bootstrap_aggregating.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      ".. _digits_dataset:\n",
      "\n",
      "Optical recognition of handwritten digits dataset\n",
      "--------------------------------------------------\n",
      "\n",
      "**Data Set Characteristics:**\n",
      "\n",
      "    :Number of Instances: 5620\n",
      "    :Number of Attributes: 64\n",
      "    :Attribute Information: 8x8 image of integer pixels in the range 0..16.\n",
      "    :Missing Attribute Values: None\n",
      "    :Creator: E. Alpaydin (alpaydin '@' boun.edu.tr)\n",
      "    :Date: July; 1998\n",
      "\n",
      "This is a copy of the test set of the UCI ML hand-written digits datasets\n",
      "https://archive.ics.uci.edu/ml/datasets/Optical+Recognition+of+Handwritten+Digits\n",
      "\n",
      "The data set contains images of hand-written digits: 10 classes where\n",
      "each class refers to a digit.\n",
      "\n",
      "Preprocessing programs made available by NIST were used to extract\n",
      "normalized bitmaps of handwritten digits from a preprinted form. From a\n",
      "total of 43 people, 30 contributed to the training set and different 13\n",
      "to the test set. 32x32 bitmaps are divided into nonoverlapping blocks of\n",
      "4x4 and the number of on pixels are counted in each block. This generates\n",
      "an input matrix of 8x8 where each element is an integer in the range\n",
      "0..16. This reduces dimensionality and gives invariance to small\n",
      "distortions.\n",
      "\n",
      "For info on NIST preprocessing routines, see M. D. Garris, J. L. Blue, G.\n",
      "T. Candela, D. L. Dimmick, J. Geist, P. J. Grother, S. A. Janet, and C.\n",
      "L. Wilson, NIST Form-Based Handprint Recognition System, NISTIR 5469,\n",
      "1994.\n",
      "\n",
      ".. topic:: References\n",
      "\n",
      "  - C. Kaynak (1995) Methods of Combining Multiple Classifiers and Their\n",
      "    Applications to Handwritten Digit Recognition, MSc Thesis, Institute of\n",
      "    Graduate Studies in Science and Engineering, Bogazici University.\n",
      "  - E. Alpaydin, C. Kaynak (1998) Cascading Classifiers, Kybernetika.\n",
      "  - Ken Tang and Ponnuthurai N. Suganthan and Xi Yao and A. Kai Qin.\n",
      "    Linear dimensionalityreduction using relevance weighted LDA. School of\n",
      "    Electrical and Electronic Engineering Nanyang Technological University.\n",
      "    2005.\n",
      "  - Claudio Gentile. A New Approximate Maximal Margin Classification\n",
      "    Algorithm. NIPS. 2000.\n"
     ]
    }
   ],
   "source": [
    "from sklearn import datasets\n",
    "import seaborn as sns\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "\n",
    "dataset = datasets.load_digits()\n",
    "\n",
    "X = dataset['data']\n",
    "y = dataset['target']\n",
    "print(dataset['DESCR'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(1797, 8, 8)\n",
      "(1797, 64)\n"
     ]
    }
   ],
   "source": [
    "print(dataset.images.shape)\n",
    "print(X.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.8341558038485413"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.model_selection import cross_val_score\n",
    "from sklearn.tree import DecisionTreeClassifier\n",
    "\n",
    "cv = 10 # number of folds\n",
    "\n",
    "# a single tree\n",
    "dt_classifier = DecisionTreeClassifier()\n",
    "(cross_val_score(dt_classifier, X, y, cv=cv)).mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9231750465549349"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.ensemble import BaggingClassifier\n",
    "\n",
    "# ensemble\n",
    "bagging = BaggingClassifier(dt_classifier, n_estimators=100)\n",
    "(cross_val_score(bagging, X, y, cv=cv)).mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "8"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "d = X.shape[1]\n",
    "n_features = int(d ** 0.5)\n",
    "n_features"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9254469273743015"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bagging = BaggingClassifier(dt_classifier, n_estimators=100, max_features=n_features)\n",
    "(cross_val_score(bagging, X, y, cv=cv)).mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9521353196772191"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# selection of random features when creating each vertex of a tree (bagging on randomized trees)\n",
    "\n",
    "dt_classifier = DecisionTreeClassifier(max_features=n_features)\n",
    "bagging = BaggingClassifier(dt_classifier, n_estimators=100)\n",
    "\n",
    "(cross_val_score(bagging, X, y, cv=cv)).mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9454531346989448"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# comparison with random forest\n",
    "\n",
    "from sklearn.ensemble import RandomForestClassifier\n",
    "\n",
    "rf_classifier = RandomForestClassifier()\n",
    "bagging = BaggingClassifier(rf_classifier)\n",
    "\n",
    "(cross_val_score(bagging, X, y, cv=cv)).mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "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": [
    "import numpy as np\n",
    "\n",
    "# dependence on the number of trees\n",
    "\n",
    "n_estimators = np.arange(5, 101, 10)\n",
    "est_scores = []\n",
    "\n",
    "for n in n_estimators:\n",
    "    rf_classifier = RandomForestClassifier(n_estimators = n, max_features = n_features)\n",
    "    est_scores.append(cross_val_score(rf_classifier, X, y, cv = cv).mean())\n",
    "    \n",
    "plt.plot(n_estimators, est_scores)\n",
    "plt.xlabel('Trees')\n",
    "plt.ylabel('Accuracy')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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x48Zkl5EwL2yr59M/3cS0saP46YolTBpdkOySRCQNmNkmd18UZVtd6T0C/Mebh/jMqteZP7mEn3xyCWOL8pJdkohkIAVGinu5uoH7n3yNd80o44f3vJvSgtxklyQiGUqBkcLcnW+s2cHUskJ+/MnFjMrTfy4RSR7NVpvCfl1zhDf2n+BPrpujsBCRpFNgpLDvPF/DpNIC7nzXGRe5i4gMOwVGitqw5xiv7D7GyvfOIj9Hd8sTkeRTYKSo7zxfw7iiPJYvnp7sUkREAAVGSnqz9gS/2tHAimsrKcxT60JEUoMCIwU9/EINpQU5uq+FiKQUBUaK2X64iWe31HHPNZWU6JoLEUkhCowU890XayjKy+YTV89MdikiIm+jwEghe4608G9vHORjV86gTNN/iEiKUWCkkEde3EludhYrrq1MdikiImdQYKSIAydaefq1Wu569zQmlGgmWhFJPQqMFPHor3ZiBiuvm53sUkRE+qXASAH1TW2s2rCfOy6vYOqYwmSXIyLSLwVGCvjBy7vpinXzJ9erdSEiqUuBkWTHWzr46W/28sFLpzBzfFGyyxERGZACI8n+4b92c6ojxr03zEl2KSIig1JgJNHJtk5+9N97uOXCicybWJLsckREBqXASKIn1u/lZFsX990wN9mliIiclQIjSU51dPHDX+/munnlXFwxOtnliIiclQIjSZ58dT/HWjq4/30auxCRkUGBkQTtXTEee2knSyrHsmjm2GSXIyISiQIjCX6xqZa6k+3c/z6NXYjIyKHAGGadsW4eeXEnl04bwzVzxiW7HBGRyBQYw2z15oPUHm/l/hvmYGbJLkdEJDIFxjCKdTvffbGG+ZNKuHHBhGSXIyIyJAkNDDNbZmbbzazGzB7o5/npZvaCmb1uZm+a2W3h+plm1mpmm8Of7yWyzuHyn789zM6GFu57n1oXIjLy5CTqhc0sG3gYuBmoBTaY2Wp3r4rb7EvAU+7+iJktBJ4BZobP7XT3yxJVXzKs2rCP6WNHcetFk5NdiojIkCWyhbEYqHH3Xe7eAawCbu+zjQOl4ePRwMEE1pNUja2drN95lFsvnkR2lloXIjLyJDIwpgL745Zrw3XxHgQ+Zma1BK2L++Oeqwy7qn5lZtf29wZmttLMNprZxoaGhvNY+vn34vZ6urqdpQsnJbsUEZFzksjA6O+f0d5neTnwI3evAG4DnjCzLOAQMN3dLwf+HPhHMyvtsy/u/pi7L3L3ReXl5ee5/PNrzZY6xhfnc/m0MckuRUTknJw1MMzsPjMrO4fXrgWmxS1XcGaX0wrgKQB3Xw8UAOPdvd3dj4brNwE7gXnnUENKaOuM8eL2em5eOJEsdUeJyAgVpYUxiWDA+qnwrKeo33gbgLlmVmlmecBdwOo+2+wDbgQwswUEgdFgZuXhoDlmNguYC+yK+L4pZ/3Oo7R0xFh64cRklyIics7OGhju/iWCL+wfAvcA1Wb212Y26P1E3b0LuA94FthKcDbUFjN7yMw+FG72OeCPzewN4EngHnd34L3Am+H6XwCfdvdj5/QXpoA1VYcpysvm6tm6sltERq5Ip9W6u5vZYeAw0AWUAb8ws7Xu/heD7PcMwWB2/Lovxz2uAq7pZ7+ngacj/QUpLtbtrK2q4/r5E8jPyU52OSIi5+ysgWFmfwrcDRwBfgD8D3fvDAenq4EBA0Ng8/7jHGnuYOlCdUeJyMgWpYUxHrjD3ffGr3T3bjP7QGLKSh9rqurIzTZumK+pQERkZIsy6P0M0Dt+YGYlZrYEwN23JqqwdODurNlSx5WzxlFakJvsckRE3pEogfEI0By33BKuk7PY2dDM7iMt6o4SkbQQJTAsPHMJCLqiSOAcVOnk2S11ANykwBCRNBAlMHaZ2Z+aWW748xlG8DURw2lNVR2XVoxm8ujCZJciIvKORQmMTwNXAwcIrt5eAqxMZFHp4HBjG2/sP8HSCzV3lIikh7N2Lbl7PcFV2jIEa7cG3VEavxCRdBHlOowCgjmfLiSYugMAd/9kAusa8dZsOUzl+CLmTChOdikiIudFlC6pJwjmk7oF+BXBJIJNiSxqpOu598XShRN1Zz0RSRtRAmOOu/8l0OLuPwbeD1yc2LJGtt57X2iyQRFJI1ECozP8fcLMLiK4M97MhFWUBtZUBfe+uGzaucwKLyKSmqJcT/FYeD+MLxFMT14M/GVCqxrB2rti/Gp7Ax+8dLJuxSoiaWXQwAgnGDzp7seBl4BZw1LVCLZ+51Ga27u4WWdHiUiaGbRLKryq+75hqiUtrKmqY1ReNlfPHp/sUkREzqsoYxhrzezzZjbNzMb2/CS8shGou+feFxeUU5Cre1+ISHqJMobRc73FvXHrHHVPnWFz7QkamtpZulBXd4tI+olypXflcBSSDtZsqSMny7jhAt37QkTST5Qrvf+wv/Xu/pPzX87ItqbqMFfOGsfoUbr3hYiknyhdUu+Oe1wA3Ai8Bigw4tTUN7OroYV7rp6Z7FJERBIiSpfU/fHLZjaaYLoQibOm6jAANy3Q6bQikp6inCXV1ylg7vkuZKRbs6WOSypGM2WM7n0hIukpyhjGvxGcFQVBwCwEnkpkUSNN/ck2Nu8/weeXzkt2KSIiCRNlDOMbcY+7gL3uXpugekak3ntf6GZJIpLGogTGPuCQu7cBmFmhmc109z0JrWwEWbOljhnjRjFX974QkTQWZQzj50B33HIsXCdAU1sn/73ziO59ISJpL0pg5Lh7R89C+DgvcSWNLC9ub6Az5uqOEpG0FyUwGszsQz0LZnY7cCTKi5vZMjPbbmY1ZvZAP89PN7MXzOx1M3vTzG6Le+4L4X7bzeyWKO+XDGuq6hhXlMcV03XvCxFJb1HGMD4N/MzMvhMu1wL9Xv0dz8yygYeBm8N9NpjZanevitvsS8BT7v6ImS0EngFmho/vIriP+BRgnZnNc/dY1D9sOLR3xXhhWz3vv1j3vhCR9Bflwr2dwJVmVgyYu0e9n/dioMbddwGY2SrgdiA+MBwoDR+PBg6Gj28HVrl7O7DbzGrC11sf8b2HxW92HaO5vUu3YhWRjHDWLikz+2szG+Puze7eZGZlZva/I7z2VGB/3HJtuC7eg8DHzKyWoHXRc1V5lH0xs5VmttHMNjY0NEQo6fxas+Uwo/KyuWaO7n0hIukvyhjGre5+omchvPvebYNs36O/Phrvs7wc+JG7V4Sv+UR4l78o++Luj7n7IndfVF5eHqGk86fn3hfXzdO9L0QkM0QZw8g2s/ywewgzKwTyI+xXC0yLW67gdJdTjxXAMgB3X29mBcD4iPsm1ZsHGqlvald3lIhkjCgtjJ8Cz5nZCjNbAawFfhxhvw3AXDOrNLM8gkHs1X222Ucw+y1mtoBgNtyGcLu7zCzfzCoJ5q56NcofNFzWbDlMdpbxvgsUGCKSGaIMev+Nmb0J3ETQVfSfwIwI+3WZ2X3As0A28Li7bzGzh4CN7r4a+BzwfTP7LEGX0z3u7sAWM3uKYIC8C7g31c6Qen5bPYtnjtW9L0QkY0TpkgI4THC190eA3cDTUXZy92cIBrPj13057nEVcM0A+34V+GrE+oZVR1c3NfXNrHyv7lIrIpljwMAws3kE3UjLgaPAPxGcVnvDMNWWsvYebaGr25k3sSTZpYiIDJvBWhjbgJeBD7p7DUDYdZTxquubAZijyQZFJIMMNuh9J0FX1Atm9n0zu5H+T3fNODvqmjCD2eUKDBHJHAMGhrv/i7t/FJgPvAh8FphoZo+Y2dJhqi8lVdc3M61sFIV5uv5CRDLHWU+rdfcWd/+Zu3+A4HqIzcAZEwlmkpq6ZuZNVOtCRDLLkO7p7e7H3P1Rd39fogpKdV2xbnYdaWbOBA14i0hmGVJgCOw5eorOmOvueiKScRQYQ1RTH0zWO1ddUiKSYRQYQ1RdF5xSqzOkRCTTKDCGqLq+mYqyQoryo14kLyKSHhQYQ1Rd36zxCxHJSAqMIYh1OzsbmpmrKUFEJAMpMIZg37FTdHR1a0oQEclICowhqK4Lz5BSYIhIBlJgDEHPpIPqkhKRTKTAGIKa+mamjC6gWGdIiUgGUmAMwY66JuaodSEiGUqBEVGs26nRKbUiksEUGBEdON5Ke1e3ZqkVkYylwIioOpxDSrPUikimUmBEpNuyikimU2BEtKOuiYml+YwuzE12KSIiSaHAiCgY8FZ3lIhkLgVGBN09Z0hpwFtEMpgCI4KDja2c6oiphSEiGU2BEUHPTZPUwhCRTKbAiKD3lFrdZU9EMlhCA8PMlpnZdjOrMbMH+nn+W2a2OfzZYWYn4p6LxT23OpF1nk11XTPji/MpK8pLZhkiIkmVsFn0zCwbeBi4GagFNpjZanev6tnG3T8bt/39wOVxL9Hq7pclqr6hqK5v1hXeIpLxEtnCWAzUuPsud+8AVgG3D7L9cuDJBNZzTtw1h5SICCQ2MKYC++OWa8N1ZzCzGUAl8Hzc6gIz22hmvzGzDw+w38pwm40NDQ3nq+63OdTYRnN7l2apFZGMl8jAsH7W+QDb3gX8wt1jceumu/si4PeBb5vZ7DNezP0xd1/k7ovKy8vfecX96L1pkloYIpLhEhkYtcC0uOUK4OAA295Fn+4odz8Y/t4FvMjbxzeGTc9tWeephSEiGS6RgbEBmGtmlWaWRxAKZ5ztZGYXAGXA+rh1ZWaWHz4eD1wDVPXddzjU1DczriiPsTpDSkQyXMLOknL3LjO7D3gWyAYed/ctZvYQsNHde8JjObDK3eO7qxYAj5pZN0GofT3+7KrhVF3frBlqRURIYGAAuPszwDN91n25z/KD/ez338DFiawtCndnR10Tt182JdmliIgkna70HkR9UztNbV2aQ0pEBAXGoDSHlIjIaQqMQfTMIaUWhoiIAmNQO+qaGTMql/HFOkNKRESBMYia+ibmTijGrL9rEEVEMosCYwDBGVLNzFF3lIgIoMAY0JHmDhpbOzVLrYhISIExAA14i4i8nQJjADqlVkTk7RQYA6iub6KkIIcJJfnJLkVEJCUoMAZQXdfMvIklOkNKRCSkwBiA7rInIvJ2Cox+HG1u52hLh2apFRGJo8DoR+9d9nTTJBGRXgqMfui2rCIiZ1Jg9KOmroni/Bwmjy5IdikiIilDgdGPnrvs6QwpEZHTFBj92FGnM6RERPpSYPRxvKWDI83tusJbRKQPBUYfNQ06Q0pEpD8KjD5655BSl5SIyNsoMPqorm9iVF42U0YXJrsUEZGUosDoo7ouOEMqK0tnSImIxFNg9FFd36QpQURE+qHAiNPY2kndyXbmacBbROQMCow4NZoSRERkQAqMODW6LauIyIASGhhmtszMtptZjZk90M/z3zKzzeHPDjM7Effc3WZWHf7cncg6e+yoa6YgN4upZTpDSkSkr5xEvbCZZQMPAzcDtcAGM1vt7lU927j7Z+O2vx+4PHw8FvgKsAhwYFO47/FE1QvBHFKzy4vJ1hlSIiJnSGQLYzFQ4+673L0DWAXcPsj2y4Enw8e3AGvd/VgYEmuBZQmsFQhmqdWAt4hI/xIZGFOB/XHLteG6M5jZDKASeH4o+5rZSjPbaGYbGxoa3lGxTW2dHGxs0ym1IiIDSGRg9Nev4wNsexfwC3ePDWVfd3/M3Re5+6Ly8vJzLDOgM6RERAaXyMCoBabFLVcABwfY9i5Od0cNdd/zQrdlFREZXCIDYwMw18wqzSyPIBRW993IzC4AyoD1caufBZaaWZmZlQFLw3UJU1PfTF5OFtPHjkrk24iIjFgJO0vK3bvM7D6CL/ps4HF332JmDwEb3b0nPJYDq9zd4/Y9ZmZ/RRA6AA+5+7FE1QpQXdekM6RERAaRsMAAcPdngGf6rPtyn+UHB9j3ceDxhBXXR3V9M1dMLxuutxMRGXF0pTfQ0t5F7fFWDXiLiAxCgQHs7L3LngJDRGQgCgzi7rKnM6RERAakwCAYv8jNNmboDCkRkQEpMAhmqZ01vpicbB0OEZGB6BuSYJbaORq/EBEZVMYHRmtHjP3HT+kMKRGRs8j4wGjp6OKDl0xh0YyxyS5FRCSlJfTCvZFgfHE+/3f55ckuQ0Qk5WV8C0NERKJRYIiISCQKDBERiUSBISIikSgwREQkEgWGiIhEosAQEXcm8r8AAATeSURBVJFIFBgiIhKJxd0ZdUQzswZgLzAeOJLkclKFjkVAxyGg4xDQcQj0HIcZ7l4eZYe0CYweZrbR3Rclu45UoGMR0HEI6DgEdBwC53Ic1CUlIiKRKDBERCSSdAyMx5JdQArRsQjoOAR0HAI6DoEhH4e0G8MQEZHESMcWhoiIJIACQ0REIkmrwDCzZWa23cxqzOyBZNeTLGa2x8zeMrPNZrYx2fUMJzN73Mzqzey3cevGmtlaM6sOf5cls8bhMMBxeNDMDoSfi81mdlsyaxwOZjbNzF4ws61mtsXMPhOuz6jPxCDHYUifibQZwzCzbGAHcDNQC2wAlrt7VVILSwIz2wMscveMuzjJzN4LNAM/cfeLwnV/Axxz96+H/5Aoc/f/mcw6E22A4/Ag0Ozu30hmbcPJzCYDk939NTMrATYBHwbuIYM+E4Mch48whM9EOrUwFgM17r7L3TuAVcDtSa5Jhpm7vwQc67P6duDH4eMfE/yPktYGOA4Zx90Puftr4eMmYCswlQz7TAxyHIYknQJjKrA/brmWczggacKBNWa2ycxWJruYFDDR3Q9B8D8OMCHJ9STTfWb2ZthlldbdMH2Z2UzgcuAVMvgz0ec4wBA+E+kUGNbPuvTobxu6a9z9CuBW4N6we0LkEWA2cBlwCPjb5JYzfMysGHga+DN3P5nsepKln+MwpM9EOgVGLTAtbrkCOJikWpLK3Q+Gv+uBfyHorstkdWEfbk9fbn2S60kKd69z95i7dwPfJ0M+F2aWS/Al+TN3/+dwdcZ9Jvo7DkP9TKRTYGwA5ppZpZnlAXcBq5Nc07Azs6JwUAszKwKWAr8dfK+0txq4O3x8N/CvSawlaXq+IEO/QwZ8LszMgB8CW939m3FPZdRnYqDjMNTPRNqcJQUQnhL2bSAbeNzdv5rkkoadmc0iaFUA5AD/mEnHwcyeBK4nmLq5DvgK8EvgKWA6sA/4PXdP6wHhAY7D9QRdDw7sAT7V04+frszsPcDLwFtAd7j6iwT99xnzmRjkOCxnCJ+JtAoMERFJnHTqkhIRkQRSYIiISCQKDBERiUSBISIikSgwREQkEgWGyBCYWSyc1XOLmb1hZn9uZuf8/5GZfTHu8cz42WVFUo0CQ2RoWt39Mne/kGBm5NsIrnE4V188+yYiqUGBIXKOwqlXVhJM3mZmlm1m/8fMNoSTuX0KwMyuN7OXzOxfzKzKzL5nZllm9nWgMGyx/Cx82Wwz+37YglljZoXJ+vtE+lJgiLwD7r6L4P+jCcAKoNHd3w28G/hjM6sMN10MfA64mGCytzvc/QFOt1j+INxuLvBw2II5Adw5fH+NyOAUGCLvXM9MyUuBPzSzzQRTT4wjCACAV8N7tcSAJ4H3DPBau919c/h4EzAzMSWLDF1OsgsQGcnCubtiBLOdGnC/uz/bZ5vrOXOq/YHm5GmPexwD1CUlKUMtDJFzZGblwPeA73gwKduzwJ+E00hjZvPCGYMBFoczKWcBHwV+Ha7v7NleJNWphSEyNIVhl1Mu0AU8AfRMF/0Dgi6k18LppBs4fevP9cDXCcYwXuL0jMKPAW+a2WvA/xqOP0DkXGm2WpEEC7ukPu/uH0h2LSLvhLqkREQkErUwREQkErUwREQkEgWGiIhEosAQEZFIFBgiIhKJAkNERCL5//R9cZAqSDeoAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# dependence on the depth of trees\n",
    "\n",
    "depths = np.arange(1, 25, 1)\n",
    "depth_scores = []\n",
    "\n",
    "for n in depths:\n",
    "    rf_classifier = RandomForestClassifier(n_estimators = 100, max_features = n_features, max_depth = n)\n",
    "    depth_scores.append(cross_val_score(rf_classifier, X, y, cv = 10).mean())\n",
    "    \n",
    "plt.plot(depths, depth_scores)\n",
    "plt.xlabel('Depth')\n",
    "plt.ylabel('Accuracy')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "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": [
    "# dependence on the number of features\n",
    "\n",
    "n_features = np.arange(5, d, 10)\n",
    "# d = X.shape[1]\n",
    "feat_scores = []\n",
    "\n",
    "for n in n_features:\n",
    "    rf_classifier = RandomForestClassifier(n_estimators = 100, max_features = n)\n",
    "    feat_scores.append(cross_val_score(rf_classifier, X, y, cv = 10).mean())\n",
    "\n",
    "plt.plot(n_features, feat_scores)\n",
    "plt.xlabel('Features')\n",
    "plt.ylabel('Accuracy')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "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": "3.7.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}