DecisionTrees.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Decision Trees\n",
    "\n",
    "We will implement decision trees for binary classification.\n",
    "\n",
    "We split a node by measuring the loss of splitting with respect to each possible feature and threshold, and split based on the feature and threshold that minimizes this loss.\n",
    "Mathematically:\n",
    "$$X_L = \\{x\\ :\\ x \\in X \\wedge  x[i] \\leq j\\}$$\n",
    "$$X_R = \\{x\\ :\\ x \\in X \\wedge  x[i] > j\\}$$\n",
    "where $x[i]$ is the $i$-th coordinate of point $x$.\n",
    "The vector of labels $y$ is split into vectors $y_L$ and $y_R$ using the same indices.\n",
    "\n",
    "The loss of splitting a training dataset into a left and right half is computed as \n",
    "$$\n",
    "\\ell(X,y,i,j) = \\frac{|y_L|}{|y|}\\ell(y_L) + \\frac{|y_R|}{|y|}\\ell(y_R) \n",
    "$$\n",
    "\n",
    "We will consider the following loss functions $\\ell$, specialized for binary classification. \n",
    "Define $\\hat p$ for a vector of labels $y$ to be $\\frac{|\\{y_j = 1 : y_j \\in y\\}|}{|y|}$, that is, the fraction of labels which are $1$.\n",
    "We have the following three loss functions.\n",
    "\n",
    "- Misclassification error:\n",
    "$$\n",
    "\\min \\{\\hat p, 1-\\hat p\\}\n",
    "$$\n",
    "- Gini coefficient:\n",
    "$$\\hat p (1 - \\hat p)$$\n",
    "- Entropy:\n",
    "$$- \\hat p \\log_2 (\\hat p) - (1 - \\hat p) \\log_2 (1 - \\hat p ) $$\n",
    "\n",
    "We do not split a node if it is pure (i.e., consists entirely of either $0$'s or $1$'s), or if a split would exceed a maximum depth hyperparameter provided to the decision tree (recall that the depth of a single-node tree is $0$).\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from numpy import linalg as LA\n",
    "import matplotlib.pyplot as plt\n",
    "import pandas as pd\n",
    "import time\n",
    "from sklearn.preprocessing import StandardScaler\n",
    "import math"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [],
   "source": [
    "class DecisionTree:\n",
    "    def __init__(self, loss):\n",
    "        self.dep = None\n",
    "        self.left, self.right, self.key = None, None, None\n",
    "        self.split_var = None\n",
    "        self.threshold = None\n",
    "        self.loss_func = loss\n",
    "        self.correct = None\n",
    "        return\n",
    "\n",
    "    def build(self, X, Y):\n",
    "        n, d = X.shape[0], X.shape[1]\n",
    "        pure = True\n",
    "        prev_y = Y[0]\n",
    "        for i in range(1, n):\n",
    "            if Y[i] != prev_y:\n",
    "                pure = False\n",
    "                break\n",
    "        if not pure:\n",
    "            x_l, x_r, y_l, y_r = np.array([[]]), np.array([[]]), np.array([]), np.array([])\n",
    "            min_loss = None\n",
    "            min_j, min_t = None, None\n",
    "            # try all variables and threshhold to split on\n",
    "            for j in range(d):\n",
    "                for i in range(n):\n",
    "                    x_ll, x_rr, y_ll, y_rr = np.array([[]]), np.array([[]]), np.array([]), np.array([])\n",
    "                    t = X[i][j]\n",
    "                    for k, row in enumerate(X):\n",
    "                        # print(row.shape)\n",
    "                        if row[j] <= t: \n",
    "                            x_ll = np.concatenate((x_ll, np.array([row])), axis=0) if len(x_ll[0]) > 0 else np.array([row])\n",
    "                            y_ll = np.append(y_ll, Y[k])\n",
    "                        else:\n",
    "                            x_rr = np.concatenate((x_rr, np.array([row])), axis=0) if len(x_rr[0]) > 0 else np.array([row])\n",
    "                            y_rr = np.append(y_rr, Y[k])\n",
    "                    # print(\"left shape {}, right shape {}\".format(x_ll.shape, x_rr.shape))\n",
    "                    loss = (len(y_ll) / n) * self.loss_func(y_ll) if len(y_ll) > 0 else 0\n",
    "                    loss += (len(y_rr) / n) * self.loss_func(y_rr) if len(y_rr) > 0 else 0\n",
    "                    if min_loss == None or loss < min_loss: \n",
    "                        x_l, x_r, y_l, y_r = x_ll, x_rr, y_ll, y_rr \n",
    "                        min_loss = loss\n",
    "                        min_j, min_t = j, t\n",
    "            count_0, count_1 = 0,0\n",
    "            for y in Y:\n",
    "                if y == 0: count_0 += 1\n",
    "                else: count_1 += 1\n",
    "            self.key = 0.0 if count_0 > count_1 else 1.0\n",
    "            self.correct = count_0 if self.key == 0 else count_1\n",
    "            if len(y_r) != 0:\n",
    "                self.left, self.right = DecisionTree(self.loss_func), DecisionTree(self.loss_func)\n",
    "                self.split_var = min_j\n",
    "                self.threshold = min_t\n",
    "                # print(\"left: {}, right: {}\".format(x_l.shape, x_r.shape))\n",
    "                # print(f\"split on {min_j} with t = {min_t}, loss value is {min_loss}\")\n",
    "                self.dep = max(self.left.build(x_l, y_l), self.right.build(x_r, y_r)) + 1\n",
    "            else:\n",
    "                self.dep = 0\n",
    "        else:\n",
    "            self.key = prev_y\n",
    "            self.correct = n\n",
    "            self.dep = 0\n",
    "        return self.dep\n",
    "    \n",
    "    def predict(self, X, depth):\n",
    "        if depth == 0 or self.dep == 0:\n",
    "            return self.key\n",
    "        elif self.dep > 0 and X[self.split_var] <= self.threshold:\n",
    "            return self.left.predict(X, depth-1)\n",
    "        elif self.dep > 0 and X[self.split_var] > self.threshold:\n",
    "            return self.right.predict(X, depth-1)\n",
    "    \n",
    "    def get_correct(self, depth):\n",
    "        if depth == 0 or self.dep == 0:\n",
    "            return self.correct\n",
    "        else:\n",
    "            return self.left.get_correct(depth-1) + self.right.get_correct(depth-1)\n",
    "\n",
    "def find_p(Y):\n",
    "    count_0, count_1 = 0,0\n",
    "    for y in Y:\n",
    "        if y == 0: count_0 += 1\n",
    "        else: count_1 += 1\n",
    "    return count_1 / len(Y)\n",
    "\n",
    "# Misclassification Error\n",
    "def misclassification(Y):\n",
    "    p = find_p(Y)\n",
    "    return min(p, 1-p)\n",
    "\n",
    "# Gini Coefficient\n",
    "def giniCoefficient(Y):\n",
    "    p = find_p(Y)\n",
    "    return p * (1-p)\n",
    "\n",
    "# Entropy\n",
    "def entropy(Y):\n",
    "    p = find_p(Y)\n",
    "    res = -1 * p * math.log(p, 2) if p != 0 else 0\n",
    "    res -= (1-p) * math.log(1-p, 2) if (1-p) != 0 else 0\n",
    "    return res"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Load data\n",
    "X_train = np.loadtxt('datasets/decision_tree data/data/X_train.csv', delimiter=\",\")\n",
    "y_train = np.loadtxt('datasets/decision_tree data/data/y_train.csv', delimiter=\",\").astype(int)\n",
    "X_test = np.loadtxt('datasets/decision_tree data/data/X_test.csv', delimiter=\",\")\n",
    "y_test = np.loadtxt('datasets/decision_tree data/data/y_test.csv', delimiter=\",\").astype(int)\n",
    "# print(X_train.shape, y_train.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Miclassification error Decision Tree\n",
    "misclassification_tree = DecisionTree(misclassification)\n",
    "misclassification_tree.build(X_train, y_train)\n",
    "misclassification_TestAccuracy = np.zeros(misclassification_tree.dep)\n",
    "misclassification_TrainAccuracy = np.zeros(misclassification_tree.dep)\n",
    "for d in range(misclassification_tree.dep):\n",
    "    misclassification_TrainAccuracy[d] = misclassification_tree.get_correct(d) / len(y_train)\n",
    "    for i, x in enumerate(X_test):\n",
    "        res = misclassification_tree.predict(x, d)\n",
    "        misclassification_TestAccuracy[d] += 1 if res == y_test[i] else 0\n",
    "misclassification_TestAccuracy /= len(X_test)\n",
    "misclassification_TrainAccuracy *= 100\n",
    "misclassification_TestAccuracy *= 100"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Gini Coefficient Decision Tree\n",
    "gini_tree = DecisionTree(giniCoefficient)\n",
    "gini_tree.build(X_train, y_train)\n",
    "gini_TestAccuracy = np.zeros(gini_tree.dep)\n",
    "gini_TrainAccuracy = np.zeros(gini_tree.dep)\n",
    "for d in range(gini_tree.dep):\n",
    "    gini_TrainAccuracy[d] = gini_tree.get_correct(d) / len(y_train)\n",
    "    for i, x in enumerate(X_test):\n",
    "        res = gini_tree.predict(x, d)\n",
    "        gini_TestAccuracy[d] += 1 if res == y_test[i] else 0\n",
    "gini_TestAccuracy /= len(X_test)\n",
    "gini_TrainAccuracy *= 100\n",
    "gini_TestAccuracy *= 100"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Entrophy Decision Tree\n",
    "entrophy_tree = DecisionTree(entropy)\n",
    "entrophy_tree.build(X_train, y_train)\n",
    "entrophy_TestAccuracy = np.zeros(entrophy_tree.dep)\n",
    "entrophy_TrainAccuracy = np.zeros(entrophy_tree.dep)\n",
    "for d in range(entrophy_tree.dep):\n",
    "    entrophy_TrainAccuracy[d] = entrophy_tree.get_correct(d) / len(y_train)\n",
    "    for i, x in enumerate(X_test):\n",
    "        res = entrophy_tree.predict(x, d)\n",
    "        entrophy_TestAccuracy[d] += 1 if res == y_test[i] else 0\n",
    "entrophy_TestAccuracy /= len(X_test)\n",
    "entrophy_TestAccuracy *= 100\n",
    "entrophy_TrainAccuracy *= 100"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f7ed9190460>"
      ]
     },
     "execution_count": 73,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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PdQHCwsJ47733uOOOOzh8+DClpaXcddddJCYmcs0113D48GFUlbvvvpsWLVpw/vnnc+mllzJnzhx7uGuCSmFJGe+tSuOF5dvYmZVP97ZN+dslA5l0UgeiIqxJZn1gwzI3EKF2vabhOVxQwvSvd/LKl9s5kFfM4E4tuGVkD87pFxf0wx/XVzYsszHGL/YdLuTlL7fz1v92kVdUysjEttw8sgendW9lTTLrKUv8xpga2bI/j+eXbWX26j2UeZTzBrXnlyO707+9Ncms7xp04lfVkChRNITqOBM6Vu86yLSlW1nwfQaR4WFcOawzN47oTqdWTQIdmvFSg0380dHRZGVl0bp1cPfwU1WysrKIjrZmbyZwVJWlKZlMW7qVr7dl07xxI24b3ZMpp3elTUxUoMMz1dRgE3/Hjh1JS0sjMzMz0KH4XXR0NB07dgx0GCYElZZ5+HhdOtOWbmNjeg7xzaJ5YGJfrhjWmZioBps+Ql6D/Zdr1KgR3bp1C3QYxgSF/TmF3Pb2ap696iTaxUZTUFzGzFW7eWH5NnZnF9CzXQyPXzqIC4d0IDIiLNDhmlpqsInfGOM7Ty9O5Zsd2Tw+bzOdWzXhlRU7yD5SzNDOLXhwYj/O7mtNMoOJJX5jQljvBz6lqNTzw+eZq9IACBOY8cvhnNK1ZVA/QwtVfr1nE5E7RWS9iGwQkbvcZa1EZKGIpLo/W/ozBmNM5fYeKuCXZ3WnRYUZrcIFRvduy9f3jWVYN2uHH6z8VuIXkQHAjcAwoBiYJyIfu8sWq+pjInIvcC/wO3/FYYw5KiOnkI/XpvPxunRW7TwIQKsmzmxxkeFhlHg8dGjR2AZPC3L+rOrpC3ytqvkAIrIUuAi4EBjlbvMasARL/Mb4TWZuEfPWp/PR2nS+2ZGNKvRNaMb/je/NxIEJ/PXTjbSNjeaqYZ15a+UuMnMLAx2y8TO/jdUjIn2BOcBwoABYDCQD16pqiwrbHVTVn1T3iMhNwE0AnTt3Pnnnzp1+idOYYJR9pJh56/cxd+1evt6WhUehV7sYzhvUnomDEujZLibQIZo6UOdj9ajqRhH5G7AQyAO+A0qrsf/zwPPgDNLmlyCNCSKH80uYv2EfH63dy4qtWZR5lO5tmnLb6J5MHNSe3vGxgQ7R1BN+bdWjqi8BLwGIyF+ANCBDRBJUNV1EEoD9/ozBmGCWU1jCwg0ZfLwuneWpmZSUKZ1bNeGms7pz3qAE+iU0swe05if8mvhFpJ2q7heRzsDFONU+3YApwGPuzzn+jMGYYHOkqJRFGzOYuzadpZszKS5zHshed0Y3zhuUwMAOzS3ZmxPydzv+WSLSGigBfqWqB0XkMWCGiFwP7AIm+zkGYxq8guIyPtu0n7lr9/LZpv0UlXqIbxbNNad14bzBCZzUqYUle+M1f1f1/GRaKVXNAsb687zGBIPCkjKWbM5k7tq9LN64n4KSMtrERHHFKZ04b3B7Tu7c0nrTmhqxnrvG1CNFpWUsTznAx+vSWfh9BnlFpbRqGsnFQzswcVACp3ZrTbgle1NLlviNCbCSMg9fbjnA3LXpzN+wj9zCUpo3bsTEgQmcNziB4d1bExFuA6MZ37HEb0wAlJZ5+HpbNnPX7mXehn0cyi8hNjqCc/rFc97gBM7s2YZGluyNn1jiN6aOlHmUldvdZL9+H1lHimkaGc64fnFMHNSesxLbEBURHugwTQiwxG+MH3k8yqpdB38YHyczt4jGjcIZ27cd5w1KYFTvdkQ3smRv6pYlfmN8TFVZs/sQc9em88m6dNIPFxIVEcbo3u04b3ACY/q0o0mk/emZwLH/fcbUUMVZq9rGRLF+Tw5z1+5l7tp09hwqIDI8jLMS23LvuX0Y2zfOpio09Yb9TzSmhp5enMo327O57uVvyCsuZWdWPhFhwohebbh7XCLj+sXRvMJY98bUF5b4jammY2et2pCeA0BEmJD8wNm0cMe3N6a+svZixlRDmUe5fUxPIip0ooqOCOPCIe1Z8fsxlvRNg2AlfmO8tHlfLve+v5bVuw4R3yyKjJwiIiPCKCrzEBsVYbNWmQbDEr8xVSgsKePZz7YwbelWmjVuxJOXD2be+n02a5VpsCzxG3MCX2/L4r7317HtwBEuHtqBByb2o1XTSC46qeMP2zw6aUAAIzSm+izxG1OJw/kl/OWTjbybvJvOrZrwxvXDGNGrbaDDMsYnLPEbU4GqMndtOn/86HsO5hfzy5HduWtsIo0jrXetCR6W+I1x7TlUwIMfrOezTfsZ2KE5r153CgM6NA90WMb4nCV+E/LKPMprK3bwxILNqMIDE/sy9fSuNhSyCVqW+E1I25iew73vr+O73YcYmdiWRycNoFOrJoEOyxi/ssRvQlJhSRn/WpzKC8u20bxxI/51xRAuGNze5q01IcESvwk5K7Yc4L7Z69iRlc/kkzty/8S+1uPWhBRL/CZkHDxSzF8+2cjMVWl0ad2Et244ldN7tgl0WMbUuSoTv4gkASOA9kABsB5YpKrZfo7NGJ9QVT78bi9/+uh7DheUcOuoHtwxtpdNgGJC1nETv4hMBe4AtgOrgM1ANHAm8DsRWQ88qKq76iBOY2pkd3Y+D85Zz5LNmQzu2JzpN5xK34RmgQ7LmIA6UYm/KXCGqhZUtlJEhgC9AEv8pt4pLfPw6ood/GNBCiLw0Pn9+PnwroSH2cNbY46b+FX13yfaUVXX+DwaY3xgw97D3DtrHev2HGZMn3Y8MmkAHVo0DnRYxtQbXj/cFZHzgQeAKOB5VX3Ob1EZUwMFxWU8tTiFF5dvp2WTSJ696iQmDkywJprGHONEdfyDVfW7CouuBU4DBPgOsMRv6o3lqZncP3s9u7LzueKUTvz+3L40b2LTHhpTmROV+G8Vp6j0B1XdB+wG/gx4gL11EZwxVck+Usyjc7/n/dV76N6mKW/feBrDe7QOdFjG1GsnquP/pYgMBv4rIsnAg8DpQBPgkTqKz5hKqSofrNnDI3M3klNQwu1jevKr0T2tiaYxXjhhHb9b1XOhW7//IfCaqr5RJ5EZcxy7s/O5/4P1LEvJ5KTOLXjs4kH0jo8NdFjGNBjHHX5QRG4WkdUi8i1O084JQEsRmS8iI+osQmNcpWUenl+2lXFPLuXbnQf504X9ee/m0y3pG1NNJ6zjV9VBIhIJfKWq7wBPi8gbONU+y+skQmOA9XsO87tZa9mwN4ez+8bxyKT+JDS3JprG1MSJEv8eEXkEaAxsKl+oqgeBe/wdmDEA+cWlPLkwhZe+2E7rmCj+c/VQJgyItyaaxtTCiRL/hcB4oARYWDfhGHPU0pRM7p+9jrSDBVx1amd+N6EPzRtbE01jautErXqKgY/qMBZjAMjKK+KRud/zwZq99GjblBm/HM6wbq0CHZYxQcOGZTb1hqoy69s9PPrx9xwpKuXOsb24dXQPoiKsiaYxvuTXxC8idwM3AAqsA67D6QfwLtAV2AFc5j43MCFsZ9YR7pu9ji+3ZJHUpSV/vXggveKstY4x/uBV4heRcCCu4vZVDccsIh1whnXup6oFIjIDuALoByxW1cdE5F7gXuB3NYzfNERbl8CeZOh2FiXtk3hx+XaeWpRCZHgYj04awFXDOhNmo2ga4zfeTMRyO/AQkIEzXAM4JfhBXh6/sYiU4JT09wK/B0a5618DlmCJP3R89hd02d+c9xLOm1FX8dyhkYzu352HL+hPfPPowMZnTAjwpsR/J9BbVbOqc2BV3SMiT+CM118ALFDVBSISp6rp7jbpItKu2lGbhmnNW+AmfQHUU8bUwjf4eeO3CfOcDt9PgF7joU3PwMZpTJA7bs/dCnYDh6t7YBFpidMktBvOtI1NReSaaux/k4gki0hyZmZmdU9v6ptv38Az+1bWlHWnUCMp1TAKieS+4ut4oWwiHDkA8++DZ0+Gp4fCvPtg21IoLQ505MYEHW9K/NuAJSLyMVBUvlBV/1nFfmcD21U1E0BE3scZ5C1DRBLc0n4CsL+ynVX1eeB5gKSkJPUiTlMPFZaUsenjZxiy5iG+8AzkxpJfMyBsB6fKRr4N60/coLO4aGJfiI2GgzshdQGkzINvXoSv/w1RzaDHGEgcDz3HQUzbQF+SMQ2eN4l/l/uKdF/e2gWcJiJNcKp6xgLJwBFgCvCY+3NOdQI29Z+qsn5PDjNX7abR6ld4kBf5Kmwoq4c/zYSDpXz4XSTrw/pQXOrh6qgI2sW69fotu8CwG51X8RGnxJ8yD1Lmw/cfAAIdk5wvgV7jIX4gWA9eY6pNVP1XmBaRPwKXA6XAapymnTHADKAzzpfDZFXNPtFxkpKSNDk52W9xGt/IyivigzV7mZm8m037crmu0UIeCn+F7A5jaDHlbcIio/nlG8m0jY3mqmGdeWvlLjJzC/nvtUknPrAqpH939G5gzypnebMO0OscSJwA3c6CyCb+v0hjGhARWaWqP/kDO27iF5GnVPUuEfkIpxXPj6jqBb4Ps3KW+Ouv0jIPy1IzmfFNGos3ZVBSpgzu2JwH2izjlE1/g94TYfIrEBHlu5PmZsCWhc6dwNbPoDgPIqKd5F9+N9Cik+/OZ0wDVZPEf7KqrhKRkZWtV9WlPo7xuCzx1z9bM/OYmZzG+9+msT+3iNZNI7nopA5MTupE7+2vOw9q+5wHl74CEdWpIaym0iLYucL5EkiZBwe3O8vb9Xe+BBInONVDYdb714Seaif++sQSf/2QV1TKx2v3MiM5jVU7DxIeJozu3ZZLT+7EmD7tiIwIgy//BQv/AP0uhEtegvA6HFRNFbK2HH0usHMFaBk0buVWCY13HhQ3blF3MRkTQDUp8X+E06pmnqqWHLOuOzAV2KGqL/s+3B+zxB84qsrK7dnMSE7jk3XpFJSU0aNtUy5L6sRFJ3WgXbMKHa6W/xMW/xH6XwwXP1+3Sb8yBYecqqCU+c7zgYJskHDocvrRu4HWPe0BsQlaNUn88Tjj7l8CZAOZQDTOGDtbgWdVtU5a5Fjir3vphwuYtSqNmavS2JmVT0xUBOcPTuDSkzsxtHOLn46Hv/Rx+PxRGDgZJk2D8Ho2/p+nDNKSnbuB1AWQsd5Z3rKb8wWQOB66nOHfailj6litqnpEpCuQgNMsM0VV830e4QlY4q8bhSVlLNqYwYzkNJanZqIKp3VvxWVJnZgwIJ4mkcdJ5ksegyV/hUFXwKTnGkZ9+qHdkDrfuRvYvgxKCyEyFnqMcr4Iep0DMdap3DRsVsdvjmv9nsPMTN7NB2v2crighPbNo7n05I5cenInOrc+QRNJVfj8L7Ds7zDkarjgmYaR9I9VnO8k//JnA7l7neUdTnZaCCWOh4TBViVkGhxL/OZHso8UM2fNHmYkp7ExPYfIiDDG94/nsqSOnN6jDeFVjY6pCp89Asv/ASddC+c/DWHejABSz6nCvnVH7wbSkgGF2ISjfQa6j4TIpoGO1JgqWeI3lJZ5WJ56gJmrdrPwe6fN/cAOzbksqSMXDO5A8yZePoxVhUUPOS14Tp4KE58MjqRfmbxMt8/APNjyGRTnQngUdBsBbfs4zw46n+bcETRk6d/B/u+h59nQaVigozE+UuPELyLnAZ+oqueEG/qRJf7a2ZaZx8xVTpv7jJwiWjWNZNKQDkxO6kjfhGbVO5gqLHgAvnoWkq6Hnz0RvEn/WKXFsOsr505gwweQuyfQEfmehMEpN8Cwm6zFUxCoTeKfDgwHZgGvqOpG/4R4fJb4qy+vqJRP1qYzc9VuvtlxkDCB0b3bMTmpI2P6xDlt7qtLFeb9Hv73HycxnPv30E0My/8Bnz0K6gHCoN8FTjVQQ5QyD76fw0866LfqfvQZh7V4apCOl/irbHOnqteISDPgSuAVEVHgFeBtVc31faimplSVb3YcZEbybj5Zl05+cRnd2zbldxP6cPHQDsQ1q8UkJ6rw6e9g5X/h1Ftgwl9DN+kDdB3hVPmUFUN4JAz/VcOtImndw7mLKb+Wi1+AIxnOsuSXnS/6yFjoMdpt8TTOWjw1cF7X8YtIG+Aa4C5gI9ATeFpVn/FbdC4r8Z9Y+uEC3v92DzOTd7MjK5+mkeGcP7g9k5M6MrRzy5+2ua8ujwc++Q0kvwTDb4NzHg3tpF9u90rYsdz5EmioSb/c8a6l+Ijb4ml+hRZPAh2GHu3/ED/I/j/UU7Wp6jkf+AXQA3gDeE1V97vDLW9U1S7+CLgiS/ywP6eQ295ezbNXnUS72GiKSstY9P1+ZiTvZnlqJh6FU7u1YnJSJ3428ARt7qvL44GP74ZVr8IZd8LZf7Q/8lBV3uKpfFykPauwFk/1W20S/+vAi6q6rJJ1Y1V1se/CrJwlfnhg9jreXLmLcwfE0y42mg/W7OFQfgkJP7S570iX1j7+g/N44KM7YPUbcOY9MPYPlvTNUcdt8eSOkpo4Hlp0DnSUIa02ib8bkK6qhe7nxkCcqu7wR6CVCeXE3/uBTykq/WmDqjCBV68bxhk9vWhzXxOeMvjwdljzJpz1Wxh9nyV9c3ylxbBrBaQsgJRPIXubs7xdvwqjpJ7SMDv4NWC1SfzJwOmqWux+jgS+VNVT/BJpJUI58e/PKeS+2etYtNGZobJRuDCuXxwPX9D/6MxVvuYpgw9uhbXvwKjfw6h7/XMeE7wOuKOkprqjpHpKoXFLZ/rMxPHQc6zz2fhVjVv1ABHlSR9AVYvd5G/qQLtm0WzLPAJAZEQYJWUeWjWJ9F/SLyuFD26GdTNh9AMw8v/8cx4T3Nr0hDa3wem3QeHhH4+Sum6GM0pq5+FHq4TaJNodZR3yJvFnisgFqvohgIhcCBzwb1imXGpGLtsOHKFvfCz/uGzID9MV+kVZKbx/I2x436nPH/Fr/5zHhJbo5tD/IuflKYM93x4dF2nhg86rZddjRkn14YxtDVVJofNFuf97Zx4JH7Yc86aqpwfwJtAeEGA38HNV3eKzKKoQylU9t0xfxbKUTJb9djStY/z4x1BWArOudzryjPuT04LHGH87nObOpTwfti1xR0mNge6jjo6SGhsX6Ch9qzgf8vZBrvvKy4DcdGdK0bx9zs/cdCg85O4Q5nwRTvmw2sm/Nh24tgKniUgMzheFddqqI2vTDvHp+n3cObaXf5N+aTG8dx1smgvn/Nm5PTemLjTvCEm/cF7F+U5fgpR5zkPiTXOdbdoPPVolFD+4/g4RUpRbSTIvf19heVHOT/cNj4SYOIiNdzrUdT0DsrY6X4Z4nM51O5b7rNTvVWNvEZkI9AeiyzsDqeqffBKBOa7H52+mRZNG3DCim/9OUloMM6fC5o9hwmNw2i3+O5cxJxLZ5GiCV4WMDUerhMrnfIiJh0S3z0C3kRAV49+YVJ2S9w+l8X2VJHO3lF5y5Kf7RzR27lhi4iGun/NQuzzBx8Q5fSBi450H3cc+49i9EnZ9fbRHddcRPrusKhO/iEwDmgCjgReBS4GVPovAVOqrrVksTz3AfT/rQ2y0n6YwLC2CGT93/rjOfRxOvck/5zGmukQgfoDzOus3cOQAbFnk/F/d8AF8+/rRZJg4wfkyaNnV++OrQn62m7QrqWYpT+x5GU7107EiY44m7vYnOYk91v1cMbFHN6/5Q+tOw5zqHT/0Dvemjn+tqg6q8DMGeF9Vz/FZFFUItTp+VeXSaV+RdjCfpf83muhGfmj7XFII717jdMCZ+A9nREZjGoKyEqckXH43kJXqLG/bx7lbaN4ZDmx2fjZu/tNkXp7QPSU/PXZUcydpl5fSj03m5e/9fafhI7Vpzln+dZcvIu2BLMCPdQ/ms037WbXzIH++aICfkn4BvHM1bF0M5z0FSdf5/hzG+Et4I2c+hG4jYPyfnbrwlPlOn4EVz4KW/XSfxq2OlsLbJB4/sTdqXPfXEwDeJP6PRKQF8DjwLc7YrS/4M6hQ5vEoj8/fTOdWTbgsqZPvT1CcD+9c5Tw0uuBZGHqt789hTF1q3QOG3+q8Pv8LLH0c8DhzCwy/Hcbcb81Dj3HCx+MiEgYsVtVDqjoL6AL0UdU/1El0IWjuunQ27cvlnnGJNAr3ceuF4iPw9uVO0p/0nCV9E3x6nu0keQl3xg3qe54l/UqcsMSvqh4R+QfORCyoahFQVBeBhaKSMg//XLCZPvGxXDC4vW8PXpQHb18BO7+Ei6bB4Ct8e3xj6gM/PhANJt5U9SwQkUtwHujW/wl6G7D3VqWxIyufF36eRJgvB14ryoU3L4PdX8NFz8Ogyb47tjH1TadhlvCr4E3ivwdoCpSKSCFO711V1WpO1mpOpLCkjH8tSuWkzi04u68PZzcqzIE3J0PaN3DJizDgEt8d2xjTIHnTcze2LgIJddO/3sm+nEL+efng2s+YVa7wMEy/BPauhktfhv6TfHNcY0yD5k0HrrMqW17ZxCymZvKKSnluyVbO7NmG03u08c1BCw7B9Ish/TuY/Cr0Pd83xzXGNHjeVPVUHJc3GhgGrALG+CWiEPTS8u1kHynmN+N7++aABQfhjYtg33q47HXoM9E3xzXGBAVvqnp+VFQUkU7A3/0WUYg5eKSYF5ZvY3z/OIZ0alH7A+Znw+sXQuYmuHw69J5Q+2MaY4JKTWbkTgMG+DqQUPWfpVs5UlzKr8/xQWn/SJaT9A+kwOVvOuOXGGPMMbyp438Gp7cuOB2+hgDf+TGmkLHvcCGvrdjBRUM6kBhXy2foRw7AaxdA9la48i2nI4sxxlTCmxJ/xdHRSoG3VfVLP8UTUp75LBWPKnePS6zdgfL2O0n/4Ha48h3oMdo3ARpjgpI3if89oFDVGflIRMJFpImq5vs3tOC2M+sI736zmyuHdaZTqyY1P1BuBrx2PhzaBVfNgO4jfRekMSYoeTMYzGKg4pB1jYFFVe0kIr1FZE2FV46I3CUirURkoYikuj9b1jT4huzJhSlEhAu3j+lZ84PkpMOrE+HwbrjmPUv6xhiveJP4o1U1r/yD+77KIqqqblbVIao6BDgZyAdmA/fiDPzWC+dL5d6aBN6QbdqXw5zv9jLl9K60axZds4Pk7HWSfs5euGYWdD3Tt0EaY4KWN4n/iIgMLf8gIicDBdU8z1hgq6ruBC4EXnOXvwZMquaxGrx/LEghJjKCW0b2qNkBDqfBKz9z6vavfR+6nO7bAI0xQc2bOv67gJkistf9nABcXs3zXAG87b6PU9V0AFVNF5FKB6YRkZuAmwA6d+5czdPVX9/uOsjC7zP49bhEWjSJrP4BDu2G185z2utf+74NRmWMqTZvOnB9IyJ9gN44A7RtUtVK5iyrnIhEAhcAv69OYKr6PPA8OFMvVmff+uyJ+Ztp3TSS686swSRmB3c6Sb/gMFz7AXQ82efxGWOCX5VVPSLyK6Cpqq5X1XVAjIjcWo1znAt8q6oZ7ucMEUlwj50A7K9u0A3Vl1sOsGJrFr8a3ZOYqGr2ndvwAUwbAflZ8PMPLOkbY2rMmzr+G1X1UPkHVT0I3FiNc1zJ0WoegA+BKe77KcCcahyrwVJV/j5/M+2bR3PVqdWsukpdBDOnQtFhKCsFT6lfYjTGhAZvEn+YVBgnWETCAa8qp0WkCTAOeL/C4seAcSKS6q57zPtwG64F32fw3e5D3Hl2r+pNoO7xwKe/44fO055SZ3YhY4ypIW/qG+YDM0RkGk72uRmY583B3U5erY9ZloXTyidklHmUfyzYTPc2TblkaMfq7bzs75C9BcIagXogPNKZUs4YY2rIm8T/O5zWNbfgPNxdALzgz6CCzZw1e0jJyOPZq04iojoTqKcuhCWPweAr4eTrYOcXNo+oMabWvGnV4wGmuS9E5EzgGeBX/g0tOBSXenhyUQr9EprxswEJ3u94cAfMugHiBsDEf0JkE+h8qt/iNMaEDq+alojIEJyHtJcD2/lxnb05gXeTd7M7u4BXrhvg/QTqJQUw4+egCpe/7iR9Y4zxkeMmfhFJxOl4dSWQBbwLiKra0I9eKigu45nFqZzStSWjEtt6v+Mnv3GmTLzyXWjV3X8BGmNC0olK/JuA5cD5qroFQETurpOogsRrX+1gf24Rz1411PsJ1Fe9Bqunw1n/Z7NnGWP84kRPGi8B9gGfi8gLIjIW5+Gu8UJOYQn/WbKVUb3bMqxbK+922rPKKe33GAOjqtXR2RhjvHbcxK+qs1X1cqAPsAS4G4gTkf+IiM3pV4UXl23jcEEJv/F2SsUjWTBjCsTEwSUvQVg12vobY0w1VNm2UFWPqOqbqnoe0BFYQwgOpVwdB/KKePGL7UwcmMCADs2r3sFTBu/fAHkZcNnr0MTLOwRjjKmBajQqB1XNVtX/quoYfwUUDJ77fCuFJWXeT6m45K+w9TP42RPQYWjV2xtjTC1UK/Gbqu05VMD0r3dy6ckd6dkupuodNs+DZY/DSdfAyVOq3t4YY2rJEr+PPb0oFYA7xvaqeuPsbfD+TZAw2CntG2NMHbDE70NbM/N479s0rjq1Mx1bVtHpqjgf3v05iDj1+o0an3h7Y4zxkWoOCm9O5MmFKURFhPGr0VVMoK4Kc++GjPVw9Uxo2bVO4jPGGLASv8+s33OYuWvT+cUZ3WgbG3XijZNfgrXvwKh7ode4ugnQGGNclvh95B8LNtO8cSNuPKuKIRbSkuHTe6HXOXDWb+smOGOMqcASvw98syObzzdncvPIHjRv3Oj4Gx454Ay+1qw9XPRfCLNfvzGm7lkdfy2pKo/P20zb2CimnN7l+BuWlcJ71zlz5l6/wDppGWMCxoqctbQ0JZOVO7K5fUxPmkSe4Hv080dh+zJnbP2EwXUXoDHGHMMSfy14PMrj8zfTsWVjrjjlBBOob5wLXzwJJ0+Fk66us/iMMaYylvhrYd6GfWzYm8PdZycSGXGcX2XWVvjgFmg/FM79e90GaIwxlbDEX0OlZR6eWLCZXu1imHRSh8o3Kj4C714DYRFOJ62IKpp5GmNMHbDEX0Pvr97Dtswj/Pqc3oRXNqWiKnx0J+zfCJe+BC061X2QxhhTCUv8NVBUWsa/FqUyqGNzxvePq3yjlc/Dupkw5gFnYhVjjKknLPHXwFv/28WeQwX83/jelU+puOt/MP8+SDwXzryn7gM0xpgTsMRfTUeKSvn351s4rXsrzuzZ5qcb5O2HmVOgeSe4aJp10jLG1DvWgauaXl2xgwN5xfz32j4/Le2XlcLM66DgENywCBq3CESIxhhzQpb4q+FQfjHTlm7l7L7tOLlLy59usPhh2PkFXPQ8xA+o8/iMMcYbVg9RDf9dto28olJ+XdkE6t/PgRXPwCk3wuDL6z44Y4zxkiV+L+3PLeSVL7dzweD29E1o9uOVmSnwwa3Q8RQY/5fABGiMMV6yxO+lf3+2hZIy5e6zj5lAvSjP6aQVEQ2TX4OIyMAEaIwxXrI6fi/szs7nrZW7uCypE13bND26QhU+vA2yUuHaD6D5cXrwGmNMPWIlfi88tSgVEeHOYydQ//o52DAbxj4E3UcGJjhjjKkmS/xVSM3IZfbqNKYM70J88+ijK3augAUPQp/z4Iw7AxegMcZUkyX+KvxjQQpNIiO4ZVSFCdRz98HMqdCqG0x6DirrvWuMMfWUJf4T+G73IeZt2McNI7rRqqn70LasxEn6Rblw+XSIbh7QGI0xprrs4e4JPLFgMy2bNOL6M7sdXbjwD7DrK7jkJWjXN3DBGWNMDVmJ/zi+2prF8tQD3DqqJ7HR7gTq62c5D3RPvQUGXhrYAI0xpob8mvhFpIWIvCcim0Rko4gMF5FWIrJQRFLdn5WMfRBYqsrj8zcR3yyaa4e7E6jv3whzbodOp8E5jwQ2QGOMqQV/l/j/BcxT1T7AYGAjcC+wWFV7AYvdz/XKZ5v28+2uQ9wxthfRjcKhMMfppBXZFCa/CuGNAh2iMcbUmN8Sv4g0A84CXgJQ1WJVPQRcCLzmbvYaMMlfMdRE+QTqXVo3YXJSR6eT1pxbIXu7k/SbJQQ6RGOMqRV/lvi7A5nAKyKyWkReFJGmQJyqpgO4P9tVtrOI3CQiySKSnJmZ6ccwf+yjtXvZtC+Xe8Yl0ig8DFY8DRs/gnF/gq5n1FkcxhjjL/5M/BHAUOA/qnoScIRqVOuo6vOqmqSqSW3btvVXjD9SUubhyYUp9ImP5fxB7WH7Mlj0MPSbBMN/VScxGGOMv/kz8acBaar6P/fzezhfBBkikgDg/tzvxxiq5b1VaezIyuc35/QmLC8d3vsFtO4JFz5rnbSMMUHDb4lfVfcBu0WkfPD6scD3wIfAFHfZFGCOv2KojsISZwL1oZ1bMDaxBcyYAiUFTietqNhAh2eMMT7j7w5ctwNvikgksA24DufLZoaIXA/sAib7OQavTP96J/tyCnny8iHIggcgbaUzzHLbSiZdMcaYBsyviV9V1wBJlawa68/zVlduYQn//nwLI3q1YfiRxbDyeRh+G/SfFOjQjDHG56znLvDSF9s5mF/CA0ke+PAO6HIGnP3HQIdljDF+EfKJP/tIMS8u385FfWLovfRWZ9C1S1+BcBvGyBgTnEI+u01bupX84mIe4SU4tAumfgyxcYEOyxhj/CakE/++w4W8tmIHz3RaSsyO+TDhb9D5tECHZYwxfhXSVT1Pf5bKaazlZ5kvwYBL4dRfBjokY4zxu5At8e84cITl36xhXpPnkJa94YKnrZOWMSYkhGyJ/+kF63m20ZM0Dit1OmlFNg10SMYYUydCssS/MT2HoRv/xuDwrXDRdGjTs+qdjDEmSIRkif+rWc9wTfhiCk+9HfqeH+hwjDGmToVc4t+4+guuynyS3S1OIfqchwMdjjHG1LmQSvyaf5BWc6/nsMTS6udvWCctY0xICp3E7/FwcPp1tCzN5JtTnqJpK5tJyxgTmkIm8euyx2m193OebvQLxo0/L9DhGGNMwIRG4t+yCJb8lVllZ9L5nDuIiggPdETGGBMwwV/JfXAnOusGtoV14cWYO/jo5I6BjsgYYwIquEv825fDy+MpLS7iFwV3cNs5g4gID+5LNsaYqgRviX/3Snj9QtAylAiS2pRx7oD4QEdljDEBF7zF3x3LUVUAwtTDr7rtIyzMxuIxxpjgTfxdR1AijSjVMEolgm5J4wMdkTHG1AtBWdXT+4FPKSr1MFR+z2lhG/na05dvnztAVMSnbH703ECHZ4wxARWUiX/5b0fz6Ccb+XSd8G1ZItGNwriwfzz3T+wb6NCMMSbggrKqp12zaGKjIij1KFERYRSVeoiNiqBdbHSgQzPGmIALyhI/wIG8Iq4+tQtXDevMWyt3kZlbGOiQjDGmXpDyli/1WVJSkiYnJwc6DGOMaVBEZJWqJh27PCireowxxhyfJX5jjAkxlviNMSbEWOI3xpgQY4nfGGNCjCV+Y4wJMQ2iOaeIZAI7a7h7G+CAD8MJJLuW+idYrgPsWuqr2lxLF1Vte+zCBpH4a0NEkitrx9oQ2bXUP8FyHWDXUl/541qsqscYY0KMJX5jjAkxoZD4nw90AD5k11L/BMt1gF1LfeXzawn6On5jjDE/FgolfmOMMRVY4jfGmBAT1IlfRCaIyGYR2SIi9wY6npoSkZdFZL+IrA90LLUhIp1E5HMR2SgiG0TkzkDHVFMiEi0iK0XkO/da/hjomGpDRMJFZLWIzA10LLUhIjtEZJ2IrBGRBj2Wu4i0EJH3RGST+zcz3GfHDtY6fhEJB1KAcUAa8A1wpap+H9DAakBEzgLygNdVdUCg46kpEUkAElT1WxGJBVYBkxrov4kATVU1T0QaAV8Ad6rq1wEOrUZE5B4gCWimqucFOp6aEpEdQJKqNvjOWyLyGrBcVV8UkUigiaoe8sWxg7nEPwzYoqrbVLUYeAe4MMAx1YiqLgOyAx1Hbalquqp+677PBTYCHQIbVc2oI8/92Mh9NchSlIh0BCYCLwY6FuMQkWbAWcBLAKpa7KukD8Gd+DsAuyt8TqOBJplgJCJdgZOA/wU4lBpzq0fWAPuBharaUK/lKeC3gCfAcfiCAgtEZJWI3BToYGqhO5AJvOJWwb0oIk19dfBgTvxSybIGWSILNiISA8wC7lLVnEDHU1OqWqaqQ4COwDARaXDVcCJyHrBfVVcFOhYfOUNVhwLnAr9yq0kboghgKPAfVT0JOAL47DllMCf+NKBThc8dgb0BisW43PrwWcCbqvp+oOPxBfcWfAkwIbCR1MgZwAVu3fg7wBgRmR7YkGpOVfe6P/cDs3GqfBuiNCCtwl3kezhfBD4RzIn/G6CXiHRzH4xcAXwY4JhCmvtA9CVgo6r+M9Dx1IaItBWRFu77xsDZwKaABlUDqvp7Ve2oql1x/kY+U9VrAhxWjYhIU7fRAG61yDlAg2wJp6r7gN0i0ttdNBbwWSOICF8dqL5R1VIRuQ2YD4QDL6vqhgCHVSMi8jYwCmgjImnAQ6r6UmCjqpEzgGuBdW7dOMB9qvpJ4EKqsQTgNbf1WBgwQ1UbdFPIIBAHzHbKF0QAb6nqvMCGVCu3A2+6BddtwHW+OnDQNuc0xhhTuWCu6jHGGFMJS/zGGBNiLPEbY0yIscRvjDEhxhK/McaEGEv8JuSIyAX1ZbRWERlV0xEx3dEbb/XFsUxoscRvQo6qfqiqjwU6Dh9oAdxa1UbGHMsSv6m3RKSrOxb5iyKyXkTeFJGzReRLEUkVkWHudsNEZIU7mNWK8t6OInKPiLzsvh/oHqOJiEwVkWfd5a+KyH/ceQK2ichId/6DjSLyaoVY8iq8v7R8nbf7H3NdE9zr+gK4uMLypu6+37jXcqG7fKqIzBGReeLML/GQu8tjQA937PnH3WUxFcZwf9PtLW3Mj6mqvexVL19AV6AUGIhTSFkFvIwzAN+FwAfuds2ACPf92cAs930YsAy4CEjGGcALYCrwrPv+VZwxasqPmXPM+Ya42+VViOtS4NXq7F9h32icUWN7ufvMAOa66/4CXOO+b4Ezn0RTN950oDXQGGcYgiT397O+wrFHAYdxxqUKA74Czgz0v6O96t/LSvymvtuuqutU1QNsABarqgLrcBIfQHNgpjgzlD0J9Adw95kKvAEsVdUvj3OOjyocM+OY83U9zj413b+Pe02p7j4VB0Q7B7jXHc5iCc6XRGd33UJVzVLVAuB94MzjxLJSVdPc86/xMn4TYoJ2rB4TNIoqvPdU+Ozh6P/fR4DPVfUid5z/JRX26YUze1l7L85R8fjHnqPi2CbRNdi/ouONkyLAJaq6+UcLRU6tZJ/jHaPi+cuOc34T4qzEb4JBc2CP+35q+UIRaQ78C2cmo9YicmktzpEhIn1FJAyn6qimNgHdRKSH+/nKCuvmA7eX18uLyEkV1o0TkVbuSKCTgC+BXCC2FrGYEGWJ3wSDvwN/FZEvcUZiLfck8JyqpgDXA4+JSLsanuNeYC7wGU59e42oaiFwE/Cx+3B3Z4XVj+BM4bjWrbZ6pMK6L3CqrNbgPMNIVtUs4Ev3ofXjGOMlG53TmHpORKbiTCB+W6BjMcHBSvzGGBNirMRvjDEhxkr8xhgTYizxG2NMiLHEb4wxIcYSvzHGhBhL/MYYE2L+Hx9sbcJN4ljnAAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(1)\n",
    "plt.plot(range(misclassification_tree.dep), misclassification_TrainAccuracy, '*-', label=\"Train\")\n",
    "plt.plot(range(misclassification_tree.dep), misclassification_TestAccuracy, '.-', label=\"Test\")\n",
    "plt.title(\"Misclassification Error Decision Tree\")\n",
    "plt.xlabel(\"maximum depth\")\n",
    "plt.ylabel(\"Accuracy (in %)\")\n",
    "plt.legend()\n",
    "\n",
    "plt.figure(2)\n",
    "plt.plot(range(gini_tree.dep), gini_TrainAccuracy, '*-',  label=\"Train\")\n",
    "plt.plot(range(gini_tree.dep), gini_TestAccuracy, '.-', label=\"Test\")\n",
    "plt.title(\"Gini Coefficient Decision Tree\")\n",
    "plt.xlabel(\"maximum depth\")\n",
    "plt.ylabel(\"Accuracy (in %)\")\n",
    "plt.legend()\n",
    "\n",
    "plt.figure(3)\n",
    "plt.plot(range(entrophy_tree.dep), entrophy_TrainAccuracy, '*-', label=\"Train\")\n",
    "plt.plot(range(entrophy_tree.dep), entrophy_TestAccuracy, '.-', label=\"Test\")\n",
    "plt.title(\"Entrophy Decision Tree\")\n",
    "plt.xlabel(\"maximum depth\")\n",
    "plt.ylabel(\"Accuracy (in %)\")\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see that the Entrophy decision tree has the best testing accuracy with the smallest depth of the decision tree among all three loss function, so it performs the best. The Misclassification decision tree has the worst testing accuracy with the largest depth of the decision tree, so it performs the worst. As the maximum depth increases, the training accuracy increases because we divide the training sets into more subsets, so the number of correct labels it predicts increase. It is reasonable to see the training set accuracy reaches about 100% at the end. The testing accuracy reaches its maximum at around 2 or 3, and gradually decreases afterwards. This is because at about level 2 or 3, the decision tree only has the general pattern of the training set and thus could be right when applying to the testing set. But once we go deeper, the decision tree includes more details of the training set, which could be very different from the testing set, so the number of correct labels we predict decreases. \n",
    "\n",
    "Overall, we have the testing set accuracy above 50% for all cases, so we conclude that the features of the decision tree are correctly labeled."
   ]
  }
 ],
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