cap2.6 - Decision Tree.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Decision Tree"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Widely used to tackle classification and regression problems. Essentially, learn a hierarchical structure of if/else statments."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1.0 Decision Tree Example"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-12-20T18:25:22.947320Z",
     "start_time": "2020-12-20T18:25:20.629023Z"
    }
   },
   "outputs": [],
   "source": [
    "import mglearn"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-12-20T18:25:23.521546Z",
     "start_time": "2020-12-20T18:25:22.949898Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "mglearn.plots.plot_animal_tree()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is a tree. A tree is a particular case of a graph. Like a graph, a tree has nodes and edges.\n",
    "In a decision tree, each node has a question and the edges are the possible answers, the exception\n",
    "occurs in the nodes (leaves) that are most distant from the root (root: \"Has feathers?\"). In this case, they have the answers we are looking for."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Suppose there are 4 animals [Hawk, Penguin, Dolphin and Bear].\n",
    "Someone select one of them randomly and you have to discover which one was selected.\n",
    "Therefore, you start asking questions based on the decision tree above: \n",
    "    You: Has feathers?\n",
    "    Answer: No\n",
    "    \n",
    "    You: Has fins?\n",
    "    Answer: yes\n",
    "    \n",
    "    You: Therefore, it is a dolphin!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2.0 Decision Tree Classifier"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-12-20T18:25:23.527248Z",
     "start_time": "2020-12-20T18:25:23.524258Z"
    }
   },
   "outputs": [],
   "source": [
    "from sklearn.tree import DecisionTreeClassifier\n",
    "from sklearn.datasets import load_breast_cancer\n",
    "from sklearn.model_selection import train_test_split"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-12-20T18:25:23.545550Z",
     "start_time": "2020-12-20T18:25:23.529541Z"
    }
   },
   "outputs": [],
   "source": [
    "cancer = load_breast_cancer()\n",
    "X_train, X_test, y_train, y_test = train_test_split(cancer.data, cancer.target, stratify=cancer.target, random_state=42)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-12-20T18:25:23.561031Z",
     "start_time": "2020-12-20T18:25:23.547561Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Accuracy on training set: 1.000\n",
      "Accuracy on test set: 0.937\n"
     ]
    }
   ],
   "source": [
    "tree = DecisionTreeClassifier(random_state=0)\n",
    "tree.fit(X_train, y_train)\n",
    "print(\"Accuracy on training set: {:.3f}\".format(tree.score(X_train, y_train)))\n",
    "print(\"Accuracy on test set: {:.3f}\".format(tree.score(X_test, y_test)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The tree has 100% accuracy on training set. This is because the tree is complex enough to memorize all labels on the training data. The problem is that it hardly will generalize well.\n",
    "The good news is that decision tree has some parameters we can tweek in order to control the tree complexity (avoid overfitting)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "One of them is \"max_depth\". This is a pre-prunning parameter. Once the tree reaches the depth specified, the algorithm stops splitting."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-12-20T18:25:23.578461Z",
     "start_time": "2020-12-20T18:25:23.564670Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Accuracy on training set: 0.988\n",
      "Accuracy on test set: 0.951\n"
     ]
    }
   ],
   "source": [
    "tree = DecisionTreeClassifier(max_depth=4, random_state=0)\n",
    "tree.fit(X_train, y_train)\n",
    "print(\"Accuracy on training set: {:.3f}\".format(tree.score(X_train, y_train)))\n",
    "print(\"Accuracy on test set: {:.3f}\".format(tree.score(X_test, y_test)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can visualize the induced decision tree with graphiz"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-12-20T18:25:23.591685Z",
     "start_time": "2020-12-20T18:25:23.582913Z"
    }
   },
   "outputs": [],
   "source": [
    "from sklearn.tree import export_graphviz\n",
    "export_graphviz(tree, out_file=\"tree.dot\", class_names=[\"malignant\", \"benign\"], feature_names=cancer.feature_names,\n",
    "               impurity=False, filled=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-12-20T18:25:23.907967Z",
     "start_time": "2020-12-20T18:25:23.596477Z"
    }
   },
   "outputs": [
    {
     "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 2.44.1 (20200629.0846)\n",
       " -->\n",
       "<!-- Title: Tree Pages: 1 -->\n",
       "<svg width=\"1023pt\" height=\"477pt\"\n",
       " viewBox=\"0.00 0.00 1023.00 477.00\" 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(4 473)\">\n",
       "<title>Tree</title>\n",
       "<polygon fill=\"white\" stroke=\"transparent\" points=\"-4,4 -4,-473 1019,-473 1019,4 -4,4\"/>\n",
       "<!-- 0 -->\n",
       "<g id=\"node1\" class=\"node\">\n",
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       "<text text-anchor=\"middle\" x=\"563.5\" y=\"-453.8\" font-family=\"Times,serif\" font-size=\"14.00\">worst radius &lt;= 16.795</text>\n",
       "<text text-anchor=\"middle\" x=\"563.5\" y=\"-438.8\" font-family=\"Times,serif\" font-size=\"14.00\">samples = 426</text>\n",
       "<text text-anchor=\"middle\" x=\"563.5\" y=\"-423.8\" font-family=\"Times,serif\" font-size=\"14.00\">value = [159, 267]</text>\n",
       "<text text-anchor=\"middle\" x=\"563.5\" y=\"-408.8\" font-family=\"Times,serif\" font-size=\"14.00\">class = benign</text>\n",
       "</g>\n",
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       "<title>1</title>\n",
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       "<text text-anchor=\"middle\" x=\"453.5\" y=\"-349.8\" font-family=\"Times,serif\" font-size=\"14.00\">worst concave points &lt;= 0.136</text>\n",
       "<text text-anchor=\"middle\" x=\"453.5\" y=\"-334.8\" font-family=\"Times,serif\" font-size=\"14.00\">samples = 284</text>\n",
       "<text text-anchor=\"middle\" x=\"453.5\" y=\"-319.8\" font-family=\"Times,serif\" font-size=\"14.00\">value = [25, 259]</text>\n",
       "<text text-anchor=\"middle\" x=\"453.5\" y=\"-304.8\" font-family=\"Times,serif\" font-size=\"14.00\">class = benign</text>\n",
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       "<title>0&#45;&gt;1</title>\n",
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       "<polygon fill=\"black\" stroke=\"black\" points=\"499.12,-369.53 489.41,-365.3 494.36,-374.67 499.12,-369.53\"/>\n",
       "<text text-anchor=\"middle\" x=\"490.35\" y=\"-386.58\" font-family=\"Times,serif\" font-size=\"14.00\">True</text>\n",
       "</g>\n",
       "<!-- 14 -->\n",
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       "<title>14</title>\n",
       "<polygon fill=\"#e78945\" stroke=\"black\" points=\"714,-365 575,-365 575,-297 714,-297 714,-365\"/>\n",
       "<text text-anchor=\"middle\" x=\"644.5\" y=\"-349.8\" font-family=\"Times,serif\" font-size=\"14.00\">texture error &lt;= 0.473</text>\n",
       "<text text-anchor=\"middle\" x=\"644.5\" y=\"-334.8\" font-family=\"Times,serif\" font-size=\"14.00\">samples = 142</text>\n",
       "<text text-anchor=\"middle\" x=\"644.5\" y=\"-319.8\" font-family=\"Times,serif\" font-size=\"14.00\">value = [134, 8]</text>\n",
       "<text text-anchor=\"middle\" x=\"644.5\" y=\"-304.8\" font-family=\"Times,serif\" font-size=\"14.00\">class = malignant</text>\n",
       "</g>\n",
       "<!-- 0&#45;&gt;14 -->\n",
       "<g id=\"edge14\" class=\"edge\">\n",
       "<title>0&#45;&gt;14</title>\n",
       "<path fill=\"none\" stroke=\"black\" d=\"M589.8,-400.88C596.8,-392.07 604.45,-382.43 611.75,-373.24\"/>\n",
       "<polygon fill=\"black\" stroke=\"black\" points=\"614.58,-375.31 618.06,-365.3 609.1,-370.95 614.58,-375.31\"/>\n",
       "<text text-anchor=\"middle\" x=\"620.91\" y=\"-386.44\" font-family=\"Times,serif\" font-size=\"14.00\">False</text>\n",
       "</g>\n",
       "<!-- 2 -->\n",
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       "<title>2</title>\n",
       "<polygon fill=\"#3c9fe5\" stroke=\"black\" points=\"351.5,-261 217.5,-261 217.5,-193 351.5,-193 351.5,-261\"/>\n",
       "<text text-anchor=\"middle\" x=\"284.5\" y=\"-245.8\" font-family=\"Times,serif\" font-size=\"14.00\">radius error &lt;= 1.048</text>\n",
       "<text text-anchor=\"middle\" x=\"284.5\" y=\"-230.8\" font-family=\"Times,serif\" font-size=\"14.00\">samples = 252</text>\n",
       "<text text-anchor=\"middle\" x=\"284.5\" y=\"-215.8\" font-family=\"Times,serif\" font-size=\"14.00\">value = [4, 248]</text>\n",
       "<text text-anchor=\"middle\" x=\"284.5\" y=\"-200.8\" font-family=\"Times,serif\" font-size=\"14.00\">class = benign</text>\n",
       "</g>\n",
       "<!-- 1&#45;&gt;2 -->\n",
       "<g id=\"edge2\" class=\"edge\">\n",
       "<title>1&#45;&gt;2</title>\n",
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       "<title>7</title>\n",
       "<polygon fill=\"#f3c3a1\" stroke=\"black\" points=\"525,-261 382,-261 382,-193 525,-193 525,-261\"/>\n",
       "<text text-anchor=\"middle\" x=\"453.5\" y=\"-245.8\" font-family=\"Times,serif\" font-size=\"14.00\">worst texture &lt;= 25.62</text>\n",
       "<text text-anchor=\"middle\" x=\"453.5\" y=\"-230.8\" font-family=\"Times,serif\" font-size=\"14.00\">samples = 32</text>\n",
       "<text text-anchor=\"middle\" x=\"453.5\" y=\"-215.8\" font-family=\"Times,serif\" font-size=\"14.00\">value = [21, 11]</text>\n",
       "<text text-anchor=\"middle\" x=\"453.5\" y=\"-200.8\" font-family=\"Times,serif\" font-size=\"14.00\">class = malignant</text>\n",
       "</g>\n",
       "<!-- 1&#45;&gt;7 -->\n",
       "<g id=\"edge7\" class=\"edge\">\n",
       "<title>1&#45;&gt;7</title>\n",
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       "<title>3</title>\n",
       "<polygon fill=\"#3b9ee5\" stroke=\"black\" points=\"210,-157 45,-157 45,-89 210,-89 210,-157\"/>\n",
       "<text text-anchor=\"middle\" x=\"127.5\" y=\"-141.8\" font-family=\"Times,serif\" font-size=\"14.00\">smoothness error &lt;= 0.003</text>\n",
       "<text text-anchor=\"middle\" x=\"127.5\" y=\"-126.8\" font-family=\"Times,serif\" font-size=\"14.00\">samples = 251</text>\n",
       "<text text-anchor=\"middle\" x=\"127.5\" y=\"-111.8\" font-family=\"Times,serif\" font-size=\"14.00\">value = [3, 248]</text>\n",
       "<text text-anchor=\"middle\" x=\"127.5\" y=\"-96.8\" font-family=\"Times,serif\" font-size=\"14.00\">class = benign</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=\"M233.53,-192.88C218.64,-183.21 202.25,-172.56 186.89,-162.59\"/>\n",
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       "</g>\n",
       "<!-- 6 -->\n",
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       "<title>6</title>\n",
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       "<text text-anchor=\"middle\" x=\"284.5\" y=\"-134.3\" font-family=\"Times,serif\" font-size=\"14.00\">samples = 1</text>\n",
       "<text text-anchor=\"middle\" x=\"284.5\" y=\"-119.3\" font-family=\"Times,serif\" font-size=\"14.00\">value = [1, 0]</text>\n",
       "<text text-anchor=\"middle\" x=\"284.5\" y=\"-104.3\" font-family=\"Times,serif\" font-size=\"14.00\">class = malignant</text>\n",
       "</g>\n",
       "<!-- 2&#45;&gt;6 -->\n",
       "<g id=\"edge6\" class=\"edge\">\n",
       "<title>2&#45;&gt;6</title>\n",
       "<path fill=\"none\" stroke=\"black\" d=\"M284.5,-192.88C284.5,-182.33 284.5,-170.6 284.5,-159.85\"/>\n",
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       "<!-- 4 -->\n",
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       "<title>4</title>\n",
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       "<text text-anchor=\"middle\" x=\"47.5\" y=\"-37.8\" font-family=\"Times,serif\" font-size=\"14.00\">samples = 4</text>\n",
       "<text text-anchor=\"middle\" x=\"47.5\" y=\"-22.8\" font-family=\"Times,serif\" font-size=\"14.00\">value = [1, 3]</text>\n",
       "<text text-anchor=\"middle\" x=\"47.5\" y=\"-7.8\" font-family=\"Times,serif\" font-size=\"14.00\">class = benign</text>\n",
       "</g>\n",
       "<!-- 3&#45;&gt;4 -->\n",
       "<g id=\"edge4\" class=\"edge\">\n",
       "<title>3&#45;&gt;4</title>\n",
       "<path fill=\"none\" stroke=\"black\" d=\"M99.52,-88.95C91.85,-79.89 83.54,-70.07 75.85,-60.99\"/>\n",
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       "<!-- 5 -->\n",
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       "<title>5</title>\n",
       "<polygon fill=\"#3b9ee5\" stroke=\"black\" points=\"218,-53 113,-53 113,0 218,0 218,-53\"/>\n",
       "<text text-anchor=\"middle\" x=\"165.5\" y=\"-37.8\" font-family=\"Times,serif\" font-size=\"14.00\">samples = 247</text>\n",
       "<text text-anchor=\"middle\" x=\"165.5\" y=\"-22.8\" font-family=\"Times,serif\" font-size=\"14.00\">value = [2, 245]</text>\n",
       "<text text-anchor=\"middle\" x=\"165.5\" y=\"-7.8\" font-family=\"Times,serif\" font-size=\"14.00\">class = benign</text>\n",
       "</g>\n",
       "<!-- 3&#45;&gt;5 -->\n",
       "<g id=\"edge5\" class=\"edge\">\n",
       "<title>3&#45;&gt;5</title>\n",
       "<path fill=\"none\" stroke=\"black\" d=\"M140.79,-88.95C144.21,-80.44 147.9,-71.26 151.37,-62.65\"/>\n",
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       "<!-- 8 -->\n",
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       "<title>8</title>\n",
       "<polygon fill=\"#7bbeee\" stroke=\"black\" points=\"528,-157 359,-157 359,-89 528,-89 528,-157\"/>\n",
       "<text text-anchor=\"middle\" x=\"443.5\" y=\"-141.8\" font-family=\"Times,serif\" font-size=\"14.00\">worst smoothness &lt;= 0.179</text>\n",
       "<text text-anchor=\"middle\" x=\"443.5\" y=\"-126.8\" font-family=\"Times,serif\" font-size=\"14.00\">samples = 12</text>\n",
       "<text text-anchor=\"middle\" x=\"443.5\" y=\"-111.8\" font-family=\"Times,serif\" font-size=\"14.00\">value = [3, 9]</text>\n",
       "<text text-anchor=\"middle\" x=\"443.5\" y=\"-96.8\" font-family=\"Times,serif\" font-size=\"14.00\">class = benign</text>\n",
       "</g>\n",
       "<!-- 7&#45;&gt;8 -->\n",
       "<g id=\"edge8\" class=\"edge\">\n",
       "<title>7&#45;&gt;8</title>\n",
       "<path fill=\"none\" stroke=\"black\" d=\"M450.25,-192.88C449.46,-184.78 448.6,-175.98 447.76,-167.47\"/>\n",
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       "<title>11</title>\n",
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       "<text text-anchor=\"middle\" x=\"626.5\" y=\"-141.8\" font-family=\"Times,serif\" font-size=\"14.00\">worst symmetry &lt;= 0.268</text>\n",
       "<text text-anchor=\"middle\" x=\"626.5\" y=\"-126.8\" font-family=\"Times,serif\" font-size=\"14.00\">samples = 20</text>\n",
       "<text text-anchor=\"middle\" x=\"626.5\" y=\"-111.8\" font-family=\"Times,serif\" font-size=\"14.00\">value = [18, 2]</text>\n",
       "<text text-anchor=\"middle\" x=\"626.5\" y=\"-96.8\" font-family=\"Times,serif\" font-size=\"14.00\">class = malignant</text>\n",
       "</g>\n",
       "<!-- 7&#45;&gt;11 -->\n",
       "<g id=\"edge11\" class=\"edge\">\n",
       "<title>7&#45;&gt;11</title>\n",
       "<path fill=\"none\" stroke=\"black\" d=\"M509.67,-192.88C526.22,-183.12 544.47,-172.37 561.52,-162.31\"/>\n",
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       "<title>9</title>\n",
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       "<text text-anchor=\"middle\" x=\"321.5\" y=\"-37.8\" font-family=\"Times,serif\" font-size=\"14.00\">samples = 10</text>\n",
       "<text text-anchor=\"middle\" x=\"321.5\" y=\"-22.8\" font-family=\"Times,serif\" font-size=\"14.00\">value = [1, 9]</text>\n",
       "<text text-anchor=\"middle\" x=\"321.5\" y=\"-7.8\" font-family=\"Times,serif\" font-size=\"14.00\">class = benign</text>\n",
       "</g>\n",
       "<!-- 8&#45;&gt;9 -->\n",
       "<g id=\"edge9\" class=\"edge\">\n",
       "<title>8&#45;&gt;9</title>\n",
       "<path fill=\"none\" stroke=\"black\" d=\"M400.83,-88.95C388.55,-79.43 375.17,-69.07 362.96,-59.62\"/>\n",
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       "<title>10</title>\n",
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       "<text text-anchor=\"middle\" x=\"443.5\" y=\"-37.8\" font-family=\"Times,serif\" font-size=\"14.00\">samples = 2</text>\n",
       "<text text-anchor=\"middle\" x=\"443.5\" y=\"-22.8\" font-family=\"Times,serif\" font-size=\"14.00\">value = [2, 0]</text>\n",
       "<text text-anchor=\"middle\" x=\"443.5\" y=\"-7.8\" font-family=\"Times,serif\" font-size=\"14.00\">class = malignant</text>\n",
       "</g>\n",
       "<!-- 8&#45;&gt;10 -->\n",
       "<g id=\"edge10\" class=\"edge\">\n",
       "<title>8&#45;&gt;10</title>\n",
       "<path fill=\"none\" stroke=\"black\" d=\"M443.5,-88.95C443.5,-80.72 443.5,-71.85 443.5,-63.48\"/>\n",
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       "<title>12</title>\n",
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       "<text text-anchor=\"middle\" x=\"565.5\" y=\"-37.8\" font-family=\"Times,serif\" font-size=\"14.00\">samples = 3</text>\n",
       "<text text-anchor=\"middle\" x=\"565.5\" y=\"-22.8\" font-family=\"Times,serif\" font-size=\"14.00\">value = [1, 2]</text>\n",
       "<text text-anchor=\"middle\" x=\"565.5\" y=\"-7.8\" font-family=\"Times,serif\" font-size=\"14.00\">class = benign</text>\n",
       "</g>\n",
       "<!-- 11&#45;&gt;12 -->\n",
       "<g id=\"edge12\" class=\"edge\">\n",
       "<title>11&#45;&gt;12</title>\n",
       "<path fill=\"none\" stroke=\"black\" d=\"M605.17,-88.95C599.5,-80.17 593.36,-70.66 587.65,-61.82\"/>\n",
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       "<!-- 13 -->\n",
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       "<text text-anchor=\"middle\" x=\"687.5\" y=\"-37.8\" font-family=\"Times,serif\" font-size=\"14.00\">samples = 17</text>\n",
       "<text text-anchor=\"middle\" x=\"687.5\" y=\"-22.8\" font-family=\"Times,serif\" font-size=\"14.00\">value = [17, 0]</text>\n",
       "<text text-anchor=\"middle\" x=\"687.5\" y=\"-7.8\" font-family=\"Times,serif\" font-size=\"14.00\">class = malignant</text>\n",
       "</g>\n",
       "<!-- 11&#45;&gt;13 -->\n",
       "<g id=\"edge13\" class=\"edge\">\n",
       "<title>11&#45;&gt;13</title>\n",
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       "<!-- 15 -->\n",
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       "<text text-anchor=\"middle\" x=\"644.5\" y=\"-238.3\" font-family=\"Times,serif\" font-size=\"14.00\">samples = 5</text>\n",
       "<text text-anchor=\"middle\" x=\"644.5\" y=\"-223.3\" font-family=\"Times,serif\" font-size=\"14.00\">value = [0, 5]</text>\n",
       "<text text-anchor=\"middle\" x=\"644.5\" y=\"-208.3\" font-family=\"Times,serif\" font-size=\"14.00\">class = benign</text>\n",
       "</g>\n",
       "<!-- 14&#45;&gt;15 -->\n",
       "<g id=\"edge15\" class=\"edge\">\n",
       "<title>14&#45;&gt;15</title>\n",
       "<path fill=\"none\" stroke=\"black\" d=\"M644.5,-296.88C644.5,-286.33 644.5,-274.6 644.5,-263.85\"/>\n",
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       "<title>16</title>\n",
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       "<text text-anchor=\"middle\" x=\"809.5\" y=\"-245.8\" font-family=\"Times,serif\" font-size=\"14.00\">worst concavity &lt;= 0.191</text>\n",
       "<text text-anchor=\"middle\" x=\"809.5\" y=\"-230.8\" font-family=\"Times,serif\" font-size=\"14.00\">samples = 137</text>\n",
       "<text text-anchor=\"middle\" x=\"809.5\" y=\"-215.8\" font-family=\"Times,serif\" font-size=\"14.00\">value = [134, 3]</text>\n",
       "<text text-anchor=\"middle\" x=\"809.5\" y=\"-200.8\" font-family=\"Times,serif\" font-size=\"14.00\">class = malignant</text>\n",
       "</g>\n",
       "<!-- 14&#45;&gt;16 -->\n",
       "<g id=\"edge16\" class=\"edge\">\n",
       "<title>14&#45;&gt;16</title>\n",
       "<path fill=\"none\" stroke=\"black\" d=\"M698.07,-296.88C713.71,-287.21 730.94,-276.56 747.08,-266.59\"/>\n",
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       "<text text-anchor=\"middle\" x=\"809.5\" y=\"-141.8\" font-family=\"Times,serif\" font-size=\"14.00\">worst texture &lt;= 30.975</text>\n",
       "<text text-anchor=\"middle\" x=\"809.5\" y=\"-126.8\" font-family=\"Times,serif\" font-size=\"14.00\">samples = 5</text>\n",
       "<text text-anchor=\"middle\" x=\"809.5\" y=\"-111.8\" font-family=\"Times,serif\" font-size=\"14.00\">value = [2, 3]</text>\n",
       "<text text-anchor=\"middle\" x=\"809.5\" y=\"-96.8\" font-family=\"Times,serif\" font-size=\"14.00\">class = benign</text>\n",
       "</g>\n",
       "<!-- 16&#45;&gt;17 -->\n",
       "<g id=\"edge17\" class=\"edge\">\n",
       "<title>16&#45;&gt;17</title>\n",
       "<path fill=\"none\" stroke=\"black\" d=\"M809.5,-192.88C809.5,-184.78 809.5,-175.98 809.5,-167.47\"/>\n",
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       "</g>\n",
       "<!-- 16&#45;&gt;20 -->\n",
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       "<title>16&#45;&gt;20</title>\n",
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       "<text text-anchor=\"middle\" x=\"809.5\" y=\"-37.8\" font-family=\"Times,serif\" font-size=\"14.00\">samples = 3</text>\n",
       "<text text-anchor=\"middle\" x=\"809.5\" y=\"-22.8\" font-family=\"Times,serif\" font-size=\"14.00\">value = [0, 3]</text>\n",
       "<text text-anchor=\"middle\" x=\"809.5\" y=\"-7.8\" font-family=\"Times,serif\" font-size=\"14.00\">class = benign</text>\n",
       "</g>\n",
       "<!-- 17&#45;&gt;18 -->\n",
       "<g id=\"edge18\" class=\"edge\">\n",
       "<title>17&#45;&gt;18</title>\n",
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       "<title>19</title>\n",
       "<polygon fill=\"#e58139\" stroke=\"black\" points=\"988,-53 875,-53 875,0 988,0 988,-53\"/>\n",
       "<text text-anchor=\"middle\" x=\"931.5\" y=\"-37.8\" font-family=\"Times,serif\" font-size=\"14.00\">samples = 2</text>\n",
       "<text text-anchor=\"middle\" x=\"931.5\" y=\"-22.8\" font-family=\"Times,serif\" font-size=\"14.00\">value = [2, 0]</text>\n",
       "<text text-anchor=\"middle\" x=\"931.5\" y=\"-7.8\" font-family=\"Times,serif\" font-size=\"14.00\">class = malignant</text>\n",
       "</g>\n",
       "<!-- 17&#45;&gt;19 -->\n",
       "<g id=\"edge19\" class=\"edge\">\n",
       "<title>17&#45;&gt;19</title>\n",
       "<path fill=\"none\" stroke=\"black\" d=\"M852.17,-88.95C864.45,-79.43 877.83,-69.07 890.04,-59.62\"/>\n",
       "<polygon fill=\"black\" stroke=\"black\" points=\"892.51,-62.13 898.27,-53.24 888.22,-56.59 892.51,-62.13\"/>\n",
       "</g>\n",
       "</g>\n",
       "</svg>\n"
      ],
      "text/plain": [
       "<graphviz.files.Source at 0x7fd87692cb80>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import graphviz\n",
    "\n",
    "with open(\"tree.dot\") as f:\n",
    "    dot_graph = f.read()\n",
    "graphviz.Source(dot_graph)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You can see that decision trees are very easy to explain, but the deeper, the more complex. An usefull method is to investigate which path, most of the data actually takes."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2.1 Decision Tree - Feature Importances"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see the feature importances according to the induced tree."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-12-20T18:25:24.222735Z",
     "start_time": "2020-12-20T18:25:24.218234Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.        , 0.        , 0.        , 0.        , 0.        ,\n",
       "       0.        , 0.        , 0.        , 0.        , 0.        ,\n",
       "       0.01019737, 0.04839825, 0.        , 0.        , 0.0024156 ,\n",
       "       0.        , 0.        , 0.        , 0.        , 0.        ,\n",
       "       0.72682851, 0.0458159 , 0.        , 0.        , 0.0141577 ,\n",
       "       0.        , 0.018188  , 0.1221132 , 0.01188548, 0.        ])"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tree.feature_importances_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The feature importances sums up to 1. Features with 0 importance are not used at all."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-12-20T18:25:25.188976Z",
     "start_time": "2020-12-20T18:25:24.691678Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "plt.rcParams['figure.figsize'] = [12, 8]\n",
    "\n",
    "def plot_feature_importances_cancer(model):\n",
    "    n_features = cancer.data.shape[1]\n",
    "    plt.barh(range(n_features), model.feature_importances_, align='center')\n",
    "    plt.yticks(np.arange(n_features), cancer.feature_names)\n",
    "    plt.xlabel(\"Feature importance\")\n",
    "    plt.ylabel(\"Feature\")\n",
    "    \n",
    "plot_feature_importances_cancer(tree)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 3.0 Decision Tree Regressor"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-12-20T18:25:25.617983Z",
     "start_time": "2020-12-20T18:25:25.614062Z"
    }
   },
   "source": [
    "The usage and analysis is very similar to the classification trees, but tree-based regression models are not able to make predic"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-12-20T18:27:14.001219Z",
     "start_time": "2020-12-20T18:27:13.015962Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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4WBIAgMGIkg14icdjtXpftRYVFmnxplK1dng0Zkisrp2eo3+bnKXE6HCnIwIAAD+hZAM+UNvcrpc3HNKiwiJtLK5VuCtEF45P17UFOZo9IoWHJQEAGOAo2YCPbSut63lYsqapXVkJkbpqWraumZatnCQelgQAYCCiZAN+0trRqSVby/T0miIt310pSZo1PFnzzsjQ3LFpyoiPdDghAADwFko24ICSmmY9W1isf35Yon2VjZKkM7LiNHdsuuaOTdf4zDgemAQAIIhRsgEHWWu1p6JRb24r05tby7T24BFZK2XGuzV3XFfhnjEsSRGhLAkIAEAwoWQDAaSyoVVvby/Xm1vLtGxXpZrbOxUTEapzR6Vq7rg0nTc6TQlRrFICAECgo2QDAaqlvVMr91RqydZyvbmtTBX1rXKFGBUMTdSF49J14bh0DU2OdjomAAA4AUo2EAQ8HquNJbV6c2uZ3txWpu2H6yVJI9NieqaVTMlJUAhLAwIAEBAo2UAQKqpu6prHva1Mq/dWq8NjlRITrgvGpGvuuHSdPSJFkeHM4wYAwCmUbCDI1Ta1692d5XpzW7ne3V6u+tYORYSGaM7IFM0dm67zx6YpLdbtdEwAAAaVvkp2qL/DADh18VFhWjA5SwsmZ6mtw6M1+6u1ZGuZlmwt05vbymWMNDknQXPHds3jHpkW45PlAT0eK2PE0oMAAJwEI9lAELPWakdZvZZs6ZpWsqG4VpKUmxTVU7jPzE/61Fu81za168k1B/W3lfs1LDVa//jSWd6IDwBAUGMkGxigjDEaMyROY4bE6esXjFRZXYve2ta1Usnjqw/o4RX7lB4XoQWTs/Rvk7M0NiP2lEah91U26pEV+/RMYXHPUoO7yhp8+I0AABgYKNnAAJIe59YNM3J1w4xcNbV16J3tFfrnhyV6ZMU+PbB0r0anx+rfpmRpweRMZSaceIt3a61W7a3Sw8v36a3t5QoLCdHlkzP1xdn5+ueHJXps1X6/ficAAIIRJRsYoKLCQ3XJxAxdMjFDRxrb9OqmUv1zfYl+/vp2/fz17ZqRn6QrpmRp/oQMxUeGqbWjUy9vKNXDy/dpa2mdkqPD9fXzR+qms3J7Hqp8e3uZWto9au3oZIdKAAD6QMkGBoHE6HDddNZQ3XTWUB2satKLH5bohfUluuv5TfrhS1t09ogUbSqpVUV9q0alx+jnV03QgslZcocdX6TjIsMkSfUtHYqIoWQDANAbSjYwyOQmR+nrF4zUHeeP0KaSWr2wvkT/2lKmcRlxuuWafM0ZmdLrvO04d1fJrmtuV0pMhD9jAwAQVCjZwCBljNHE7ARNzE7QPZeN79d74iK7/sqoa+nwZTQAAIJeiNMBAASPY0eyAQBA7yjZAPrt6JzsuhZKNgAAfaFkA+i3j0aymS4CAEBfKNkA+u2jOdmMZAMA0BdKNoB+iwxzyRVimJMNAMBJULIB9JsxRnHuUEayAQA4CUo2gFMSFxmmWuZkAwDQJ0o2gFOSGhOhivoWp2MAABDQKNkATklGQqQO1VCyAQDoCyUbwCnJTHDrcG2LPB7rdBQAAAIWJRvAKcmMj1Rbp0eVja1ORwEAIGBRsgGcksyESElSKVNGAADoVcCXbGPMZ4wxy4wx9xtjPuN0HmCwy4h3S5IO1TQ7nAQAgMDlSMk2xjxsjCk3xmz+2PF5xpgdxpjdxpi7ug9bSQ2S3JKK/Z0VwPGOjmQfqmUkGwCA3jg1kv2opHnHHjDGuCT9UdJ8SeMkXW+MGSdpmbV2vqTvSfqxn3MC+JjEqDC5w0IYyQYAoA+OlGxr7VJJ1R87fKak3dbavdbaNklPSVpgrfV0nz8iKcKPMQGcgDFGmfGRKq2lZAMA0JtQpwMcI0tS0TGviyXNMMZcKekiSQmS/tDbm40xt0q6VZJyc3N9GBNAZkKkSnjwEQCAXgVSyT4ha+3zkp7vx3UPSHpAkgoKCljAF/ChjHi3du6scDoGAAABK5BWFymRlHPM6+zuYwACTGZCpCoaWtXW4Tn5xQAADEKBVLLXSBppjMk3xoRLuk7SSw5nAnACmQluWSuV1TFlBACAE3FqCb8nJa2SNNoYU2yMucVa2yHpDklvSNomaZG1dosT+QD07egyfiWsMAIAwAk5MifbWnt9L8cXS1rs5zgATlFGfFfJ3l/ZqLOGJTucBgCAwBNI00UABIncpCjlJkXpp69u08rdlU7HAQAg4FCyAZyy8NAQLfrKTGUmuPWFR9Zo8aZSpyMBABBQKNkATsuQeLcWfWWmJmTH62tPrNPj7x9wOhIAAAGDkg3gtCVEhevxW2bo/NFp+s9/btZv3twpa1mmHgAASjaATyUy3KX7PzdNV03N1m/e3KV739jRc279wSOMcAMABqWA3/ERQOALc4Xol9dMVHhoiP707h6NSo/VZ8en644n1qu0tllXTs1SVDh/3QAABg/+1QPgFcYY/feC8dpT0aDvPbdRr29O61lHe0NRrWYOZ6k/AMDgwXQRAF4T5grRn2+cqpSYCL2+5bA+Oy5dkrS+6IjDyQAA8C9KNgCvSo6J0ENfKNBVU7P1f1dN1LCUaK07UNPne8rqWuTx8MAkAGDgYLoIAK8bMyROv1o4SZI0JTdR7+0sl7VWxpiea1raO/XqxlI9tmq/NhTXKishUldNzdJV07I1NDnaoeQAAHgHJRuAT03JTdBz64pVVN2s3OQoFR9p0j9WH9TTa4pU3dim4anR+vaFo7Rmf7V+/85u/e7t3TozP0lXT8vWJRMyFB3BX1MAgODDv14AfGpKboKkrnnZZfUtuu6B92Wt1dyx6fr8rDzNGp7cM8J9qKZZL6wv0TOFRfrusxv1o5e26OIJGbp6WrZm5CcdNxIOAEAgo2QD8KnR6bGKCndp/cEaLd9Vqahwl167c46yE6M+cW1mQqS+dt4IffUzw7X2wBE9U1isVzYe0rNri5WbFKWrpmbrwnHpenz1Ad08K08j02Md+EYAAJwcJRuAT4W6QjQxO14f7KvWodpmzR2bfsKCfSxjjAryklSQl6R7Lh+n1zcf1rNri3Xfmzt135s7JUkpMRH69oWUbABAYKJkA/C5qbmJ+tO7eyRJ884YckrvjQoP1ZVTs3Xl1GwVVTfp5Y2H9IvXd6i8rsUXUQEA8AqW8APgc1NyEyVJUeEunTsq9bTvk5MUpa9+ZoQm5ySo+Eiziqqb9ML6Ym/FBADAayjZAHzu6MOP541OkzvM9anvl50YqeIjTbr7+U361tMb1Nja8anvCQCAN1GyAfhcSkyEfrJgvL45d6RX7pedGKX9VU1avrtSklR0pMkr9wUAwFso2QD84nMzvbcaSHZipCQpzNW1pN/BKko2ACCwULIBBJ3cpK7VSW4/d7gkqehIs5NxAAD4BEo2gKAze0SK/njDVH39gpGKiQhVUTUj2QCAwMISfgCCjivE6JKJGZK6VhyhZAMAAg0j2QCC2pghsXpnR7m+9sQ6yjYAIGD0ayTbGBMpKddau8PHeQDglPzw0nFKj3Pr76v2q7qhTU/eepbTkQAAOPlItjHmMkkfSnq9+/VkY8xLvg4GAP2RGB2uu+aP0Z1zR2rV3iptLql1OhIAAP2aLvIjSWdKqpEka+2HkvJ9mAkATtl1Z+YqJiJUf1221+koAAD0q2S3W2s/PjRkfREGAE5XnDtM103P0SsbS1VSw5J+AABn9adkbzHG3CDJZYwZaYz5vaSVPs4FAKfs5rO7fsj2yPJ9DicBAAx2/SnZX5c0XlKrpCck1Uq605ehAOB0ZCVE6tKJGXryg4MqZqt1AICD+lOyL7HW/sBaO737139KutzXwQDgdNxx3giFhBhd9eeV2nG43uk4AIBBqj8l++5+HgMAx41Mj9Wir8yUtdI196/Umv3VTkcCAAxCvZZsY8z87vnXWcaY3x3z61FJHX5LCACnaGxGnJ67fZZSYiJ004OrtWRr2Wndx1qrd3aU68YH39ftj6+VtTzzDQDon75Gsg9JKpTUImntMb9eknSR76MBwOnLSYrSM7fN1JiMOH3l74V66oOD/X5vW4dHz60t1rzfLNPNj6zRxuJavbb5sF7dVOrDxACAgaTXHR+ttRskbTDGHJH0irXW479YAPDpJcdE6IkvzdDt/1inu57fpMqGVn3tvBEyxpzw+obWDj31wUE9tHyfSmtbNDo9Vr9eOEkXT8jQFX9aqZ8t3q65Y9PlDnP5+ZsAAIJNf+ZkL5S0yxjzC2PMGF8HAgBvio4I1UOfL9AVU7L0y3/t1I9e2qJOz/HTPsrrW/SL17dr5s/e0k9f3aahyVF65Obpev2bc3Tl1Gy5w1z6r0vHqqSmWQ+xPCAAoB96Hck+ylp7kzEmTtL1kh41xlhJj0h60lrLo/sAAl6YK0S/umaSUmLC9ddl+7SjrF7nj0nTyLRYvbHlsJ5fV6J2j0fzzxiiW88Zrsk5CZ+4x6zhKbpofLr++M5uXTMtW2lxbge+CQAgWJj+PshjjEmW9DlJ35S0TdIISb+z1v7ed/FOT0FBgS0sLHQ6BoAA9MiKfXpw2b6eXSHDQ0N0zbRsfXnOMOWlRPf53gNVjbrw10u1YHKm7r1mkj/iAgACmDFmrbW24ETnTjqSbYy5XNLN6irVj0k601pbboyJkrRVUsCVbADozc2z83Xz7HxVNbRqx+F6jRoSq5SYiH69d2hytG4+O08PLN2rf5+ZpwnZ8T5OCwAIVv2Zk32VpPustROstfdaa8slyVrbJOkWn6YDAB9JjonQrBEp/S7YR91x3gglR4frJ69sZUk/AECvTlqyrbWfl7TTGHO5MeYyY8yQY8695dN0ABBgYt1h+s5nR+uD/dV6bfNhp+MAAALUSUu2MeYWSR9IulLS1ZLeN8Z80dfBACBQLSzI0ZghsfrfxdvU0t7pdBwAQADqz3SR70qaYq39Qveo9jRJ3/NtLAAIXK4Qox9eNk7FR5r116V7P3G+vK5FHxbVOJAMABAo+lOyqyQdu1RfffcxABi0Zg1P0cUThujXb+7UX5fuPW5+9nee2aBr/7JKNU1tDiYEADip19VFjDHf7v7jbkmrjTEvSrKSFkja6IdsABDQfr1wsow26H8Wb9OB6kb96LLx2lpap2W7KiVJz64t1pfmDHM4JQDACX0t4Rfb/fue7l9Hvei7OAAQPNxhLv3++inKSYrS/e/tUfGRZhlJce5Q5SZH6R+rD+qWs/N73cYdADBw9VqyrbU/9mcQAAhGISFGd80fo9ykKP3Xi5vV6bH6xvkjlJcSrW8v2qCVe6o0e0SK0zEBAH7W13SRl/p6o7X2cu/HAYDgdMOMXGUlRurJ1Qd18+x8RYa79JNXturx9w9QsgFgEOprushMSUWSnpS0WhI/7wSAPpw7KlXnjkrteX1NQY4eWr5PZXUtSo9zO5gMAOBvfa0uMkTS9yWdIem3ki6UVGmtfc9a+54/wgFAMLv+zFx1eqyeXlPkdBQAgJ/1WrKttZ3W2te718Y+S12rjLxrjLnDb+kAIIjlp0RrzsgUPfnBQXV0epyOAwDwoz7XyTbGRBhjrpT0uKSvSfqdpBf8EQwABoIbZ+SqtLZF7+yocDoKAMCP+nrw8TF1TRVZLOnH1trNfksFAAPE3LHpSo+L0OPvH9CF49IlSXUt7fq/17ZraFKUrp2eo4SocIdTAgC8ra8HH2+S1CjpTknfOGadVyPJWmvjfJwNAIJeqCtE103P1e/e3qWDVU1yuYy++Mga7Sqvl8dK9725U1dMydLnZ+VpzBD+WgWAgaKvdbL7s+U6AOAkrjszR394Z7d+9to2rT1wRM1tnXrsizOUHBOux1bt1wvrS/TkB0WaOSxZn5+VpwvHpcsVwoJOABDMjLX2xCeMWStpuaTXJL1rrW3xZ7BPo6CgwBYWFjodAwB63PpYof61tUyZ8W49cvOZGj0ktudcTVObnl5TpMdWHVBJTbOyEiL1pxunalJOgoOJAQAnY4xZa60tOOG5Pkp2qKSzJc2TdJ6kKklvSHrNWrvTR1m9gpININBsP1ynvy7dp+/OG93rmtkdnR69ua1cP355i2LdoXr1G3MU5uKHigAQqE6rZJ/gJpnqKtzzJI2Q9L619qteS+lFlGwAwezNrWX60mOF+v7FY1tCC78AACAASURBVHTrOcOdjgMA6EVfJbvfQyTW2kPW2oettQslFUj6h7cCAgA+MndcuuaOTdNv3tyl0tpmp+MAAE7DydbJHm+MSe3+c7Ix5kFjzFOSRltrV/glIQAMQvdcNl6dHqufvLLV6SgAgNNwspHsvxzz5/+RdFhdm9E84rNEAADlJEXpjvNGaPGmw1qytUydnv5N7QMABIa+NqO5R9JwSbebrkWyr5D0sKQxkrKNMT9U16ojS/2SFAAGmVvPHabn15foy48VyhgpOTpcKTERSo2NUEpMhC4cl66LJ2Q4HRMAcAJ9PvjYvYzflZLSJf3MWntB9/Hl1tqz/RPx1PHgI4CBorS2WUu2lqmyvlUVDW2qqG9VZUOrio80q7qxVc9/dbYms9QfADiirwcf+9rxUZJ+KmmVpDZJ13ffbLykcq8m7IMxZqy6dp1MkfSWtfbP/vpsAHBaRnyk/n1m3ieO17W066L7luo7iz7Uq9+YI3eYy//hAAC96nNOtrX2BWttprU2z1q7qvvYFmvtlZ/mQ40xDxtjyo0xmz92fJ4xZocxZrcx5q7uz9tmrb1N0kJJsz/N5wLAQBHnDtPPr5qoPRWN+vWSgN66AAAGJad2OXhUXett9zDGuCT9UdJ8SeMkXW+MGdd97nJJr0pa7N+YABC4zhmVqhtm5Oqvy/aqcH+103EAAMdwpGR3Pyz58X8RzpS021q711rbJukpSQu6r3/JWjtf0o3+TQoAge37F49VVkKk/t8zG9Tc1ul0HABAt0DarzdLUtExr4slZRljPmOM+Z0x5i/qYyTbGHOrMabQGFNYUVHh66wAEBBiIkL1i6snan9Vk37++nan4wAAup3swUdJPVM50o+93lp70FehjmWtfVfSu/247gFJD0hdq4v4NhUABI5Zw1P0hVl5enTlfg1PjdbnTvCgJADAv05aso0xX5d0j6QySZ7uw1bSRC9nKZGUc8zr7O5jAICTuGv+GBUfadZ/vbhFlQ1t+ubckera4gAA4IT+jGTfqa5t1Kt8nGWNpJHGmHx1levrJN3g488EgAHBHebS/TdN1V3Pb9Jv39ql6sY2/ejy8XKFULQBwAn9KdlFkmq9+aHGmCclfUZSijGmWNI91tqHjDF3SHpDkkvSw9baLd78XAAYyEJdIbr36olKjgnXX97bqyHxbn3tvBFOxwKAQak/JXuvpHeNMa9Kaj160Fr769P9UGvt9b0cXyyW6QOA02aM0d3zx2r13mq9s72ckg0ADunP6iIHJS2RFC4p9phfAIAANT0vURtLatXawbJ+AOCEk45kW2t/7I8gAADvmTY0SX9dtk+bS2o1bWiS03EAYNDptWQbY35jrf2mMeZlda0mchxr7eU+TQYAOG3ThiZKkgr3H6FkA4AD+hrJ/nv377/0RxAAgPekxkYoLzlKhQeO6CsOfH6nx+rh5ftU19Le6zXpcW7dOCOXpQYBDEi9lmxr7dru39/zXxwAgLdMG5qkd3eUy1rr9yK7rbRO/7N4m4yRTvTJVpK1UkFeosYMifNrNgDwh37t+AgACD4FeYl6bl2x9lc1KT8l2q+fXdfcNYL95JfP0lnDkj9x/nBti8762Vt6e3s5JRvAgNSf1UUAAEGooGdedrXfP7uupUOSFBNx4rGcIfFujc+M0zvby/0ZCwD8pt8l2xgT5csgAADvGp4ao/jIMK09cMTvn93Q2lWy49xhvV5zwZg0rT1wREca2/wVCwD85qQl2xgzyxizVdL27teTjDF/8nkyAMCnEhJiNDU3QYUOlOz67gceY929z0o8b0yaPFZauqvCX7EAwG/6M5J9n6SLJFVJkrV2g6RzfBkKAOAdBXlJ2l3eoKqG1pNf7EX1R6eL9FGyJ2UnKDk6XG9tY8oIgIGnX9NFrLVFHzvEFmIAEAQ+MzpVkvTKxlK/fm5Da4fcYSEKc/X+z0xIiNGMYUnaWFzjx2QA4B/9WV2kyBgzS5I1xoRJulPSNt/GAgB4w/jMeI3PjNPfVu3XiVbxGxLn1mfHD/H659a3tCu2j/nYR6XHufXeDqaLABh4+lOyb5P0W0lZkkok/UvS13wZCgDgPZ+flafvPrtRP3xxywnPr/nBXKXGRnj1M+taOhTby8oix0qLdauxrVONrR2K7sf1ABAsTvo3mrW2UtKNfsgCAPCBhQU5umjcEHV4PMcdX767Unc+9aFKapq9XrIbWjr6fOjxqKOfW1HfSskGMKD0Z3WRvxljEo55nWiMedi3sQAA3hQfFabkmIjjfo1Mi5UkHapp9vrn9Xe6SNrRku3nBzMBwNf68+DjRGttz1Mp1tojkqb4LhIAwB+yEiIl+apkd/S6Ec2xjh3JBoCBpD8lO8QYk3j0hTEmSWzHDgBBLy4yVNHhLh2qafH6vRta+zdd5OhIdnmd9zMAgJP6U5Z/JWmVMeYZSUbS1ZL+x6epAAA+Z4xRRkKkV0eyW9q7Vnitb+no13SRxKhwuUIM00UADDj9efDxMWNMoaTzuw9daa3d6ttYAAB/yEyI1M6yer2++fAnzuWlRGnMkLh+3+snr2zVQ8v39byOjzx5yQ4JMUqJCdeGolodrGpSTlKkzInWGgSAINNryTbGxFlr67qnhxyW9MQx55KstdX+CAgA8J2RaTFaurNCtz2+9hPnQoz0pxun6oKx6X1uKiNJy3ZV6KHl+3TxhCGakJUgV4j0b5Oz+pXhC7Py9fPXt+uce9/Rb6+brAX9fB8ABDJjrT3xCWNesdZeaozZJ+nYi4wka60d5o+Ap6OgoMAWFhY6HQMAAl5bh0d7Khr08X8KOjwe3f74OpXUNOviCUP0pxun9XoPa60u/8MK1Ta361/fOkfuMNcp53h/b5Wue+B9feXcYbp7/thTfj8AOMEYs9ZaW3Cic72OZHcXbCPpXGvtQZ+lAwA4Jjw0RGMzTjwl5NnbZ+qu5zZp8abDWrG7UpNyulZzbevw6IcvblZiVLhW7KlURX2r6ls69POrJpxWwZaks4Yla3hqtA5UNp32dwGAQNLnnGxrrTXGvCppgp/yAAACREZ8pP5441Sd/8t3deODq3u97t8mZ2pocrSunJr9qT5vaHK0DlRTsgEMDP1ZXWSdMWa6tXaNz9MAAAJKTESoFt85R//aUqbG1o6e4weqG/X4+wcVGebSL66epPDQ/qwI27fcpCit3lslay0PPwIIev0p2TMk3WSM2S+pUR/NyZ7oy2AAgMCQEhOhG2bkHnesor5Vj79/UNPzk7xSsCUpLzlKjW2dqmxo8/o27wDgb/0p2Rf5PAUAIKikxkbozgtG6sz8JK/dMz81RpK0el+VLp2Y6bX7AoAT+lrCzy3pNkkjJG2S9JC1tqO36wEAg8u3Lhzl1fvNGp6sUekx+t9Xtyk7MUqTux+0BIBg1NfP+P4mqUBdBXu+unZ+BADAJ8JcIfrF1ZPU7rG65v6VWrOf7RgABK++SvY4a+1N1tq/qGsr9Tl+ygQAGKQm5yRoybfOUXZilG56cLUeXLZX1Y1tamrjB6kAgktfJbv96B+YJgIA8JeEqHA9fetZOntEin766jZN/ckSTf3JEq3cXel0NADot752fOxU12oiUteKIpGSmvTR6iIn3r0gALDjIwAEP2ut3t5erqLqJj26cr86PFZvfPMcRUf055l9APC9093x8fS27QIAwAuMMbpgbLokaXxWvBb+ZZX+++Wt+vGC8ae9syQA+It3FjcFAMCHpucl6ZbZ+Xq6sEg3Prhavf0UFgACBSUbABAUfnDJWP3nJWO19sARvbezwuk4ANAnSjYAICgYY/TvM/OUEe/Wwyv2Ox0HAPpEyQYABI3w0BBdMiFD7++tUnNbp9NxAKBXlGwAQFCZMypVbR0erd5X5XQUAOgVJRsAEFRm5CcpIjREb28vdzoKAPSKkg0ACCruMJfmjk3XKxtL1d7pcToOAJwQJRsAEHSumJKl6sY2vbWN0WwAgYmSDQAIOueOTlVuUpR+99YueTwnXjO7qa1DS3dWqLOX8wDgS+xNCwAIOmGuEH3rwpH61tMbdPHvlslaqay+RVLXxjVTchO05VCdXt1YqpnDkvXEl2fIGONwagCDCSUbABCUFkzKUn1Lh/61pUwRoSE6Mz9J7Z0eLdlapiVby3quW7W3Sit2V+nskSle+2xrLaUdQJ/MQNyatqCgwBYWFjodAwDgkNc3H9aDy/bqvmsn6/I/LNeRpnbdPDtP91w2/lPfu/hIk27462rdPX+M5k/IkNRVuj1Wqmlq08sbDunSSZlKiYn41J8FILAZY9ZaawtOdI6RbADAgDPvjCGad8YQSdL9N03Twyv26ZEV+9XU2qn4qDB9aU6+0mLdp3Xv+5bs0sHqJv345a2qamxTS3unnltXom2ldT3X/Pm9PXrhq7OVmRDple8DIPgwkg0AGPAaWjt08yMfaG9Fo+pa2pUaE6E3v3Ou9lU2KjUmQmlxHxXu1o5OWdu1VODH1bW0a+p/L9G0oYlas79aR5+pHBLn1sLpOQp3GQ1PjdF3ntmgMUNi9V+XjtOU3MQ+s1U3tqmj03NcBgDBgZFsAMCgFhMRqmdumyVJendHub7wyBpd8Kv3VFrbohFpMXrl62f3lOrvPbtRRUea9dztsz5xn2U7K9XhsfrOZ0dreGq0Oj1WEWEuxUSEyhXy0Rzttk6P/uPZjbriTys1KTteoa4QDYlzKz4qTBeOTVeMu+uf38r6Vt351Idq93h079WTdOnEjBOWewDBh5INABhUzhmZKkkqrW1RZrxbu8sbdP97e/TNuaNkrdXSXZWqbmxTWV2L0uPcOlTTrD+9u1vNbR5tLqlVnDtUU3MTFOrqfRXcBZOzNHdsuv7wzm5tLqlVp8dqa2mdKupb9cTqg8ddmxHvVmS4S//vmQ368Utb9P1Lxuq66Tk8WAkEOUo2AGBQCQkxuvfqiVqxu1L3XjNJdzyxTg8t36ebZ+ersqFV1Y1tkqS/rdyvs4Yl63dv7dLGklqldj/I+IVZeX0W7KOiI0L1vXljjjvW1NahDw/WyGOlTmu1oahGl07MUHJ0hBZvLtVLHx7S3c9v0o7D9frR5Z/+IU0AzmFONgBgUNt6qE6X/H6ZJmbFKyEqXO/trFCsO1T1LR0919x37SRdMSXb51k8HqsfvrRZ/1h9UM/eNkvThvY9nxuAs/qak03JBgAMeq9sPKT/fXWbmts7NSItRn+4YaqKjzRJkuIjwzUiLcZvWRpaO/TZX7+ntk6rF++YrSxWKAECFiUbAIAgsuNwvS76zVL94OKx+vI5w5yOA6AXfZXsk08qAwAAfjV6SKwSosK0r6rR6SgAThMlGwCAAJSfEq39lZRsIFhRsgEACED5KdHaR8kGghYlGwCAAJSfHK3S2hY1t3U6HQXAaaBkAwAQgPJToyVJO8vqHU4C4HRQsgEACEAzhyUr3BWi59YVOx0FwGmgZAMAEICSYyJ06cQMPbe2WI2tHSd/A4CAQskGACBAXT45U41tndpYXOt0FACniJINAECAOiMrXpK05RAlGwg2AV+yjTHDjDEPGWOedToLAAD+lBITofS4CG05VOd0FACnyJGSbYx52BhTbozZ/LHj84wxO4wxu40xd0mStXavtfYWJ3ICAOC08ZnxjGQDQcipkexHJc079oAxxiXpj5LmSxon6XpjzDj/RwMAIHCckRWv3eUNqm9pdzoKgFPgSMm21i6VVP2xw2dK2t09ct0m6SlJC/weDgCAADI9L1EeK607WON0FACnIJDmZGdJKjrmdbGkLGNMsjHmfklTjDF39/ZmY8ytxphCY0xhRUWFr7MCAOAXU3MT5Qox+mBfldNRAJyCQCrZJ2StrbLW3matHW6t/Vkf1z1grS2w1hakpqb6MyIAAD4THRGqM7Li9drmw2pgvWwgaARSyS6RlHPM6+zuYwAADGrfnDtSB6qadNvf16qtw+N0HAD9EEgle42kkcaYfGNMuKTrJL3kcCYAABx33ug0/d+VE7R8d6X+umyv03EA9INTS/g9KWmVpNHGmGJjzC3W2g5Jd0h6Q9I2SYustVucyAcAQKC5piBH+SnR2lrKmtlAMAh14kOttdf3cnyxpMV+jgMAQFDIToxUcXWT0zEA9EMgTRcBAAB9yE6MVPGRZqdjAOgHSjYAAEEiOzFKVY1tampjlREg0FGyAQAIEtmJkZKkEkazgYBHyQYAIEhkJ0ZJku56fpPq2GYdCGiUbAAAgsTI9Bhlxru19sARPbJ8v9NxAPSBkg0AQJCIc4dp5d0X6NxRqfrH6gNq72RjGiBQUbIBAAgy107PUXl9qzYW1zgdBUAvKNkAAASZgqGJkqT1Bz8q2dZaPbH6oL7y90LVM18bcJwjm9EAAIDTlxbnVlZCpNYXfVSyFxUW6fsvbJIkTck9qNvOHe5UPABiJBsAgKA0JTdB6w8ckbVWzW2d+umr23TWsCTNGp6sh5bvU20To9mAkyjZAAAEobOGJetQbYt2lTfo/b1Vqm/p0O2fGaH/uGi0apra9OW/F6qhlU1rAKdQsgEACEIXjkuXJP1ry2G9s6NckWEuzchP0pTcRP1q4WStPXBEP3xxs8MpgcGLOdkAAASh9Di3puQm6P739qrD49HZI1LkDnNJki6flKlXNx7ShiJWHwGcQskGACBIffvCUXryg4MyMvri2XnHnctPidHb28vV6bFyhRhnAgKDGCUbAIAgNWdkquaMTD3hufyUKLV3WpUcaVZucpSfkwFgTjYAAANQfkqMJGlfVaPDSYDBiZINAMAAlJfSNXq9r6LBa/csrW3WtJ8s0ZZDtV67JzBQUbIBABiAUmMiFB3u0o9e3qpNxd4pxdtL61XV2KZ1B3mgEjgZSjYAAAOQMUafn5UnSXpre5lX7nm4rkWSVFzd5JX7AQMZJRsAgAHqu/PGKCYiVHXN3tmU5nBtV8k+SMkGToqSDQDAABbnDlV9i3e2WC/rHskuOkLJBk6Gkg0AwAAW6w5TnZdKdmn3SHZRdbNX7gcMZJRsAAAGsLhI700XOTqSXdvcrvL6Fq/cExioKNkAAAxgcacwkr2xuEYlNb2PUh+ua9HU3ASFu0L01cfXeSsiMCBRsgEAGMBi3aH9KtnWWn3hkTX67Zs7T3i+pb1TNU3tumBsuu6cO1KFB46oor7V23GBAYOSDQDAABYXGab6lpNPFyk+0qzqxjZtOVSnTcW16vTY484Xda8okpngVsHQREnS5hI2pQF6Q8kGAGAAi3OHqa65Xav3Vum6B1bpne3lx523tqtMHy3MWw7V6bI/LNcrGw8dd93G7g1tzsiM1/iseBkjbaJkA72iZAMAMIDFukPlsdJjqw7o/b3VuuOJdWrr8EiSVuyuVP7di7WnokGbP7ZV+vbD9ce93lhco+hwl4alxigmIlT5KdEnLNkfFtXol2/s0NoD1b77UkAQCHU6AAAA8J24yDBJ0js7ukawG9s6tWZ/tYYmR+mP7+yWJH2wr1qbSuqOe9+BqsbjXn9YXKsJ2fFyhRhJ0oSseH2w7/gi/f7eKn3uodVq77R6e3u5Ft85xyffCQgGjGQDADCAxbm7SnZTW6e+cf4IhYeG6LvPbtTZP39HK/dUSeqab73lY6PS+yo/2nCmobVDWw/VanJOYs+xCVnxKq1tUWXDRw8/Pr+uWJFhLn3lnGHaWlqn8jqW+cPgRckGAGAAi3V/9EPr88ak6dxRqapsaNUlEzJ6ji/bVamqxrae17lJUTpQ1dgzX3v5rgq1d1p9ZnRqzzVnZMVL6pqX3dLeKWutVu+r1oxhybpsUqYkaemuSp9+NyCQMV0EAIABLDPBLUm6ckqWpuQm6r5rJ6uj06OEqHD9qL5VP3xxs17bfFiSFBsRqvrWDg1LjdbB6iZV1LcqLc6t1zcfVpw7tGdVEUkanxknSVq9t1o3P7JG103P0YGqJn3urKEanxmn1NgIvbezQldPy/b/lwYCACPZAAAMYCPSYrXq7vP1q4WTJEkxEaFKiAqXJKXGRmhUemzPtfPOGCJJOmdk14j1txZ9qPuW7NQ/PzykK6dmK9T1UW2IdYdpWGq0FhUWSZKeWtP1+1nDkmWM0TkjU7VsV8UnlgIEBgtGsgEAGOAy4iN7Pfe5mUMV6w5VXnK0zh6Zornj0nXR+CGKdYfq7uc3acXuKi2YnKn/vGTsJ947c1iy/rH6YM/r/JTonhHuc0en6rl1xdpQXKOpuYmfeC8w0FGyAQAYxFJiIvSlOcN6Xl80vms0+5qCHOWlRGv9wSO65exhPauKHOv8MWn6x+qDGhLn1tiMWP3gkrEypuu6OSNSJHWtXELJxmBEyQYAACc0PS9J0/OSej0/a3iKosNdumxShn5wybjjziVGhys+MkyHapp9HRMISJRsAABwWiLDXVp85xylxESc8HxGvFultSzjh8GJkg0AAE7b0OToXs8NiXertJaRbAxOrC4CAAB8IiM+UocZycYgRckGAAA+kRHvVmVDm1o7Op2OAvgdJRsAAPjEkPiujXDKaltPciUw8FCyAQCAT2R2r8996e+XqaKeoo3BhZINAAB8Ykpugs4Zlaq6lg79a+thp+MAfkXJBgAAPhEdEaq/3TxdWQmRWrqzwuk4gF9RsgEAgM8YY3TOqBS9saVMn3totdNxAL+hZAMAAJ+6eXa+Qoy0bFelniks0s6yeqcjAT5HyQYAAD41Kj1Wz94+S5L0H89uPOmIdl1Lu55ec1DWWn/EA3yCkg0AAHxuQlZ8z5/jI8P6vPaVDaX63nObtLmkztexAJ+hZAMAAJ8Lc4VoXEacJOmMYwr3iRyq6dqKfVNJrc9zAb5CyQYAAH7x7O0zFecOlZHp87pDtV0le/MhSjaCFyUbAAD4RVR4qFJiItTS3vc266U1LZKkzYxkI4hRsgEAgN8MTY7S3srGPq85XNdVsreX1qutw+OPWIDXUbIBAIDfDEuN0b7KBnk8J145xFqrQzXNyoh3q63To13lLPeH4ETJBgAAfjMsNVot7R6Vdo9WH1Ve16LapnbVNLWrtcOjC8elS2LKCIIXJRsAAPjN8NQYSdLOw8ePUP/7wx/onHvf0S//tUOSdNawZMVGhGrF7iptPVSn5ra+53GfzM9e26Y7nlj3qe4BnIpQpwMAAIDB42jJvvnRNbr/pmmad8YQSVJdc7ua2jr0j9UHJXXN3Z6Uk6CXNhzSSxsOKTLMpfPHpOniCRk6b0yqosL7X2GstfrLe3slSXfNb1J2YpRaOzpVUd+qsrpWVdS3qKyuVTVN7brprFwlx0Qc9/5Oj9UTqw/o6mk5igx3eeN/BgwClGwAAOA3qbER+s21k/WrJTv05/f29JRsSVowOUtXTs2SrDQuI06/vGaSPiyqUYfHo1V7qvTGlsN6dVOp3GEh+vysPN09f2yvn/P3Vft1/th0ZSVE6lDtR1NTrvrzSrV1ePT/27vz+Kqqc//jnyfJyUhmkmAGgSCgDEIgIjiBVgG1V0S0DhVtte2tl/u7bV9eW3q19rb+bltrr6231Ko/xWrLz7ZaW3Go1AEcQIaAQJjCDAlTgAQICZCQrPvH2UDABBI8U5Lv+/Xar+yz9t7rPDuP5/C4s/ba1XUNLR63fd8hHr35wpPaFm6q4gevraTJwd2X9Ppc5y9dh4psERERCakbi/LYf6iBH85cydpdNfTLSQbAgEv6dD++X4/UeMan+ovwL16Yy48nDGLhpioefXsNf1lc0WKRXVFdx7MfbeJ38zbz1AcbmTv1KhZvqQZgTP8sfNFRZCfHkZMST05KHNnJ8WSn+F9Pe389v5+/hX8eXUihd8UdoLyqDoA3S3eoyJY2U5EtIiIiITekIA2ArXvrjhfZZxIdZYzqk8moPpk8+9F+nHOYnXiwTXVtPROfnMeeg0cA2LbvEJU1h/njwq0kxkbz7F3FxES3fjvalCvP488l5fzy3XX8+vai4+3l1f4ie9HmKioPHCY7Jb7d5ytdj258FBERkZDLTfUXqtNmr2fe+j20PKFfy1LifTQ0Og43nJhDu7yqjsnTF7Cvrp6ZUy7jqTuHAXDpz95n0eYq7h/b/7QFNviHstxzaW9eX7adGQu2nNR3XEwUzsGslTvbEal0ZbqSLSIiIiGXnRLPT28azC/fWcsdzy5o17EpCf7y5cDhBuJ9Ucwp282v3lvHlj11TLtjGIPzUxmYm8IjNw5i7c4a7hrVk75tvFr+r1edx8rt+3nwryuorq1nypXnUVF9iKEFaeytrefN0h1MHtWrvacrXZCKbBEREQmL20ecy8SiPF5eXMEL8zYzIDelTcelxPsAmD53EynxPh6b5Z/270c3DGTcQP8Y7qgoY/LInu2OKd4XzTN3FfPdV5bzi3+sZW9tPVur6riiXxYXF2Yy7f117K45QlZy3Jk7ky4t4otsMysEHgRSnXM3hzseERERCZx4XzSTR/ZsV0GckuAvso9NywfwwLj+fPnicwMSky86iv++ZQjpibFMn7sJgIL0RMYNyuF/3lvHrJU7ufMsCnjpWoI6JtvMpptZpZmtOKV9vJmVmdl6M5t6uj6ccxudc/cGM04RERHpOFK9IvuYr13WmylXnnfGMdftERVl/OCLF/DAuP4A9M3pRv+cZAqzknirdEfA3kc6r2Bfyf4dMA148ViDmUUDvwGuASqARWY2E4gGfnrK8fc45yqDHKOIiIh0ICnxJ8qXKVf24Zuj+wTlfcyMKVeexw1DcslLS8DMuGZADtM/3sSh+kY9mEZOK6hXsp1zHwJVpzSPANZ7V6jrgT8CE5xzpc65L56yqMAWERGRk6Q0u5J93eBzSI73nWbvz68gI5GoKP9UgSMLM2lodCzZWv2Z/V5ZXMGLn2ymobHpM9uk6wnHFH55QHmz1xVeW4vMLNPMngKKzOz7p9nvG2ZWYmYlu3fvDly0IiIiElGSm13J7hHiOauLe6YTHWXM37j3pPaK6jq+/+py1+HFJgAAE1VJREFUHn5tJdc98dHxubql64r4ebKdc3udc990zvVxzp06nKT5fs8454qdc8VZWVmhDFFERERCKC7mxDCN9MTYkL53cryPQbkpLNh48h/qn/vYf4PkQ9dfwLrKg8wp0wW/ri4cRfY2oKDZ63yvTURERKRdjg3jCKWRhZksLd/H/I17mfjkXOZt2MM/Vu5idL9sJg3LB2DtrpqQxyWRJRxF9iKgr5n1NrNY4DZgZhjiEBEREWm3kYWZ1Dc2ceezC/h06z6+8vwitu07xJj+WaQl+hg3MIdnPtz4mSEl0rUEewq/l4BPgP5mVmFm9zrnjgL/CswCVgN/ds6tDGYcIiIi0rk8dP0FPDppcFjeu7hXOjFRRk5KPK9NuZT89AQAxvTPwsx44rYikuNjeLmkIizxSWQw51y4Ywi44uJiV1JSEu4wREREpJNavKWKgvREslPiqaqtZ+2uGkYWZh7f/t1XlvHm8h2UPHSNpvrrxMxssXOuuKVtEX/jo4iIiEikGd4zg2xvZpOMpNiTCmyACUPzqK1v5IO1ugGyq1KRLSIiIhJgI3pnkBwfw3urd4U7FAkTFdkiIiIiAeaLjmJM/2xml1XS1NT5hubKmanIFhEREQmCqy/IZs/BepZW7At3KBIGKrJFREREgmBMv2yio0xDRrooFdkiIiIiQZCa6GNErwzeWL6D+qNN4Q5HQkxFtoiIiEiQfO3y3mzZW3f8sevSdajIFhEREQmSL1yQw9gBOTzx3lrKq+rCHY6EkIpsERERkSD64Q0DiTLj6y+WsG3foXCHIyGiIltEREQkiPLSEnh68nC27TvEhGlzWV9ZE+6QJARUZIuIiIgE2eV9s/jrv1xCk3NM/Uup5s7uAlRki4iIiITAednJPDCuPyVbqvm0vDrc4UiQqcgWERERCZEx/bMAWLHtQJgjkWBTkS0iIiISIj1S4slIimXl9v3hDkWCTEW2iIiISIiYGQNzU/h06z4aNS67U1ORLSIiIhJCg/JSWVd5kCt+PjuoM408/cEGpsxYoqdNhklMuAMQERER6Uq+emkv0hN9/L+PNnHr0/O5b0wfoqOMxNhorr8wl25xn788qzxwmMffWcuRo02kJfq4sn82FxdmkBzvC8AZSFuYc53vTxXFxcWupKQk3GGIiIiItGrj7oNMfm7hSQ+oyUyK5cHrL+CmYfnt7m99ZQ2ZSXEkxEbzi1llPD9vM/904Tn8bel2AG67qICfTbowYPELmNli51xxS9t0JVtEREQkDAqzujHngTHUHjkKwIbdtTzyxioeeGU5Y/pnk5EU2+a+3l21i/tmLCYzKY6dBw4DcNOwPB67eQhJcTHMWLCVvy3dxvfGn096O/qVs6cx2SIiIiJh4ouOIi0xlrTEWIb3TOeRCYNobHK8u2pXm/v4cO1u7puxmLy0BHYeOEyfrCT6ZCXxb1f1JTrK+K+Jg/nHd67gcEMTf5i/JYhnI83pSraIiIhIhBiUl0J+egJ/X7GDL11U0KZjfvnuWvLTE/nblEvZvKeWvjndSIw9ucTrl5PM6H5ZvPDJFr4xupC4mOhghC/N6Eq2iIiISIQwM8YP7MHc9Xs5cLjhjPtX1hxmafk+JhblkZrgY0hB2mcK7GO+emkv9hw8wuw1lYEOW1qgIltEREQkglw7uAf1jU1tKobfW12Jc3DNgJwz7nvZed3JSIrlzdKdgQhTzkBFtoiIiEgEKSpIJycljjeW7zjjvu+s2kV+egLn90g+474x0VGMH9SD91bv4lB9YyBCldNQkS0iIiISQaKijBuG5DJ7TSV7Dx5pdb/aI0f5eP0erhmQg5m1qe8vDj6HuvpG5pRpyEiwqcgWERERiTCThudztMkxc9n2Vvf5cO1u6o82tWmoyDEjemeQmRTLG6Vnvkoun4+KbBEREZEIc36PFAbnpfJySUWL20s2V/H7+Vvo3i2OEb0y2txvTHQU4wb1YPaaSj1uPchUZIuIiIhEoJuH57NqxwFWbt/P4YZGynbWUHO4ge+/WsrNT33CvA17mViUS0x0+8q5Mf2yqKtvZMnW6iBFLqB5skVEREQi0oShuTz69hqenLOBpibH31ecmBXk1uICtu8/xF2jerW735F9MgG47Zn5fHN0Hy44J5mhBWn0zEwKVOiCimwRERGRiJSWGMs9l/Zm2uz1gL+w7pEaz9CCNK48P/us+02J91HcM52SLdU89/FGGhodvmjjb1MuZWBuaqDCP63Siv3kpMaRnRwfkvcLBxXZIiIiIhHqn0cXUlVXT2qCj29f3TdgT2qcdscwDjU0kp+eQNnOGm767TxeLqlg4A3BL7LLq+qY9NQ8vnB+Nr+9c3jQ3y9cVGSLiIiIRKjkeB8/mTg44P32SD1xBXlQXirXDMhh5rLtPHj9BfjaOca7reaUVbJk6z7Kdh6g/mgTs8sqqas/SmJsDI1Njt9/splPy/cB4IuO4p5LezMgNyUosYSCimwRERGRLu6mojzeXL6DD8p2c3U7pgRsq/kb9/KV5xcdf3153+58tG4Pc8p2MzgvlftfXsbCTVXkpSXgizb21tbz+rLt/HjCQG696NyAxxMKKrJFREREurgr+mWRmRTLq59WBLzILq+qY3ZZJTFRxuRRPVmypZqn7hzO1Y9/wE/eWs2+ugYAfnHLECYNy8PM2HPwCN/501K+95dSfNFR3DQsP6AxhYKKbBEREZEuzhcdxQ1Dc5kxfyv76xpITfQFpN8lW6uZ9Nt5OAdDCtL44T8NPL7tJzcN5qvPL2JE7wz++5YhFGQkHt/WvVsc079yEZOfW8B//LWUi3plnLS9I9A82SIiIiLCpGH51Dc28UZp60+ZbAvnHP/3jVV87YUSfvjaSpzzt/fpfvIUgVf2z2be1Kt46esjWyygfdFRPP6loUSZ8fBrK3DHOuogVGSLiIiICANzU+iX041Xl2z7XP38aVE5z368iXdX76J0236+fXVfkuNiuLn4s0M+ctMSiI6yVvvKTUvg/rH9mV22m7dKd7a6XyRSkS0iIiIimBk3Dctn8ZZqNu+pPas+Vmzbz8MzV3J53+5MGJrL2AE5fOsLfSn90Tgu6dP9rPq8e1RPBuWl8J+vr2T/oYaz6iMcVGSLiIiICAA3Ds3DDP5cUt7uYw8eOcp9MxaTmRTLE7cV8cRtRTw9eThmrV+pbouY6Ch+OvFC9h48wn+8WkpTU8cYNqIbH0VEREQE8M+ffe2gHjz94Ubq6hsZ1SeTC/NTqT3SyNpdNWQlx1FUkEZMC3NpzymrpLzqEL+/dwQZSbEAn7vAPmZwfipTrz2fn7y1hsKsJO4f2z8g/QaTimwREREROe6xm4fQ1LSMlxZu5XfzNn9me3SU0SMlngG5Kfz69iLiff6nUJZsriYxNppRhZlBievrlxeyobKWX7+/nqJz07jq/MDP5x1IKrJFRERE5LikuBiemjycI0cbKa3Yz+qdNST6oumXk8ymvbWs21XDmp01vLNqFx+t28M13rzaizZXUXRuy1e5A8HMeOTGQXxaXs1Df13BS9/oRs/MpDMfGCYaky0iIiIinxEXE01xrwwmj+zJpOH5DM5P5YYhudw/tj9PfnkYqQk+/l66A4D1lQdZveMAxT0zghpTbEwUj908hNr6Rsb/6iN+M3t9UN/v81CRLSIiIiLt4ouOYuyAHP6xahcfr9vDlBlLSEuM5Y6Lg/8I9CEFabz5b5dxSZ9MHptVxsrt+4P+nmdDRbaIiIiItNt9Y/qQ2S2WO59bQNmuGn5561ByUuJD8t756Yk8futQUhN8TH5uIc/P3RSS920PjckWERERkXYrzOrGG//nMn7+dhmFWUmM7pcV0vdPTfDxh3sv5on31nLkaFNI37strKM9orItiouLXUlJSbjDEBEREZEQcM4FbLrA9jCzxc654pa2abiIiIiIiHRo4Siwz0RFtoiIiIhIgKnIFhEREREJMBXZIiIiIiIBpiJbRERERCTAVGSLiIiIiASYimwRERERkQBTkS0iIiIiEmAqskVEREREAkxFtoiIiIhIgKnIFhEREREJMBXZIiIiIiIBpiJbRERERCTAVGSLiIiIiASYimwRERERkQBTkS0iIiIiEmAqskVEREREAkxFtoiIiIhIgJlzLtwxBJyZ7Qa2hDuOEOsO7Al3ENIi5SayKT+RS7mJXMpNZFN+Qqency6rpQ2dssjuisysxDlXHO445LOUm8im/EQu5SZyKTeRTfmJDBouIiIiIiISYCqyRUREREQCTEV25/FMuAOQVik3kU35iVzKTeRSbiKb8hMBNCZbRERERCTAdCVbRERERCTAVGRHMDObbmaVZraiWdsQM/vEzErN7HUzS2m27UJv20pve7zXPtx7vd7M/sfMLBzn05m0Jzdm9mUzW9psaTKzod425SbA2pkbn5m94LWvNrPvNztmvJmVebmZGo5z6YzamZ9YM3vea19mZmOaHaPPToCZWYGZzTazVd6/I9/y2jPM7B0zW+f9TPfazfvdrzez5WY2rFlfd3v7rzOzu8N1Tp3FWeTmfO8zdcTM/v2UvvTdFirOOS0RugBXAMOAFc3aFgGjvfV7gEe89RhgOTDEe50JRHvrC4GRgAF/B64N97l19KU9uTnluMHAhmavlZsw5ga4A/ijt54IbAZ6AdHABqAQiAWWAQPCfW6dYWlnfqYAz3vr2cBiIMp7rc9O4HNzDjDMW08G1gIDgJ8DU732qcCj3vp13u/evFws8NozgI3ez3RvPT3c59eRl7PITTZwEfBfwL8360ffbSFcdCU7gjnnPgSqTmnuB3zorb8DTPLWxwLLnXPLvGP3OucazewcIMU5N9/5P2EvAjcGP/rOrZ25ae524I8Ayk1wtDM3DkgysxggAagHDgAjgPXOuY3OuXr8OZsQ7Ni7gnbmZwDwvndcJbAPKNZnJzicczucc0u89RpgNZCH/7/9F7zdXuDE73oC8KLzmw+kebkZB7zjnKtyzlXjz+n4EJ5Kp9Pe3DjnKp1zi4CGU7rSd1sIqcjueFZy4gNxC1DgrfcDnJnNMrMlZvZdrz0PqGh2fIXXJoHXWm6auxV4yVtXbkKntdy8AtQCO4CtwC+cc1X481De7HjlJrhay88y4AYzizGz3sBwb5s+O0FmZr2AImABkOOc2+Ft2gnkeOutfU70+QmiNuamNcpNCKnI7njuAf7FzBbj/5NRvdceA1wGfNn7OdHMvhCeELus1nIDgJldDNQ551a0dLAEVWu5GQE0ArlAb+B+MysMT4hdWmv5mY6/CCgBfgXMw58vCSIz6wb8Bfi2c+5A823eXw40LVmYKDcdS0y4A5D2cc6twT80BDPrB1zvbaoAPnTO7fG2vYV/3OMfgPxmXeQD20IWcBdymtwccxsnrmKDPw/KTQicJjd3AG875xqASjObCxTjv9LT/C8Ryk0QtZYf59xR4DvH9jOzefjHolajz05QmJkPfxE3wzn3qte8y8zOcc7t8IaDVHrt22j5c7INGHNK+5xgxt0VtDM3rWktZxIEupLdwZhZtvczCngIeMrbNAsYbGaJ3vjS0cAq789IB8xspHf3/V3Aa2EIvdM7TW6OtX0Jbzw2+MfYodyExGlysxW4ytuWhP/mrTX4b8Tra2a9zSwW//8gzQx13F1Fa/nxvs+SvPVrgKPOOX2vBYn3u3wOWO2ce7zZppnAsRlC7ubE73omcJc3y8hIYL+Xm1nAWDNL92a7GOu1yVk6i9y0Rt9toRTuOy+1tL7gv+q5A/+NCxXAvcC38F/JWQv8DO+BQt7+d+If27gC+Hmz9mKvbQMwrfkxWkKWmzHA/Bb6UW7CmBugG/Cy97lZBTzQrJ/rvP03AA+G+7w6y9LO/PQCyvDf5PUu0LNZP/rsBD43l+EfbrAcWOot1+Gfreo9YJ2XhwxvfwN+4+WgFChu1tc9wHpv+Wq4z62jL2eRmx7e5+sA/huGK/DfLKzvthAueuKjiIiIiEiAabiIiIiIiEiAqcgWEREREQkwFdkiIiIiIgGmIltEREREJMBUZIuIiIiIBJiKbBGRTsqbv/hjM7u2WdstZvZ2OOMSEekKNIWfiEgnZmaD8M8FXoT/Kb+fAuOdcxs+R58xzv80RhERaYWuZIuIdGLOuRXA68D3gIeBF51zG8zsbjNbaGZLzexJ72mLmNkzZlZiZivN7OFj/ZhZhZn9zMw+BSaG5WRERDqQmHAHICIiQfcjYAlQDxR7V7cnApc4546a2TP4H6/8/4GpzrkqM4sBZpvZK865VV4/lc65onCcgIhIR6MiW0Skk3PO1ZrZn4CDzrkjZnY1cBFQYmYACUC5t/vtZnYv/n8fcoEB+B85D/Cn0EYuItJxqcgWEekamrwFwIDpzrkfNN/BzPoC3wJGOOf2mdkfgPhmu9SGJFIRkU5AY7JFRLqed4EvmVl3ADPLNLNzgRSgBjhgZucA48IYo4hIh6Yr2SIiXYxzrtTMfgS8693w2AB8EyjBPzRkDbAFmBu+KEVEOjZN4SciIiIiEmAaLiIiIiIiEmAqskVEREREAkxFtoiIiIhIgKnIFhEREREJMBXZIiIiIiIBpiJbRERERCTAVGSLiIiIiASYimwRERERkQD7X7apSWcLH+LuAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import pandas as pd\n",
    "ram_prices = pd.read_csv(\"https://raw.githubusercontent.com/amueller/introduction_to_ml_with_python/master/data/ram_price.csv\")\n",
    "\n",
    "plt.semilogy(ram_prices.date, ram_prices.price)\n",
    "plt.xlabel(\"Year\")\n",
    "plt.ylabel(\"Price in $/Mbyte\");"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-12-20T18:31:56.958305Z",
     "start_time": "2020-12-20T18:31:56.948956Z"
    }
   },
   "outputs": [],
   "source": [
    "from sklearn.tree import DecisionTreeRegressor\n",
    "from sklearn.linear_model import LinearRegression\n",
    "\n",
    "data_train = ram_prices[ram_prices.date < 2000]\n",
    "data_test = ram_prices[ram_prices.date >= 2000]\n",
    "\n",
    "X_train = data_train.date.values[:, np.newaxis]\n",
    "\n",
    "y_train = np.log(data_train.price) #log-transform to get a simpler relathinship daxa x target\n",
    "\n",
    "tree = DecisionTreeRegressor().fit(X_train, y_train)\n",
    "linear_reg = LinearRegression().fit(X_train, y_train)\n",
    "\n",
    "X_all = ram_prices.date.values[:, np.newaxis]\n",
    "pred_tree = tree.predict(X_all)\n",
    "pred_lr = linear_reg.predict(X_all)\n",
    "\n",
    "price_tree = np.exp(pred_tree)\n",
    "price_lr = np.exp(pred_lr)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-12-20T18:32:23.688972Z",
     "start_time": "2020-12-20T18:32:23.259957Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7fd8792609a0>"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.semilogy(data_train.date, data_train.price, label=\"Training data\")\n",
    "plt.semilogy(data_test.date, data_test.price, label=\"Test data\")\n",
    "plt.semilogy(ram_prices.date, price_tree, label=\"Tree prediction\")\n",
    "plt.semilogy(ram_prices.date, price_lr, label=\"Linear prediction\")\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A strong drawback for tree-based regressions is that it usually do not generalize :/"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 4.0 Strengths, weaknesses and parameters "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The model complexity in tree-based models can be controlled by prunning the tree. In sklearn, we have the parameters\n",
    "max_depth, max_leaf_nodes and min_samples_leaf that are related to pre-prunning technique. Usually one of them are chose to control the model complexity."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Decision trees are very easy to explain and can deal with features of different scales. Therefore, we don't need to normalize or standardize the dataset."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A strong drawback is that tree models tend to overfitting (even with parameter control)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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