\", linewidth=2)\n",
    "plt.text(1.40, 1.0, \"Depth=0\", fontsize=15)\n",
    "plt.text(3.2, 1.80, \"Depth=1\", fontsize=13)\n",
    "plt.text(4.05, 0.5, \"Depth=2\", fontsize=11)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Graph shows this Decision Tree's boundaries. Thick line represents the decision boundary for root node (depth-0): petal length=2.45cm. Since left hand are is pure (only *Iris Setosa*) it cannot be split any further. However, the right hand area is impure, so depth-1 right node splits it at petal width = 1.75cm (represented by dashed line). Since `max_depth` was set to 2, the Decision Tree stops right there. If we set `max_depth` to 3 (see below code), then the two depth-2 nodes would each add another decision boundaries (represnted by dotted lines)."
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Trying `max_depth`= 3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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      ],
      "text/plain": [
       "DecisionTreeClassifier(max_depth=3)"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tree_clf_depth_3 = DecisionTreeClassifier(max_depth=3)\n",
    "tree_clf_depth_3.fit(X,y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "export_graphviz(tree_clf_depth_3,out_file=\"./decision_tree_images/iris_tree_depth_3.dot\", feature_names=iris.feature_names[2:], class_names=iris.target_names, rounded=True, filled=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
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     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Source.from_file(os.path.join(\"./decision_tree_images\", \"iris_tree_depth_3.dot\"))"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Estimating Class Probabilities"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A Decision Tree can also estimate the probability that an instance belongs to a particular\n",
    "class *k*. First it traverses the tree to find the leaf node for this instance, and then it returns the\n",
    "ratio of training instances of class *k* in this node. \n",
    "\n",
    "For example, suppose we have found a flower whose petals are 5 cm long and 1.5 cm wide. The corresponding leaf node is the depth-2 left node, so the Decision Tree should output the following probabilities: 0% for *Iris setosa* (0/54), 90.7% for *Iris versicolor* (49/54), and 9.3% for *Iris virginica* (5/54). And if\n",
    "you ask it to predict the class, it should output Iris versicolor (class 1) because it has the\n",
    "highest probability. Let’s check this:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.        , 0.90740741, 0.09259259]])"
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     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tree_clf.predict_proba([[5,1.5]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1])"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tree_clf.predict([[5, 1.5]])"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## The CART Training Algorithm"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Computational Complexity"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Gini Impurity or Entropy?"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Regularization Hyperparameters"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Below graph shows two Decision Trees trained on the moons dataset.\n",
    "On the left the Decision Tree is trained with the default hyperparameters (i.e., no\n",
    "restrictions), and on the right it’s trained with `min_samples_leaf=4`. It is quite obvious that\n",
    "the model on the left is overfitting, and the model on the right will probably generalize\n",
    "better."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x400 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.datasets import make_moons\n",
    "\n",
    "Xm, ym = make_moons(n_samples=100, noise=0.25, random_state=53)\n",
    "\n",
    "deep_tree_clf1 = DecisionTreeClassifier(random_state=42)\n",
    "deep_tree_clf2 = DecisionTreeClassifier(min_samples_leaf=4, random_state=42)\n",
    "deep_tree_clf1.fit(Xm, ym)\n",
    "deep_tree_clf2.fit(Xm, ym)\n",
    "\n",
    "fig, axes = plt.subplots(ncols=2, figsize=(10,4), sharey=True)\n",
    "plt.sca(axes[0])\n",
    "plot_decision_boundary(deep_tree_clf1, Xm, ym, axes=[-1.5, 2.4, -1, 1.5], iris=False)\n",
    "plt.title(\"No Restrictions\", fontsize=16)\n",
    "plt.sca(axes[1])\n",
    "plot_decision_boundary(deep_tree_clf2, Xm, ym, axes=[-1.5, 2.4, -1, 1.5], iris=False)\n",
    "plt.title(\"min_samples_leaf = {}\".format(deep_tree_clf2.min_samples_leaf), fontsize=14)\n",
    "plt.ylabel(\"\")\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Visualizing decision trees for both graph"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [],
   "source": [
    "export_graphviz(deep_tree_clf1,out_file=\"./decision_tree_images/deep_tree_clf1.dot\", feature_names=['featue_1', 'feature_2'], class_names=['class_0', 'class_1'], rounded=True, filled=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
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       "<text text-anchor=\"middle\" x=\"542.5\" y=\"-283.3\" font-family=\"Helvetica,sans-Serif\" font-size=\"14.00\">gini = 0.0</text>\n",
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       "<text text-anchor=\"middle\" x=\"678.5\" y=\"-290.8\" font-family=\"Helvetica,sans-Serif\" font-size=\"14.00\">featue_1 &lt;= 0.639</text>\n",
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     },
     "execution_count": 31,
     "metadata": {},
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   "source": [
    "Source.from_file(os.path.join(\"./decision_tree_images/\", \"deep_tree_clf1.dot\"))"
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  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [],
   "source": [
    "export_graphviz(deep_tree_clf2,out_file=\"./decision_tree_images/deep_tree_clf2.dot\", feature_names=['featue_1', 'feature_2'], class_names=['class_0', 'class_1'], rounded=True, filled=True)"
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  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
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       "<title>1</title>\n",
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       "<text text-anchor=\"middle\" x=\"195.5\" y=\"-647.8\" font-family=\"Helvetica,sans-Serif\" font-size=\"14.00\">featue_1 &lt;= 1.195</text>\n",
       "<text text-anchor=\"middle\" x=\"195.5\" y=\"-632.8\" font-family=\"Helvetica,sans-Serif\" font-size=\"14.00\">gini = 0.071</text>\n",
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       "<title>0&#45;&gt;1</title>\n",
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       "<title>6</title>\n",
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       "<text text-anchor=\"middle\" x=\"347.5\" y=\"-647.8\" font-family=\"Helvetica,sans-Serif\" font-size=\"14.00\">featue_1 &lt;= 1.36</text>\n",
       "<text text-anchor=\"middle\" x=\"347.5\" y=\"-632.8\" font-family=\"Helvetica,sans-Serif\" font-size=\"14.00\">gini = 0.441</text>\n",
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       "<title>0&#45;&gt;6</title>\n",
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       "<text text-anchor=\"middle\" x=\"326.37\" y=\"-683.78\" font-family=\"Helvetica,sans-Serif\" font-size=\"14.00\">False</text>\n",
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       "<title>2</title>\n",
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       "<!-- 1&#45;&gt;2 -->\n",
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       "<title>1&#45;&gt;2</title>\n",
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       "<title>3</title>\n",
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       "<text text-anchor=\"middle\" x=\"195.5\" y=\"-498.8\" font-family=\"Helvetica,sans-Serif\" font-size=\"14.00\">samples = 8</text>\n",
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       "<title>1&#45;&gt;3</title>\n",
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       "<title>4</title>\n",
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       "<text text-anchor=\"middle\" x=\"75.5\" y=\"-402.3\" font-family=\"Helvetica,sans-Serif\" font-size=\"14.00\">gini = 0.375</text>\n",
       "<text text-anchor=\"middle\" x=\"75.5\" y=\"-387.3\" font-family=\"Helvetica,sans-Serif\" font-size=\"14.00\">samples = 4</text>\n",
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       "<!-- 3&#45;&gt;4 -->\n",
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       "<title>3&#45;&gt;4</title>\n",
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       "<title>5</title>\n",
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       "<text text-anchor=\"middle\" x=\"202.5\" y=\"-387.3\" font-family=\"Helvetica,sans-Serif\" font-size=\"14.00\">samples = 4</text>\n",
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       "<title>3&#45;&gt;5</title>\n",
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       "<title>7</title>\n",
       "<path fill=\"#eba069\" stroke=\"black\" d=\"M401,-544C401,-544 294,-544 294,-544 288,-544 282,-538 282,-532 282,-532 282,-473 282,-473 282,-467 288,-461 294,-461 294,-461 401,-461 401,-461 407,-461 413,-467 413,-473 413,-473 413,-532 413,-532 413,-538 407,-544 401,-544\"/>\n",
       "<text text-anchor=\"middle\" x=\"347.5\" y=\"-528.8\" font-family=\"Helvetica,sans-Serif\" font-size=\"14.00\">featue_1 &lt;= &#45;0.379</text>\n",
       "<text text-anchor=\"middle\" x=\"347.5\" y=\"-513.8\" font-family=\"Helvetica,sans-Serif\" font-size=\"14.00\">gini = 0.316</text>\n",
       "<text text-anchor=\"middle\" x=\"347.5\" y=\"-498.8\" font-family=\"Helvetica,sans-Serif\" font-size=\"14.00\">samples = 61</text>\n",
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       "<!-- 6&#45;&gt;7 -->\n",
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       "<title>6&#45;&gt;7</title>\n",
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       "<title>20</title>\n",
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       "<!-- 6&#45;&gt;20 -->\n",
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       "<title>8</title>\n",
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       "<text text-anchor=\"middle\" x=\"341.5\" y=\"-402.3\" font-family=\"Helvetica,sans-Serif\" font-size=\"14.00\">gini = 0.0</text>\n",
       "<text text-anchor=\"middle\" x=\"341.5\" y=\"-387.3\" font-family=\"Helvetica,sans-Serif\" font-size=\"14.00\">samples = 22</text>\n",
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       "<text text-anchor=\"middle\" x=\"341.5\" y=\"-357.3\" font-family=\"Helvetica,sans-Serif\" font-size=\"14.00\">class = class_0</text>\n",
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       "<!-- 7&#45;&gt;8 -->\n",
       "<g id=\"edge8\" class=\"edge\">\n",
       "<title>7&#45;&gt;8</title>\n",
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       "<title>9</title>\n",
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       "<text text-anchor=\"middle\" x=\"477.5\" y=\"-409.8\" font-family=\"Helvetica,sans-Serif\" font-size=\"14.00\">featue_1 &lt;= 0.466</text>\n",
       "<text text-anchor=\"middle\" x=\"477.5\" y=\"-394.8\" font-family=\"Helvetica,sans-Serif\" font-size=\"14.00\">gini = 0.426</text>\n",
       "<text text-anchor=\"middle\" x=\"477.5\" y=\"-379.8\" font-family=\"Helvetica,sans-Serif\" font-size=\"14.00\">samples = 39</text>\n",
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       "<title>10</title>\n",
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       "<text text-anchor=\"middle\" x=\"404.5\" y=\"-290.8\" font-family=\"Helvetica,sans-Serif\" font-size=\"14.00\">feature_2 &lt;= 0.769</text>\n",
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       "<text text-anchor=\"middle\" x=\"404.5\" y=\"-260.8\" font-family=\"Helvetica,sans-Serif\" font-size=\"14.00\">samples = 20</text>\n",
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       "<title>9&#45;&gt;10</title>\n",
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       "<title>15</title>\n",
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       "<text text-anchor=\"middle\" x=\"551.5\" y=\"-290.8\" font-family=\"Helvetica,sans-Serif\" font-size=\"14.00\">featue_1 &lt;= 0.639</text>\n",
       "<text text-anchor=\"middle\" x=\"551.5\" y=\"-275.8\" font-family=\"Helvetica,sans-Serif\" font-size=\"14.00\">gini = 0.188</text>\n",
       "<text text-anchor=\"middle\" x=\"551.5\" y=\"-260.8\" font-family=\"Helvetica,sans-Serif\" font-size=\"14.00\">samples = 19</text>\n",
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     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Source.from_file(os.path.join(\"./decision_tree_images/\", \"deep_tree_clf2.dot\"))"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Regression"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Decision Trees are also capable of performing regression tasks. Let’s build a regression tree\n",
    "using Scikit-Learn’s `DecisionTreeRegressor` class, training it on a noisy quadratic dataset\n",
    "with max_depth=2:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Quadratic Training Set + noise\n",
    "np.random.seed(42)\n",
    "m = 200\n",
    "X = np.random.rand(m,1)\n",
    "y = 4 * (X - 0.5) ** 2\n",
    "y = y + np.random.rand(m, 1) / 10"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
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      ],
      "text/plain": [
       "DecisionTreeRegressor(max_depth=2, random_state=42)"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.tree import DecisionTreeRegressor\n",
    "\n",
    "tree_reg = DecisionTreeRegressor(max_depth=2, random_state=42)\n",
    "tree_reg.fit(X,y)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Resulting Tree is shown below:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
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       "</svg>\n"
      ],
      "text/plain": [
       "<graphviz.sources.Source at 0x7f38d3fc6740>"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "export_graphviz(tree_reg, \"./decision_tree_images/tree_reg.dot\", feature_names=[\"x1\"], rounded=True, filled=True)\n",
    "Source.from_file(os.path.join(\"./decision_tree_images/\", \"tree_reg.dot\"))"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This tree looks very similar to the classification tree we built earlier. The main difference is\n",
    "that instead of predicting a class in each node, it predicts a value. For example, suppose we\n",
    "want to make a prediction for a new instance with $x_1$ = 0.6. We traverse the tree starting at\n",
    "the root, and we eventually reach the leaf node that predicts value=0.22. This prediction\n",
    "is the average target value of the 134 training instances associated with this leaf node, and it\n",
    "results in a mean squared error equal to 0.021 over these 134 instances."
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Predictions of two Decision Tree Regressor Models:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 1000x400 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.tree import DecisionTreeRegressor\n",
    "\n",
    "tree_reg1 = DecisionTreeRegressor(max_depth=2, random_state=42)\n",
    "tree_reg2 = DecisionTreeRegressor(max_depth=3, random_state=42)\n",
    "tree_reg1.fit(X,y)\n",
    "tree_reg2.fit(X,y)\n",
    "\n",
    "def plot_regression_predictions(tree_reg, X, y , axes=[0, 1, -0.2, 1], ylabel=\"$y$\"):\n",
    "    x1 = np.linspace(axes[0], axes[1], 500).reshape(-1,1)\n",
    "    y_pred = tree_reg.predict(x1)\n",
    "    plt.axis(axes)\n",
    "    plt.xlabel(\"$x_1$\", fontsize=18)\n",
    "    if ylabel:\n",
    "        plt.ylabel(ylabel, fontsize=18, rotation=0)\n",
    "    plt.plot(X, y, \"b.\")\n",
    "    plt.plot(x1, y_pred, \"r.-\", linewidth=2, label=r\"$\\hat{y}$\")\n",
    "\n",
    "fig, axes = plt.subplots(ncols=2, figsize=(10,4), sharey=True)\n",
    "plt.sca(axes[0])\n",
    "plot_regression_predictions(tree_reg1, X, y)\n",
    "for split, style in ((0.15, \"k-\"), (0.095, \"k--\"), (0.831, \"k--\")):\n",
    "    plt.plot([split,split], [-0.2, 1], style, linewidth=2)\n",
    "plt.text(0.21, 0.65, \"Depth=0\", fontsize=15)\n",
    "plt.text(0.01, 0.2, \"Depth=1\", fontsize=13)\n",
    "plt.text(0.65, 0.8, \"Depth=1\", fontsize=13)\n",
    "plt.legend(loc=\"upper center\", fontsize=18)\n",
    "plt.title(\"max_depth=2\", fontsize=14)\n",
    "\n",
    "plt.sca(axes[1])\n",
    "plot_regression_predictions(tree_reg2, X, y, ylabel=None)\n",
    "for split, style in ((0.15, \"k-\"), (0.095, \"k--\"), (0.831, \"k--\")):\n",
    "    plt.plot([split, split], [-0.2, 1], style, linewidth=2)\n",
    "for split in (0.049, 0.118, 0.258, 0.916):\n",
    "    plt.plot([split, split], [-0.2, 1], \"k:\", linewidth=1)\n",
    "plt.text(0.3, 0.5, \"Depth=2\", fontsize=13)\n",
    "plt.title(\"max_depth=3\", fontsize=14)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Model’s predictions with `max_depth=2` are represented on the left in above graph. If we set `max_depth=3`,\n",
    "we get the predictions represented on the right. Notice how the predicted value for each\n",
    "region is always the average target value of the instances in that region. The algorithm splits\n",
    "each region in a way that makes most training instances as close as possible to that predicted\n",
    "value."
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The CART algorithm works mostly the same way as earlier, except that instead of trying to\n",
    "split the training set in a way that minimizes impurity, it now tries to split the training set in\n",
    "a way that minimizes the MSE."
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Instability"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Below graph shows a simple linearly separable dataset: on the left, a Decision Tree can split it easily, while on the right, after the dataset is rotated by 45°, the decision boundary looks unnecessarily convoluted. Although both Decision Trees fit\n",
    "the training set perfectly, it is very likely that the model on the right will not generalize well.\n",
    "One way to limit this problem is to use Principal Component Analysis (see Chapter 8),\n",
    "which often results in a better orientation of the training data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x400 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "np.random.seed(6)\n",
    "Xs = np.random.rand(100, 2) - 0.5\n",
    "ys = (Xs[:, 0] > 0).astype(np.float32) * 2\n",
    "\n",
    "angle = np.pi / 4\n",
    "rotation_matrix = np.array([[np.cos(angle), -np.sin(angle)], [np.sin(angle), np.cos(angle)]])\n",
    "Xsr = Xs.dot(rotation_matrix)\n",
    "\n",
    "tree_clf_s = DecisionTreeClassifier(random_state=42)\n",
    "tree_clf_s.fit(Xs, ys)\n",
    "tree_clf_sr = DecisionTreeClassifier(random_state=42)\n",
    "tree_clf_sr.fit(Xsr, ys)\n",
    "\n",
    "fig, axes = plt.subplots(ncols=2, figsize=(10, 4), sharey=True)\n",
    "plt.sca(axes[0])\n",
    "plot_decision_boundary(tree_clf_s, Xs, ys, axes=[-0.7, 0.7, -0.7, 0.7], iris=False)\n",
    "plt.sca(axes[1])\n",
    "plot_decision_boundary(tree_clf_sr, Xsr, ys, axes=[-0.7, 0.7, -0.7, 0.7], iris=False)\n",
    "plt.ylabel(\"\")\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exercises"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 7.\n",
    "\n",
    "Train and fine-tune a Decision Tree for the moons dataset by following these steps:\n",
    "\n",
    "a) Use `make_moons(n_samples=10000, noise=0.4)` to generate a moons\n",
    "dataset.\n",
    "\n",
    "b) Use `train_test_split()` to split the dataset into a training set and a test\n",
    "set.\n",
    "\n",
    "c) Use grid search with cross-validation (with the help of the `GridSearchCV`\n",
    "class) to find good hyperparameter values for a `DecisionTreeClassifier`.\n",
    "Hint: try various values for `max_leaf_nodes`.\n",
    "\n",
    "d) Train it on the full training set using these hyperparameters, and measure\n",
    "your model’s performance on the test set. You should get roughly 85% to\n",
    "87% accuracy."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [],
   "source": [
    "# a) \n",
    "\n",
    "from sklearn.datasets import make_moons\n",
    "\n",
    "X, y = make_moons(n_samples=1000, noise=0.4, random_state=42)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [],
   "source": [
    "# b)\n",
    "from sklearn.model_selection import train_test_split\n",
    "\n",
    "X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2, random_state=42)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Fitting 3 folds for each of 294 candidates, totalling 882 fits\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<style>#sk-container-id-4 {color: black;background-color: white;}#sk-container-id-4 pre{padding: 0;}#sk-container-id-4 div.sk-toggleable {background-color: white;}#sk-container-id-4 label.sk-toggleable__label {cursor: pointer;display: block;width: 100%;margin-bottom: 0;padding: 0.3em;box-sizing: border-box;text-align: center;}#sk-container-id-4 label.sk-toggleable__label-arrow:before {content: \"▸\";float: left;margin-right: 0.25em;color: #696969;}#sk-container-id-4 label.sk-toggleable__label-arrow:hover:before {color: black;}#sk-container-id-4 div.sk-estimator:hover label.sk-toggleable__label-arrow:before {color: black;}#sk-container-id-4 div.sk-toggleable__content {max-height: 0;max-width: 0;overflow: hidden;text-align: left;background-color: #f0f8ff;}#sk-container-id-4 div.sk-toggleable__content pre {margin: 0.2em;color: black;border-radius: 0.25em;background-color: #f0f8ff;}#sk-container-id-4 input.sk-toggleable__control:checked~div.sk-toggleable__content {max-height: 200px;max-width: 100%;overflow: auto;}#sk-container-id-4 input.sk-toggleable__control:checked~label.sk-toggleable__label-arrow:before {content: \"▾\";}#sk-container-id-4 div.sk-estimator input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-4 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-4 input.sk-hidden--visually {border: 0;clip: rect(1px 1px 1px 1px);clip: rect(1px, 1px, 1px, 1px);height: 1px;margin: -1px;overflow: hidden;padding: 0;position: absolute;width: 1px;}#sk-container-id-4 div.sk-estimator {font-family: monospace;background-color: #f0f8ff;border: 1px dotted black;border-radius: 0.25em;box-sizing: border-box;margin-bottom: 0.5em;}#sk-container-id-4 div.sk-estimator:hover {background-color: #d4ebff;}#sk-container-id-4 div.sk-parallel-item::after {content: \"\";width: 100%;border-bottom: 1px solid gray;flex-grow: 1;}#sk-container-id-4 div.sk-label:hover label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-4 div.sk-serial::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: 0;}#sk-container-id-4 div.sk-serial {display: flex;flex-direction: column;align-items: center;background-color: white;padding-right: 0.2em;padding-left: 0.2em;position: relative;}#sk-container-id-4 div.sk-item {position: relative;z-index: 1;}#sk-container-id-4 div.sk-parallel {display: flex;align-items: stretch;justify-content: center;background-color: white;position: relative;}#sk-container-id-4 div.sk-item::before, #sk-container-id-4 div.sk-parallel-item::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: -1;}#sk-container-id-4 div.sk-parallel-item {display: flex;flex-direction: column;z-index: 1;position: relative;background-color: white;}#sk-container-id-4 div.sk-parallel-item:first-child::after {align-self: flex-end;width: 50%;}#sk-container-id-4 div.sk-parallel-item:last-child::after {align-self: flex-start;width: 50%;}#sk-container-id-4 div.sk-parallel-item:only-child::after {width: 0;}#sk-container-id-4 div.sk-dashed-wrapped {border: 1px dashed gray;margin: 0 0.4em 0.5em 0.4em;box-sizing: border-box;padding-bottom: 0.4em;background-color: white;}#sk-container-id-4 div.sk-label label {font-family: monospace;font-weight: bold;display: inline-block;line-height: 1.2em;}#sk-container-id-4 div.sk-label-container {text-align: center;}#sk-container-id-4 div.sk-container {/* jupyter's `normalize.less` sets `[hidden] { display: none; }` but bootstrap.min.css set `[hidden] { display: none !important; }` so we also need the `!important` here to be able to override the default hidden behavior on the sphinx rendered scikit-learn.org. See: https://github.com/scikit-learn/scikit-learn/issues/21755 */display: inline-block !important;position: relative;}#sk-container-id-4 div.sk-text-repr-fallback {display: none;}</style><div id=\"sk-container-id-4\" class=\"sk-top-container\"><div class=\"sk-text-repr-fallback\"><pre>GridSearchCV(cv=3, estimator=DecisionTreeClassifier(random_state=42),\n",
       "             param_grid={&#x27;max_leaf_nodes&#x27;: [2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12,\n",
       "                                            13, 14, 15, 16, 17, 18, 19, 20, 21,\n",
       "                                            22, 23, 24, 25, 26, 27, 28, 29, 30,\n",
       "                                            31, ...],\n",
       "                         &#x27;min_samples_split&#x27;: [2, 3, 4]},\n",
       "             verbose=1)</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 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 sk-toggleable__label-arrow\">GridSearchCV</label><div class=\"sk-toggleable__content\"><pre>GridSearchCV(cv=3, estimator=DecisionTreeClassifier(random_state=42),\n",
       "             param_grid={&#x27;max_leaf_nodes&#x27;: [2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12,\n",
       "                                            13, 14, 15, 16, 17, 18, 19, 20, 21,\n",
       "                                            22, 23, 24, 25, 26, 27, 28, 29, 30,\n",
       "                                            31, ...],\n",
       "                         &#x27;min_samples_split&#x27;: [2, 3, 4]},\n",
       "             verbose=1)</pre></div></div></div><div class=\"sk-parallel\"><div class=\"sk-parallel-item\"><div class=\"sk-item\"><div class=\"sk-label-container\"><div class=\"sk-label 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 sk-toggleable__label-arrow\">estimator: DecisionTreeClassifier</label><div class=\"sk-toggleable__content\"><pre>DecisionTreeClassifier(random_state=42)</pre></div></div></div><div class=\"sk-serial\"><div class=\"sk-item\"><div class=\"sk-estimator sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-6\" type=\"checkbox\" ><label for=\"sk-estimator-id-6\" class=\"sk-toggleable__label sk-toggleable__label-arrow\">DecisionTreeClassifier</label><div class=\"sk-toggleable__content\"><pre>DecisionTreeClassifier(random_state=42)</pre></div></div></div></div></div></div></div></div></div></div>"
      ],
      "text/plain": [
       "GridSearchCV(cv=3, estimator=DecisionTreeClassifier(random_state=42),\n",
       "             param_grid={'max_leaf_nodes': [2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12,\n",
       "                                            13, 14, 15, 16, 17, 18, 19, 20, 21,\n",
       "                                            22, 23, 24, 25, 26, 27, 28, 29, 30,\n",
       "                                            31, ...],\n",
       "                         'min_samples_split': [2, 3, 4]},\n",
       "             verbose=1)"
      ]
     },
     "execution_count": 69,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# c)\n",
    "from sklearn.model_selection import GridSearchCV\n",
    "\n",
    "params = {\"max_leaf_nodes\": list(range(2,100)), 'min_samples_split': [2, 3, 4]}\n",
    "grid_search_cv = GridSearchCV(DecisionTreeClassifier(random_state=42), params, verbose=1, cv=3)\n",
    "\n",
    "grid_search_cv.fit(X_train, y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>#sk-container-id-5 {color: black;background-color: white;}#sk-container-id-5 pre{padding: 0;}#sk-container-id-5 div.sk-toggleable {background-color: white;}#sk-container-id-5 label.sk-toggleable__label {cursor: pointer;display: block;width: 100%;margin-bottom: 0;padding: 0.3em;box-sizing: border-box;text-align: center;}#sk-container-id-5 label.sk-toggleable__label-arrow:before {content: \"▸\";float: left;margin-right: 0.25em;color: #696969;}#sk-container-id-5 label.sk-toggleable__label-arrow:hover:before {color: black;}#sk-container-id-5 div.sk-estimator:hover label.sk-toggleable__label-arrow:before {color: black;}#sk-container-id-5 div.sk-toggleable__content {max-height: 0;max-width: 0;overflow: hidden;text-align: left;background-color: #f0f8ff;}#sk-container-id-5 div.sk-toggleable__content pre {margin: 0.2em;color: black;border-radius: 0.25em;background-color: #f0f8ff;}#sk-container-id-5 input.sk-toggleable__control:checked~div.sk-toggleable__content {max-height: 200px;max-width: 100%;overflow: auto;}#sk-container-id-5 input.sk-toggleable__control:checked~label.sk-toggleable__label-arrow:before {content: \"▾\";}#sk-container-id-5 div.sk-estimator input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-5 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-5 input.sk-hidden--visually {border: 0;clip: rect(1px 1px 1px 1px);clip: rect(1px, 1px, 1px, 1px);height: 1px;margin: -1px;overflow: hidden;padding: 0;position: absolute;width: 1px;}#sk-container-id-5 div.sk-estimator {font-family: monospace;background-color: #f0f8ff;border: 1px dotted black;border-radius: 0.25em;box-sizing: border-box;margin-bottom: 0.5em;}#sk-container-id-5 div.sk-estimator:hover {background-color: #d4ebff;}#sk-container-id-5 div.sk-parallel-item::after {content: \"\";width: 100%;border-bottom: 1px solid gray;flex-grow: 1;}#sk-container-id-5 div.sk-label:hover label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-5 div.sk-serial::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: 0;}#sk-container-id-5 div.sk-serial {display: flex;flex-direction: column;align-items: center;background-color: white;padding-right: 0.2em;padding-left: 0.2em;position: relative;}#sk-container-id-5 div.sk-item {position: relative;z-index: 1;}#sk-container-id-5 div.sk-parallel {display: flex;align-items: stretch;justify-content: center;background-color: white;position: relative;}#sk-container-id-5 div.sk-item::before, #sk-container-id-5 div.sk-parallel-item::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: -1;}#sk-container-id-5 div.sk-parallel-item {display: flex;flex-direction: column;z-index: 1;position: relative;background-color: white;}#sk-container-id-5 div.sk-parallel-item:first-child::after {align-self: flex-end;width: 50%;}#sk-container-id-5 div.sk-parallel-item:last-child::after {align-self: flex-start;width: 50%;}#sk-container-id-5 div.sk-parallel-item:only-child::after {width: 0;}#sk-container-id-5 div.sk-dashed-wrapped {border: 1px dashed gray;margin: 0 0.4em 0.5em 0.4em;box-sizing: border-box;padding-bottom: 0.4em;background-color: white;}#sk-container-id-5 div.sk-label label {font-family: monospace;font-weight: bold;display: inline-block;line-height: 1.2em;}#sk-container-id-5 div.sk-label-container {text-align: center;}#sk-container-id-5 div.sk-container {/* jupyter's `normalize.less` sets `[hidden] { display: none; }` but bootstrap.min.css set `[hidden] { display: none !important; }` so we also need the `!important` here to be able to override the default hidden behavior on the sphinx rendered scikit-learn.org. See: https://github.com/scikit-learn/scikit-learn/issues/21755 */display: inline-block !important;position: relative;}#sk-container-id-5 div.sk-text-repr-fallback {display: none;}</style><div id=\"sk-container-id-5\" class=\"sk-top-container\"><div class=\"sk-text-repr-fallback\"><pre>DecisionTreeClassifier(max_leaf_nodes=4, 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 sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-7\" type=\"checkbox\" checked><label for=\"sk-estimator-id-7\" class=\"sk-toggleable__label sk-toggleable__label-arrow\">DecisionTreeClassifier</label><div class=\"sk-toggleable__content\"><pre>DecisionTreeClassifier(max_leaf_nodes=4, random_state=42)</pre></div></div></div></div></div>"
      ],
      "text/plain": [
       "DecisionTreeClassifier(max_leaf_nodes=4, random_state=42)"
      ]
     },
     "execution_count": 70,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "grid_search_cv.best_estimator_"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "By default, `GridSearchCV` trains the best model found on the whole training set (we can change this by setting `refit=False`), so we don't need to do it again. We can simply evaluate the model's accuracy:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.855"
      ]
     },
     "execution_count": 71,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# d)\n",
    "from sklearn.metrics import accuracy_score\n",
    "\n",
    "y_pred = grid_search_cv.predict(X_test)\n",
    "accuracy_score(y_test, y_pred)\n"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 8.\n",
    "\n",
    "Grow a forest by following these steps:\n"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "a) Continuing the previous exercise, generate 1,000 subsets of the training set,\n",
    "each containing 100 instances selected randomly. Hint: you can use Scikit-\n",
    "Learn’s `ShuffleSplit` class for this."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.model_selection import ShuffleSplit\n",
    "\n",
    "n_trees = 1000\n",
    "n_instances = 100\n",
    "\n",
    "mini_sets = []\n",
    "\n",
    "rs = ShuffleSplit(n_splits=n_trees, test_size=len(X_train) - n_instances, random_state=42)\n",
    "\n",
    "for mini_train_index , mini_test_index in rs.split(X_train):\n",
    "    X_mini_train = X_train[mini_train_index]\n",
    "    y_mini_train = y_train[mini_train_index]\n",
    "    mini_sets.append((X_mini_train, y_mini_train))"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "b) Train one Decision Tree on each subset, using the best hyperparameter\n",
    "values found in the previous exercise. Evaluate these 1,000 Decision Trees\n",
    "on the test set. Since they were trained on smaller sets, these Decision\n",
    "Trees will likely perform worse than the first Decision Tree, achieving only\n",
    "about 80% accuracy."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.817115"
      ]
     },
     "execution_count": 74,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.base import clone\n",
    "\n",
    "forest = [clone(grid_search_cv.best_estimator_) for _ in range(n_trees)]\n",
    "\n",
    "accuracy_scores = []\n",
    "\n",
    "for tree, (X_mini_train, y_mini_train) in zip(forest, mini_sets):\n",
    "    tree.fit(X_mini_train, y_mini_train)\n",
    "\n",
    "    y_pred = tree.predict(X_test)\n",
    "    accuracy_scores.append(accuracy_score(y_test, y_pred))\n",
    "\n",
    "np.mean(accuracy_scores)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "c) Now comes the magic. For each test set instance, generate the predictions\n",
    "of the 1,000 Decision Trees, and keep only the most frequent prediction\n",
    "(you can use SciPy’s `mode()` function for this). This approach gives you\n",
    "majority-vote predictions over the test set."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {},
   "outputs": [],
   "source": [
    "Y_pred = np.empty([n_trees, len(X_test)], dtype=np.uint8)\n",
    "\n",
    "for tree_index , tree in enumerate(forest):\n",
    "    Y_pred[tree_index] = tree.predict(X_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/tmp/ipykernel_6899/3687693452.py:3: FutureWarning: Unlike other reduction functions (e.g. `skew`, `kurtosis`), the default behavior of `mode` typically preserves the axis it acts along. In SciPy 1.11.0, this behavior will change: the default value of `keepdims` will become False, the `axis` over which the statistic is taken will be eliminated, and the value None will no longer be accepted. Set `keepdims` to True or False to avoid this warning.\n",
      "  y_pred_majority_votes , n_votes = mode(Y_pred, axis=0)\n"
     ]
    }
   ],
   "source": [
    "from scipy.stats import mode\n",
    "\n",
    "y_pred_majority_votes , n_votes = mode(Y_pred, axis=0)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "d) Evaluate these predictions on the test set: you should obtain a slightly\n",
    "higher accuracy than your first model (about 0.5 to 1.5% higher).\n",
    "Congratulations, you have trained a Random Forest classifier!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.85"
      ]
     },
     "execution_count": 82,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "accuracy_score(y_test, y_pred_majority_votes.reshape([-1]))"
   ]
  }
 ],
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