notebooks/L04demo_fundamentals.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# CPSC 340: Fundamentals of Learning (demo)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "from sklearn import datasets\n",
    "from sklearn.tree import DecisionTreeClassifier"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### The handwritten digits data set\n",
    "\n",
    "Load the handwritten digits data set and display one example:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "n= 1797\n",
      "d= 64\n"
     ]
    }
   ],
   "source": [
    "digits = datasets.load_digits()\n",
    "X, y = digits['data'], digits['target']\n",
    "n, d = X.shape\n",
    "print(\"n=\",n)\n",
    "print(\"d=\",d)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAPgAAAEICAYAAAByNDmmAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDIuMi4zLCBodHRwOi8vbWF0cGxvdGxpYi5vcmcvIxREBQAADWlJREFUeJzt3XusZeVdxvHv43ATmJEgYJAh0FYYQ5tQGpymQWtlUKggNFQSUGpsmhCd0ABKKm3QoImJ/gGUBKmZUGqVmy2XQBosEi5pSSxyLWWY4RqUU0oHMnIbigj8/OPsMVM8Z846s9e+nJfvJ9lhX9Ze77MzeVhrr7P2elNVSGrTz0w6gKTRseBSwyy41DALLjXMgksNs+BSwyz4EpLkgiRXbuf19Uk+sch1/lqSx4YOp6lkwadIkte2ub2T5CfbPP79hd5fVR+sqrsWM2ZVfbeqVu1w6I6SrEmyMcnrSe5MctCox5QFnypVtefWG/CfwO9s89xVk863o5LsA9wA/DmwN3Af8M8TDfUeYcGXnl2S/GOSVwe75EdufSHJM0mOGdxfneS+JK8k+XGSi+ZaWZJPJJnZ5vGfJfnhYP2PJVkzz/uOT/LgYP3PJrlgO5lPBtZX1Ter6g3gAuDwJL+8+I+vxbDgS8+JwLXAXsDNwKXzLHcJcElVrQA+AHxjoRUnWQWcCfxKVS0HjgWemWfxLcAfDHIcD/xxkk/Ns+wHge9vfVBVW4CnBs9rhCz40nN3Vd1SVW8D/wQcPs9y/wP8UpJ9quq1qvpeh3W/DewKHJZk56p6pqqemmvBqrqrqn5QVe9U1cPANcCvz7PePYGX3/Xcy8DyDpk0BAu+9Dy/zf3Xgd2S7DTHcp8DDgU2Jrk3yQkLrbiqngTOZnYXelOSa5P84lzLJvno4GDZC0leBv4I2GeeVb8GrHjXcyuAVxfKpOFY8EZV1RNVdRqwH/C3wHVJ9ujwvqur6leBg4AavHcuVzP7FeHAqvo54O+BzLPserbZ0xjk+MDgeY2QBW9UktOT7FtV7wAvDZ5+e4H3rEpydJJdgTeAn2znPcuBzVX1RpLVwO9tZ9U3Ah9K8ukkuwF/ATxcVRsX85m0eBa8XccB65O8xuwBt1MHR7C3Z1fgb4AXmf0qsB/wpXmWXQv8VZJXmS3svAfxquoF4NPAXwP/BXwUOLX7R9GOihd8kNrlFlxqmAWXGmbBpYZZcKlhc50gMbQkTR65O/TQQ8c63rJly8Y21ssvv/tEs9F57rnnxjZWy6pqvvMO/s9IjqK3WvDbb799rOOtWPHuk79G59Zbbx3bWOeff/7YxmpZl4K7iy41zIJLDbPgUsMsuNQwCy41zIJLDbPgUsMsuNQwCy41rFPBkxw3uITuk0nOG3UoSf1YsOBJlgF/B3wSOAw4Lclhow4maXhdtuCrgSer6umqepPZa3KfNNpYkvrQpeAHAM9u83hm8NxPSXLGYCaN+/oKJ2k4XX4uOtcvVv7fr8Wqah2wDtr9NZm01HTZgs8AB27zeCXgD3qlJaBLwe8FDknyviS7MHu525tHG0tSHxbcRa+qt5KcCdwKLAOuqCpnpJCWgE6XbKqqW4BbRpxFUs88k01qmAWXGmbBpYZZcKlhFlxqmAWXGmbBpYYt+ZlNTj755HENxfXXXz+2sVp2xx13jG2sNWvWjG2scXNmE+k9zoJLDbPgUsMsuNQwCy41zIJLDbPgUsMsuNQwCy41zIJLDesys8kVSTYleWQcgST1p8sW/B+A40acQ9IILFjwqvoOsHkMWST1rNNVVbtIcgZwRl/rkzS83gru1EXS9PEoutQwCy41rMufya4B/g1YlWQmyedGH0tSH7rMTXbaOIJI6p+76FLDLLjUMAsuNcyCSw2z4FLDLLjUMAsuNay3c9HVv3PPPXdsY23ePL4fDF522WVjG+uQQw4Z21gATzzxxFjHW4hbcKlhFlxqmAWXGmbBpYZZcKlhFlxqmAWXGmbBpYZZcKlhFlxqWJdrsh2Y5M4kG5KsT3LWOIJJGl6Xc9HfAv60qh5Ishy4P8ltVfXoiLNJGlKXqYt+VFUPDO6/CmwADhh1MEnDW9SvyZIcDBwB3DPHa05dJE2ZzgVPsidwPXB2Vb3y7tedukiaPp2OoifZmdlyX1VVN4w2kqS+dDmKHuCrwIaqumj0kST1pcsW/CjgM8DRSR4a3H57xLkk9aDL1EV3AxlDFkk980w2qWEWXGqYBZcaZsGlhllwqWEWXGqYBZcaZsGlhi35ucmOOeaYsY31+OOPj20sgAsvvHCs47XonHPOGet4a9euHet4C3ELLjXMgksNs+BSwyy41DALLjXMgksNs+BSwyy41DALLjWsy0UXd0vy70m+P5i66C/HEUzS8LqcqvrfwNFV9drg8sl3J/mXqvreiLNJGlKXiy4W8Nrg4c6DmxMbSEtA14kPliV5CNgE3FZVc05dlOS+JPf1HVLSjulU8Kp6u6o+DKwEVif50BzLrKuqI6vqyL5DStoxizqKXlUvAXcBx40kjaRedTmKvm+SvQb3fxY4Btg46mCShtflKPr+wNeTLGP2fwjfqKpvjTaWpD50OYr+MLNzgktaYjyTTWqYBZcaZsGlhllwqWEWXGqYBZcaZsGlhllwqWFLfuqicZqZmZl0BGlR3IJLDbPgUsMsuNQwCy41zIJLDbPgUsMsuNQwCy41zIJLDbPgUsM6F3ww+cGDSbzgorRELGYLfhawYVRBJPWv69RFK4HjgctHG0dSn7puwb8MfAF4Z74FnJtMmj5dZjY5AdhUVfdvbznnJpOmT5ct+FHAiUmeAa4Fjk5y5UhTSerFggWvqi9W1cqqOhg4Fbijqk4feTJJQ/Pv4FLDFnXJpqq6i9npgyUtAW7BpYZZcKlhFlxqmAWXGmbBpYZZcKlhFlxq2JKfuuipp54a21gnnXTS2MYC2Hvvvcc21jg/28UXXzy2sc4555yxjTWN3IJLDbPgUsMsuNQwCy41zIJLDbPgUsMsuNQwCy41zIJLDbPgUsM6nao6uKLqq8DbwFteGllaGhZzLvpvVNWLI0siqXfuoksN61rwAv41yf1JzphrAacukqZP1130o6rquST7Abcl2VhV39l2gapaB6wDSFI955S0AzptwavqucF/NwE3AqtHGUpSP7pMPrhHkuVb7wO/BTwy6mCShtdlF/0XgBuTbF3+6qr69khTSerFggWvqqeBw8eQRVLP/DOZ1DALLjXMgksNs+BSwyy41DALLjXMgksNS1X/p423ei76Sy+9NNbxtmzZMraxxjlN0iOPjO9EyGOPPXZsYwFs3rx5bGNVVRZaxi241DALLjXMgksNs+BSwyy41DALLjXMgksNs+BSwyy41DALLjWsU8GT7JXkuiQbk2xI8rFRB5M0vK7XRb8E+HZV/W6SXYDdR5hJUk8WLHiSFcDHgT8EqKo3gTdHG0tSH7rsor8feAH4WpIHk1w+uD76T3HqImn6dCn4TsBHgK9U1RHAFuC8dy9UVeuq6kinFpamR5eCzwAzVXXP4PF1zBZe0pRbsOBV9TzwbJJVg6fWAI+ONJWkXnQ9iv554KrBEfSngc+OLpKkvnQqeFU9BPjdWlpiPJNNapgFlxpmwaWGWXCpYRZcapgFlxpmwaWGWXCpYV3PZBNw6aWXjnW8U045ZWxj3XTTTWMba+3atWMb673OLbjUMAsuNcyCSw2z4FLDLLjUMAsuNcyCSw2z4FLDLLjUsAULnmRVkoe2ub2S5OxxhJM0nAVPVa2qx4APAyRZBvwQuHHEuST1YLG76GuAp6rqP0YRRlK/Fvtjk1OBa+Z6IckZwBlDJ5LUm85b8ME10U8EvjnX605dJE2fxeyifxJ4oKp+PKowkvq1mIKfxjy755KmU6eCJ9kd+E3ghtHGkdSnrlMXvQ78/IizSOqZZ7JJDbPgUsMsuNQwCy41zIJLDbPgUsMsuNQwCy41LFXV/0qTF4DF/qR0H+DF3sNMh1Y/m59rcg6qqn0XWmgkBd8RSe5r9ZdorX42P9f0cxddapgFlxo2TQVfN+kAI9TqZ/NzTbmp+Q4uqX/TtAWX1DMLLjVsKgqe5LgkjyV5Msl5k87ThyQHJrkzyYYk65OcNelMfUqyLMmDSb416Sx9SrJXkuuSbBz8231s0pmGMfHv4IPJFB5n9pJQM8C9wGlV9ehEgw0pyf7A/lX1QJLlwP3Ap5b659oqyZ8ARwIrquqESefpS5KvA9+tqssHVxLevapemnSuHTUNW/DVwJNV9XRVvQlcC5w04UxDq6ofVdUDg/uvAhuAAyabqh9JVgLHA5dPOkufkqwAPg58FaCq3lzK5YbpKPgBwLPbPJ6hkSJsleRg4Ajgnskm6c2XgS8A70w6SM/eD7wAfG3w9ePyJHtMOtQwpqHgmeO5Zv52l2RP4Hrg7Kp6ZdJ5hpXkBGBTVd0/6SwjsBPwEeArVXUEsAVY0seEpqHgM8CB2zxeCTw3oSy9SrIzs+W+qqpaueT0UcCJSZ5h9uvU0UmunGyk3swAM1W1dU/rOmYLv2RNQ8HvBQ5J8r7BQY1TgZsnnGloScLsd7kNVXXRpPP0paq+WFUrq+pgZv+t7qiq0yccqxdV9TzwbJJVg6fWAEv6oOhiJx/sXVW9leRM4FZgGXBFVa2fcKw+HAV8BvhBkocGz32pqm6ZYCYt7PPAVYONzdPAZyecZygT/zOZpNGZhl10SSNiwaWGWXCpYRZcapgFlxpmwaWGWXCpYf8LRyRysjvEQCYAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "idx = np.random.randint(0, n) \n",
    "plt.imshow(digits['images'][idx], cmap='Greys_r')\n",
    "plt.title('This is a %d' % digits['target'][idx]);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Some EDA on feature and target values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(y);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(X.flatten());"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Decision stump (depth=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "stump = DecisionTreeClassifier(max_depth=1)\n",
    "stump.fit(X,y);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "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 2.40.1 (20161225.0304)\n",
       " -->\n",
       "<!-- Title: Tree Pages: 1 -->\n",
       "<svg width=\"588pt\" height=\"165pt\"\n",
       " viewBox=\"0.00 0.00 588.00 165.00\" 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(4 161)\">\n",
       "<title>Tree</title>\n",
       "<polygon fill=\"#ffffff\" stroke=\"transparent\" points=\"-4,4 -4,-161 584,-161 584,4 -4,4\"/>\n",
       "<!-- 0 -->\n",
       "<g id=\"node1\" class=\"node\">\n",
       "<title>0</title>\n",
       "<polygon fill=\"none\" stroke=\"#000000\" points=\"437,-157 93,-157 93,-89 437,-89 437,-157\"/>\n",
       "<text text-anchor=\"middle\" x=\"265\" y=\"-141.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">X[36] &lt;= 0.5</text>\n",
       "<text text-anchor=\"middle\" x=\"265\" y=\"-126.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 1797</text>\n",
       "<text text-anchor=\"middle\" x=\"265\" y=\"-111.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">value = [178, 182, 177, 183, 181, 182, 181, 179, 174, 180]</text>\n",
       "<text text-anchor=\"middle\" x=\"265\" y=\"-96.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">class = 3</text>\n",
       "</g>\n",
       "<!-- 1 -->\n",
       "<g id=\"node2\" class=\"node\">\n",
       "<title>1</title>\n",
       "<polygon fill=\"none\" stroke=\"#000000\" points=\"232,-53 0,-53 0,0 232,0 232,-53\"/>\n",
       "<text text-anchor=\"middle\" x=\"116\" y=\"-37.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 275</text>\n",
       "<text text-anchor=\"middle\" x=\"116\" y=\"-22.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">value = [174, 0, 4, 1, 6, 25, 5, 0, 3, 57]</text>\n",
       "<text text-anchor=\"middle\" x=\"116\" y=\"-7.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">class = 0</text>\n",
       "</g>\n",
       "<!-- 0&#45;&gt;1 -->\n",
       "<g id=\"edge1\" class=\"edge\">\n",
       "<title>0&#45;&gt;1</title>\n",
       "<path fill=\"none\" stroke=\"#000000\" d=\"M212.4682,-88.9777C197.3397,-79.1798 180.884,-68.5222 165.9186,-58.8298\"/>\n",
       "<polygon fill=\"#000000\" stroke=\"#000000\" points=\"167.5968,-55.7468 157.3008,-53.2485 163.7916,-61.6222 167.5968,-55.7468\"/>\n",
       "<text text-anchor=\"middle\" x=\"162.5288\" y=\"-73.9957\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">True</text>\n",
       "</g>\n",
       "<!-- 2 -->\n",
       "<g id=\"node3\" class=\"node\">\n",
       "<title>2</title>\n",
       "<polygon fill=\"none\" stroke=\"#000000\" points=\"580,-53 250,-53 250,0 580,0 580,-53\"/>\n",
       "<text text-anchor=\"middle\" x=\"415\" y=\"-37.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 1522</text>\n",
       "<text text-anchor=\"middle\" x=\"415\" y=\"-22.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">value = [4, 182, 173, 182, 175, 157, 176, 179, 171, 123]</text>\n",
       "<text text-anchor=\"middle\" x=\"415\" y=\"-7.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">class = 1</text>\n",
       "</g>\n",
       "<!-- 0&#45;&gt;2 -->\n",
       "<g id=\"edge2\" class=\"edge\">\n",
       "<title>0&#45;&gt;2</title>\n",
       "<path fill=\"none\" stroke=\"#000000\" d=\"M317.8844,-88.9777C333.1144,-79.1798 349.6806,-68.5222 364.7464,-58.8298\"/>\n",
       "<polygon fill=\"#000000\" stroke=\"#000000\" points=\"366.9057,-61.6024 373.4221,-53.2485 363.1184,-55.7154 366.9057,-61.6024\"/>\n",
       "<text text-anchor=\"middle\" x=\"368.1195\" y=\"-73.9797\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">False</text>\n",
       "</g>\n",
       "</g>\n",
       "</svg>\n"
      ],
      "text/plain": [
       "<graphviz.files.Source at 0x1a1b70d9b0>"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.tree import export_graphviz\n",
    "import graphviz # requires `conda install graphviz` and `pip install graphviz`\n",
    "\n",
    "graphviz.Source(export_graphviz(stump, out_file=None, class_names=digits.target_names.astype(str), impurity=False))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Error rate: 0.80189204229271\n"
     ]
    }
   ],
   "source": [
    "yhat = stump.predict(X)\n",
    "print(\"Error rate:\", np.sum(y!=yhat)/n) # or np.mean(y!=yhat)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "(Random guessing would get us an error rate of 0.9.)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Decision tree (depth=2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "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 2.40.1 (20161225.0304)\n",
       " -->\n",
       "<!-- Title: Tree Pages: 1 -->\n",
       "<svg width=\"1089pt\" height=\"269pt\"\n",
       " viewBox=\"0.00 0.00 1088.50 269.00\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n",
       "<g id=\"graph0\" class=\"graph\" transform=\"scale(1 1) rotate(0) translate(4 265)\">\n",
       "<title>Tree</title>\n",
       "<polygon fill=\"#ffffff\" stroke=\"transparent\" points=\"-4,4 -4,-265 1084.5,-265 1084.5,4 -4,4\"/>\n",
       "<!-- 0 -->\n",
       "<g id=\"node1\" class=\"node\">\n",
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     "execution_count": 12,
     "metadata": {},
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   ],
   "source": [
    "tree = DecisionTreeClassifier(max_depth=2)\n",
    "tree.fit(X,y)\n",
    "\n",
    "graphviz.Source(export_graphviz(tree, out_file=None, class_names=digits.target_names.astype(str), impurity=False))"
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  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "scrolled": true
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   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Error rate: 0.6811352253756261\n"
     ]
    }
   ],
   "source": [
    "yhat = tree.predict(X)\n",
    "print(\"Error rate:\", np.sum(y!=yhat)/n) # or np.mean(y!=yhat)"
   ]
  },
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   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
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      ],
      "text/plain": [
       "<graphviz.files.Source at 0x1a1b4a6198>"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tree = DecisionTreeClassifier(max_depth=100)\n",
    "tree.fit(X,y)\n",
    "yhat = tree.predict(X)\n",
    "print(\"Error rate:\", np.sum(y!=yhat)/n) # or np.mean(y!=yhat)\n",
    "graphviz.Source(export_graphviz(tree, out_file=None, class_names=digits.target_names.astype(str), impurity=False))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### How does error rate change vs. depth?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "errors = []\n",
    "depths = range(1,20)\n",
    "for max_depth in depths:\n",
    "    tree = DecisionTreeClassifier(max_depth=max_depth)\n",
    "    tree.fit(X,y)\n",
    "    yhat = tree.predict(X)\n",
    "    errors.append(np.mean(y!=yhat))\n",
    "plt.plot(depths, errors)\n",
    "plt.xlabel(\"Max depth\")\n",
    "plt.ylabel(\"Classification error\");"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "errors[-1]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Overfitting"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- With this decision tree, \"training accuracy\" is 1.\n",
    "- It perfectly labels the data we used to make the tree.\n",
    "- We are now given features for 100 new digits.\n",
    "- What is the \"testing accuracy\" on the new data?\n",
    "- How does it do on data not used to make the tree?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Training error, 0.0\n"
     ]
    }
   ],
   "source": [
    "from sklearn.model_selection import train_test_split\n",
    "\n",
    "Xtrain, Xtest, ytrain, ytest = train_test_split(X,y,test_size=0.2)\n",
    "\n",
    "tree = DecisionTreeClassifier(max_depth=20)\n",
    "tree.fit(Xtrain,ytrain)\n",
    "yhat = tree.predict(Xtrain)\n",
    "train_err = np.mean(ytrain!=yhat)\n",
    "print(\"Training error,\", train_err)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Test error, 0.16111111111111112\n"
     ]
    }
   ],
   "source": [
    "yhat = tree.predict(Xtest)\n",
    "train_err = np.mean(ytest!=yhat)\n",
    "print(\"Test error,\", train_err)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- Overfitting: lower accuracy on new data.\n",
    "- Our rules got too specific to our exact training dataset.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Training vs. test error"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "train_errors = []\n",
    "test_errors = []\n",
    "for max_depth in depths:\n",
    "    tree = DecisionTreeClassifier(max_depth=max_depth)\n",
    "    tree.fit(Xtrain,ytrain)\n",
    "    train_errors.append(np.mean(ytrain!=tree.predict(Xtrain)))\n",
    "    test_errors.append(np.mean(ytest!=tree.predict(Xtest)))\n",
    "plt.plot(depths, train_errors, label=\"train\")\n",
    "plt.plot(depths, test_errors, label=\"test\")\n",
    "plt.xlabel(\"Max depth\")\n",
    "plt.ylabel(\"Classification error\")\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}