{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Exploring random forest hyper-parameters using a League of Legends dataset\n", "\n", "In [previous](http://www.trailofpapers.net/2015/10/playing-in-random-forests-in-league-of.html) [notebooks](http://www.trailofpapers.net/2015/11/influence-of-region-skill-and-patch-on.html), I have used random forests to predict who will win a game of League of Legends. In making those notebooks, I learned how important it is to optimize machine learning algorithms. In this notebook I am going to explore how random forest hyper-parameters like forest size, node size, and sample size can influence prediction accuracy. Near the end, I will do a grid search for optimal parameters, and finally compare random forest performance to Naive Bayes.\n", "\n", "### Table of contents:\n", "[Basic question](#basic)\n", "\n", "[Forest size](#forestsize)\n", "\n", "[Node size](#nodesize)\n", "\n", "[Sample size](#sample)\n", "\n", "[Grid search](#gridsearch)\n", "\n", "[PCA](#PCA)\n", "\n", "[Champions as features](#champions)\n", "\n", "[Naive Bayes](#naivebayes)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Load libraries and API key" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false }, "outputs": [], "source": [ "import numpy as np\n", "from lolML.src import feature_calc\n", "import importlib\n", "import pandas as pd\n", "import pickle\n", "import os\n", "import matplotlib\n", "import matplotlib.pyplot as plt\n", "import lolML.src.plotting as lol_plt\n", "%matplotlib inline\n", "import warnings\n", "warnings.filterwarnings('ignore')\n", "\n", "# load sklearn packages\n", "from sklearn import cross_validation\n", "from sklearn.ensemble import RandomForestClassifier" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# load in 30,000 games from North America, and calculate features\n", "#working_dir = 'C:\\\\Users\\\\Me\\\\Documents\\\\GitHub\\\\lolML'\n", "working_dir = 'C:\\\\Users\\\\Chauncey\\\\Documents\\\\GitHub\\\\lolML'\n", "os.chdir(working_dir)\n", "with open('NA combined_df.pickle', 'rb') as pickle_file:\n", " na_timelines_df = pickle.load(pickle_file)\n", "na_timelines_df = [feature_calc.calc_secondary_features(x) for x in na_timelines_df]\n", "na_timelines_df = feature_calc.calc_second_diff(na_timelines_df)" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# which features are important, taken from previous notebooks\n", "important_col = ['blue_inhibs', 'blue_barons', 'drag_diff', 'first_baron', 'first_inhib',\n", " 'gold_diff', 'gold_diff_diff', 'kill_diff', 'kill_diff_diff', 'red_barons',\n", " 'red_inhibs', 'tower_diff']\n", "timeline_end = 55\n", "time_indices = np.arange(5, timeline_end, 5)" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# plotting defaults\n", "import matplotlib as mpl\n", "mpl.rc('font', size=20)\n", "mpl.rc('lines', linewidth=2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "## The basic question\n", "\n", "League of Legends is an online team game where two teams destroy each others' bases. Games usually take 30-40 minutes. I wanted to see whether, using machine learning, I could predict the winner of the game before it ended, say 5 minutes into the game.\n", "\n", "As an example of this, here is how well a random forest model can predict the winner of games at 5 minute intervals. Snapshots of games were taken every 5 minutes, and the winner was predicted using features like gold or kills. As the game gets longer, the accuracy improves; at late times, however, accuracy goes down, since long games are inherently harder to predict." ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": true }, "outputs": [], "source": [ "rfc = RandomForestClassifier(n_jobs = 2, n_estimators = 25, max_features = 'sqrt')\n", "def cross_validate_score(cur_df):\n", " return cross_validation.cross_val_score(rfc, cur_df[important_col], cur_df['winner'], cv=5, n_jobs = 2)\n", "\n", "default_scores = [cross_validate_score(x) for x in na_timelines_df]" ] }, { "cell_type": "code", "execution_count": 23, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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B65t+eysyLrZYfJpvfbNv+t6rV8dqIoqgBZFyUVJQeueeC0OHxi/57bfDbjXV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\n7LNTlmPlqrb9KXHO9wGXA/2T129sZuu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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.figure(figsize = [8, 6])\n", "plt.plot(time_indices, np.mean(default_scores, axis=1))\n", "plt.ylim( 0.5, 1)\n", "plt.xlabel('Time in game (min)')\n", "plt.ylabel('Prediction accuracy')\n", "plt.xticks(time_indices)\n", "lol_plt.prettify_axes(plt.gca())\n", "plt.legend(fontsize=14, frameon=False);" ] }, { "cell_type": "markdown", "metadata": { "collapsed": true }, "source": [ "\n", "## Impact of forest size on prediction accuracy\n", "\n", "One obvious question when using random forests is, how many trees do you need in the forest? Here I am going to try forest sizes ranging from 1-50 trees, and see how it impacts accuracy. Note that I am using around a dozen features.\n", "\n", "In the first cell, I perform the prediction on the accuracy for the data ten minutes into the game (using default random forest parameters). In the second cell, I plot performance as a function of trees. How does increasing the forest size impact the accuracy of the model?" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false }, "outputs": [], "source": [ "forest_sizes = [1,5,10, 25, 50]\n", "cur_df = na_timelines_df[1] # this is the 10 minute dataframe\n", "def score_by_size(cur_size):\n", " size_forest = RandomForestClassifier(n_jobs = 2, n_estimators = cur_size, max_features = 'sqrt')\n", " return cross_validation.cross_val_score(size_forest, cur_df[important_col], cur_df['winner'], cv=4, n_jobs = 3)\n", "\n", "size_scores = list(map(score_by_size, forest_sizes))" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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IXTC1eB7YRdISkgYBY4EnIuK1ojKrA9NrrNdY0F3jtUfMzKyZ1ZKQ7AH8NSIu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\nAf5dcu7vFZ67ko2z2ztLT0TEfEn3Aod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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(1, figsize = [8, 6])\n", "plt.errorbar(forest_sizes, np.mean(size_scores, 1), np.std(size_scores, 1) / np.sqrt(4), capsize = 0)\n", "lol_plt.prettify_axes(plt.gca())\n", "plt.ylabel('Accuracy at 10\\nminutes in game')\n", "plt.xlabel('Number of trees in forest')\n", "ax.set_xticks(forest_sizes);\n", "plt.ylim([0.6, 0.7]);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The performance of the random forest increases as you add more trees, and seems to plateau around 25 trees. It may be a good rule of thumb to use forests with a number of trees around double the number of features.\n", "\n", "\n", "## Impact of node size on prediction accuracy\n", "\n", "In scikit-learn, with default parameters, each tree is built until each leaf of the tree is pure. However, there are options to adjust the minimum leaf size, and minimum split size. Here, I'm going to build forests using minimum split sizes ranging from 1-25." ] }, { "cell_type": "code", "execution_count": 27, "metadata": { "collapsed": false }, "outputs": [], "source": [ "def score_by_min_split(cur_min_split, cur_df):\n", " split_forest = RandomForestClassifier(n_jobs = -1, n_estimators = 25,\n", " max_features = 'sqrt', min_samples_split = cur_min_split)\n", " return cross_validation.cross_val_score(split_forest, cur_df[important_col], \n", " cur_df['winner'], cv=5, n_jobs = -1)\n", "\n", "min_samples_array = [1, 2, 5, 10, 20, 50, 100, 200, 500, 1000, 2000, 5000]\n", "#min_samples_array = list(range(1, 101, ))\n", "min_split_scores = list(map(lambda x: score_by_min_split(x, na_timelines_df[1]), min_samples_array))" ] }, { "cell_type": "code", "execution_count": 31, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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M7AQzW6o0Mf1kTeDuaks2pDplX0rZf38lGyIixYoyLXY94DpgipkNM7NNSxTD\ndOCHEp1LJFZDhsAzz4RLKddfn3Q0IiKVI0rCsTJwLvAlcBTwmpm9YWbHmFnHVsTwMFBnpqvgkm7j\nx8Npp4X7118PK66YaDgiIhUl8hiOTGKwE3AMsCdh5sh3wB3AEHd/O+L5lgP+DbwAnOLusyIFlGIa\nw1E93OE3vwnVjf33h3vuSToiEZFUim3xtq6EasfRwGqEmSSvA38D7nT3uUWc4zmgE7AhMBv4GPg2\n37Huvn2Lg02AEo7q8be/wfHHh0sp77+v6oaISAHxNf4yszbAHoTxHStl7foauBi4uqlPXTOrL/a1\n3L2iWrEr4agso0eH2+DB4fHAgeHruuvCgAFhoOjdd8MBByQVoYhI6pU+4TCzHoTKRn9CorEAeAS4\nBdgUOBZYAbjY3c9t0YtUOCUclalhNJE71NeHSynPPhsSjbvvTjY2EZGUK03Ckalm7EpIJnYljN/4\nHBgGDHX3SVnHLgU8A/Rw9+4ti7uyKeGoTNkJx403wgknwAorhEspK6yQbGwiIinX+tbmZnYeoZqx\ncmbT88CNwD/dfZHOoO7+nZk9DAyOFqtIOowb1zgr5YYblGyIiLRGlNbmg4CZwPXADUU26noTGJG9\nwcx6EwaXjnH3OWa2bbEBuPsLxYcr0jr9+8Ps2aG51/77Jx2NiEhlK/qSipkdC9zu7rNb9YJhkKgD\n67n7RxEGjbq7R1q8zcxOAE4DugLvAye5+4vNPOck4DjCrJtvgBHuflbW/t8BvwdWBSYAF7n7bQXO\npUsqFSi7I4wupYiIRNL6SyruPqQ0sXA+IeH4OutxUSFEeREz6wtcDRxPWBTud8AoM/u5u08s8Jyr\ngN2AU4F3gWWAbln7jwcuJQyWfRXYArjJzKa7+yNR4pPKcOONSjZEREohSoVjE8KH8VB3/zzP/q6E\nZmAPRW3+FQczexV4292Pzdr2EXCvu5+d5/h1CEnGL9z9wwLnfAl42d3/lLXtCmALd98mz/GqcFQY\nd2iTmXzdty+MHJlsPCIiFab1i7cBfyL8ZT+twP5phEGlfyqwv2zMbDFgY+DJnF1PAlsVeNpewFig\nj5mNNbNxZjbczLL/vl2MRdd9mQtsbmaRLvdIOj3+eOP9665LLg4RkWoTJeHYEhjt7nnHXGS2P0fh\nD/RyWp4wZfeLnO3TCOM58ulJGJdxIHA4cBiwLvBw1jovTwBHmdmmFmxKSMLaZV5TKtiCBXDGGY2P\nl9d3VEQqKWdIAAAgAElEQVSkZKLMUukK5B37kGUKUKk9N9oAHYDD3P0TADM7DPgQ2Ax4DbiA8D68\nRCgbfQ4MB04H8iZigwYN+ul+XV0ddXV1MYUvrXX77fDuu0lHISJSnaIkHHMInUObsgLpWGr+K0Ln\n0y4527sAUws8ZyowvyHZyPgkc56Vgdcya8P0N7Njss51HPCdu3+Z76TZCYek19y58Oc/Jx2FiEj1\ninJJ5S1gr0wH0UWY2dKE1WMTHzDq7j8CbxBWtc32G0J1Ip8XgXZm1jNrW0/CpZnPcs6/wN2nZEaE\nHgQ8XJLAJTHXXQcTJ8KGGyYdiYhIdYqScAwlVDCeMrOFfi2b2UbAU5n9Q0sXXqtcBfQzs/5mtp6Z\nXUO4HPI3ADO7xMyezjr+aUKjspvNbCMz+xVwM/CKu7+eec5aZnZY5uvmZjYS+DmwyKwXqRzTp8PF\nF4f7l16abCwiItUqSh+Ou8xsV8KAyjfN7AtgMmHhtoaBmLe5+x2lDzM6d7/bzJYDziX00ngX6JPV\ng6MroYLRcLyb2e7AtcALhEtITwKnZJ22LXAysA4wD3gW2MrdJ8T8z5EYXXppSDq23x523jnpaERE\nqlPUxdsMGAD8AVg/a9d7wLXuPqxkgYWpresD3xfqi5F26sORfhMnwlprwQ8/wJgxsOmmCy/eJiIi\nkcSyPH1HoBPwbWvanZvZgcD+wPHu/nVm2xrA48AahA6jDwEH5FskLs2UcKTfkUfC8OGhyddxx8Ho\n0YseU1cXbiIi0qzSJxylYmaPAyu5+y+ytj1AGID6HNAZ2BA4zt3TMj6kKEo40u3dd8Mg0Xbt4IMP\nYI01ko5IRKTilaTTaFx+DoxpeGBmywB9gHvcfQdgc+B/QL9EopOqddZZ4bLJcccp2RARiVuUPhyY\n2ZLACYTppisRGmUtdAhh/GXP3Oc2YQVCw7AGvTJxjSScbJ6ZPUWYfipSEs8/D48+CksuCeeem3Q0\nIiLVr+iEw8w6Af8G1gO+A5YCZhCSjsUzh00hzN6IYhZhVdYGvTNfs5eRnwssHfG8Inm5w+mnh/un\nnw4rrphsPCIitSDKJZVzCcnG0YTBohCWf+9IWD/lLeBTwiWSKD4GdjWzxTMzUw4E/pPTuXNVCi8a\nJxLJfffBa69Bly5wyinNHy8iIq0XJeHYE/iXu9+cNRLSM14BdiUsdnZOxBiGEPphfAR8kLl/S84x\nGwPvRzyvyCLmzYOzM23aBg2Cjh0TDUdEpGZESThWBl7PelxP1hgOd59GmMraN0oA7j4CuJRQKVkG\n+GvmBoCZ/RpYkzBjRaRVhg2Djz+GtdeG/v2TjkZEpHZEGTT6PQuviDqTRZd6/wLoETUIdz+bwu3B\nxxCmxs6Kel6RbLNmweDB4f4ll0D79snGIyJSS6IkHJMIVY4G/wW2NbM27t6QiPyasGR7yWQWYvux\nlOeU2nTllfDFF9CrF+yzT9LRiIjUliiXVEYDdZn25hCmra4BjDKz35nZvcCWwGMtCcTMNjSzy8zs\nITN7Jmv7amZ2oJl1bsl5RSAkGldcEe7/5S+N7ctFRKQ8olQ4biWM2VgZmEAY7Lk9sDdh2XcI02Yj\ndzUwswsIl1QaPgay23O2JSQ3JxEWVhOJ7IILwiWVPfaAbbZJOhoRkdrT6tbmZrYpYVDnOGBM1uWV\nYp9/EHAH8ARwJmFa7Fnu3ibrmNeAGe7+m/xnSSe1Nk+Hjz+Gn/8c6uvhP/+B9ddv/jkiItIiBevH\nURp/9SZ86L+dvd3dX2fh2StR/ZHQv2Nvd//BzPJdXf+AxoZgIpGcey7Mnw9HHaVkQ0QkKVHGcDwL\nHBNDDL8AHnf3H5o4ZgqLzogRadaYMXD33bD44o0zVEREpPyiJBxfA3NiiMFYeLptPl0I7c1Fipbd\nwvzEE6FH5AnbIiJSKlESjucILcxL7ZOmzmtmbQjTbdVpVCIZNQpGj4bOneHMM5OORkSktkVJOP4M\nrGNmF5pZKVsm3QVsYmanFth/NrAWYWCpSFEWLGhMMs45Bzp1avp4ERGJV9GzVMzsFkLfja0Jzb3e\nyXxd5ATuflTRAZj9jLAy7EaErqIAmwFXAdsCmwKvAL3dPepKtInSLJXkjBgB/frBKqvAhx+GMRwi\nIhK7grNUoiQcRU93zZ7SWuS5OxFWnj2Uhasu9cA/gN+7+3dRzpkGSjiSMXduWCtl4kS49VY47LCk\nIxIRqRklSThWK/bV3H18scfmvMZyhOrGcsAM4NWcZeorihKOZFxxBZx2Gmy4Ibz5JrSJlP6KiEgr\ntD7hkOiUcJTf9Omwxhrh66hRsMsuSUckIlJTCiYcif/tZ2b1ZnZeM8ecY2YLyhWTVK5LLgnJxvbb\nw847Jx2NiIg0iNJpdJVij3X3CS0Lp/DL00TWJAJhzMa1mdV2LrtMC7SJiKRJlMXbxhNmpOT7Nd5w\n3cAy99u2LqxFLIsaf0kzzjsPfvgB+vaFTTdNOhoREckWdbXYfDoRprSuQljC/rPmTmRm2zbczXxd\nLWtbtrbAqsAhwIcRYpUa8+67YSps+/Zw0UVJRyMiIrlKMmjUzNoSlqU/HtjM3Sc2c3ykFWUJ02OP\ncPd/tDDERGjQaPnsvjs8+ij84Q+Nl1VERKTsyjNLxcxeAca6+yHNHDco6+F5wPOZW64FhDVcnnX3\n/5UqznJRwlEezz8PdXWw5JLw6aew4opJRyQiUrNavzx9kV4Cmm2z5O6DGu6bWT/gAXe/psSxSA3I\nXqDt9NOVbIiIpFWpE45lgSWjPMHdVytxDFJD7rsPXnsNunSBU05JOhoRESmkZH04zOw3QF/gvVKd\nU6Qp8+bB2WeH+4MGQceOiYYjIiJNiNKH4znyLNSWOcfKhNkkDpwfJYAmzrsId98+yrmlut10E3z8\ncVg3pX//pKMREZGmlGrxtunAq8AV7v5spABiXBQuaRo0Gp9Zs0IL82nTwmWVffdNOiIREaEUg0bj\n+rAvdN7MCrKbAn8h9OA4NI7Xl8p05ZUh2ejVC/bZJ+loRESkOalfvM3MOhPGhVzj7pclHU8UqnDE\n44svQnVj9mx44QXYZpukIxIRkYz0Lt7WHHf/BhgF6Cq9AHDBBSHZ2GMPJRsiIpWi6ITDzM41s3lm\n1r3A/h6Z/WeWLryfzCQMSpUa9/HHMGQItGkTVoYVEZHKEKXCsQfwvLtPybfT3ScBzwJ7lSKwBma2\nBNAHmFbK80plOuccmD8f+vWD9ddPOhoRESlWlMZfawK3N3PMB8BvowRgZkdQeLrtKoSF29YErohy\nXqk+r70G99wDiy8OgwcnHY2IiEQRJeFYAvi+mWPmAktHjOGWZvbXA7cRFoeTGuUOZ5wR7p94IvTo\nkWw8IiISTZSEYzLQq5ljtsgcF8VRBbbXE/p7jHH3zyOeU6rMqFEwejR07gxnxjFKSEREYhUl4RgF\n/N7MDnL3kbk7zewgoDdwY5QA3H14lOOl9ixY0JhknHMOdOqUbDwiIhJdlE6jPYB3gE7AQ4QEZDLQ\nA9gV2JNQkdjI3SfGEm2FUR+O0hgxIgwSXWUV+PDDMIZDRERSqWAfjkiNv8xsU+Ae8k9RHQ8c4O5v\nRI0u6/w/I6w42zbffnef0NJzJ0EJR/FGjw63hsGgAweGr1ttBUcfDRMnwq23wmGHJRWhiIgUoTQJ\nB4CZLUaYItuLUO34FngZeNjd57UoOrPDgTOAdZsI1t09byKSVko4orPMd7/hbbviCjjtNNhwQ3jz\nzdB/Q0REUqt0CUepmVk/4GZgAfASMBGYn+dQd/cjyxhaqynhiC474Zg+PbQwnz49DBrdZZdkYxMR\nkWa1fvG2GJ1KqJL82t0/SDoYSY9LLgnJxvbbw847Jx2NiIi0Rhpam68J3K1kQ7JNnAjXXhvuX3ZZ\nY+VDREQqUxpam08Hfoj4HKly550HP/wAffvCppsmHY2IiLRWlIRjTeD9Zo75IHNcFA8DdWb6G1Ya\njRgB7dvDRRclHYmIiJRClIQjrtbmZwEdgCFmtmTE50qVcofjjguDRkVEpPJFafz1MTDJ3bdr4pjn\ngFXdvWfRAYTndAI2BGYDHxMGkS7C3bcv9rxpoFkq0TXUuZZcEj79FFZcMdl4REQkkpLMUomltXnm\nOQ06AhtFfL5Uiezc7PTTlWyIiFQTtTaPkSoc0dx7LxxwQLg/axZ07JhsPCIiEllltDavNko4ijd/\nPmywQVgrBRaudoiISMUoTeMvd3/dzNahxK3NRUaMaEw2RESk+pS0tbmZtQV2d/cHmzimN+DAGHef\nY2bbFnt+d3+hBGGWjSocxZk7F9ZaCyZNatymt01EpCLF29rczFYDjgaOBLpSYLXXjOcICcd6wEfA\n6CJfxps5r1SoG24IycaGG8I77yQdjYiIxKHFCYeZtSN0FT0G2JHGrOapZp56PiF5+DrrcTH0N28V\nmjkTLr443L/4Ythtt2TjERGReLRkefo1gAFAP6Bh4uKXwBDg7+7+WSkDrGS6pNK8QYNg8GDYemt4\n4YXG5ef1tomIVKTWzVIxs/bAPoRqxnaZE/4IPALsCwxz92NKEmoVUcLRtC+/hJ49wxTYf/0rJB3Z\ny9OLiEjFadkYDjNbm1DNOAJYPrP5LeAW4A53/8bM6ksVpdSWiy8OyUafPiHZEBGR6tVkhSMrmfgS\n+Adwi7u/m+eYVlU4zGxl4GRCe/MeQPt8x0VpmZ4GqnAUNmFCmJny44/w9tthwCiowiEiUuFaPUtl\nFHBvbrJRCmZWlzl/B2A+MC3zNZc+gqrIoEEh2Tj44MZkQ0REqldzFY5zCNNdGzqLfgQMB2519ymZ\nY1pV4TCzMcAvgf6EyzRVc4lGFY78PvggdBVt0ybcX3PNxn2qcIiIVLSWDxo1MwN2Iozl2JNQFVlA\nmP46AriT1iUcc4C73f2Iljw/zZRw5Lf//nDffWH5+RszS/2NHh1uuerqwk1ERCpCydZS6UJo7nU0\nkD2e4nXgBHd/PXJkZlOBO939lKjPTTslHIsaMwY23xyWWAI++QS6d086IhERKaGCCUebKGdx9y/c\n/VJgLeA3hIXc5gGbAq+a2dtm9vuIwT3KwkvUSxU7++zw9Q9/ULIhIlJLWr2WipmtQJg2O4CQiLi7\nF92CPPP8V4HHgdPcfXarAkoRVTgW9swzsOOOsMwyMHYsdO6cdEQiIlJipbmk0uyrhBknR7v7oRGf\nty7wCmGtlI+AGfmOc/ftWxtjOSnhaOQOvXrBa6/BRRc1VjpERKSqlCfhaAkz24CwgFuzf++6e6RL\nQElTwtHo/vth332hSxf49FPo2DHpiEREJAalGcMRk6uAZYHzCNNvF3P3NvluyYYpLbVgAZxzTrj/\n5z8r2RARqUVp+BDvBdzv7he6+0R3z9f0q0XM7AQzG2dmc8zsdTNrtoG2mZ1kZv8zs7lmNsXMLsnZ\nf5iZvWNms81sqpndlpm9IwXcdlvot7H66jBgQNLRiIhIEtKQcMwDxpX6pGbWF7gauBDYCHgJGJVp\no17oOVcBxwOnAesCuwLPZ+3vTWh8djPwc2BvYD1C23fJ44cfYODAcH/wYFhssWTjERGRZKRhDMe9\nwAruXtKpsWb2KvC2ux+bte0jQov2RYYsmtk6wLvAL9z9wwLnPBX4vbuvlrXtSOBad18qz/E1P4bj\n2mvhxBNDZ9G334a2Rc9fEhGRCpTqMRxnAD83s7MyXU1bzcwWAzYGnszZ9SSwVYGn7QWMBfqY2djM\npZjhmWm7DZ4CVjCz3S1YHjiI0EtEcnz3HVx4Ybh/0UVKNkREalmxi7fF6VzgPeAi4Ggze5vC02KP\nKvKcyxOm2H6Rs30a0LXAc3oSBq0eCBye2XYF8LCZbenBO2Z2KKGdewfC+/cU0K/IuGrK1VfDl1/C\nllvCHnskHY2IiCQpDQlH9hoqq2duhRSbcLREG0IScZi7fwJhgCjwIaGT6hgz60UYwzEIeALoDlwO\nDGHhf0fN++oruOKKcP+SSxoXZRMRkdqUhoSjZ/OHRPYVYYG53NkjXYCpBZ4zFZjfkGxkfJI5zyrA\nGOBk4Gl3vzKz/z0zmw38y8zOalhBN9ugQYN+ul9XV0ddjaxEdumlMHMm7Lwz9FbjehGRmpd4wuHu\n42M4549m9gZhldv7snY1rP+Sz4tAOzPr6e5jM9t6Ei7NfJZ5bEB9zvMaHucdD5OdcNSKSZPguuvC\n/YsvTjYWERFJhzQMGo3LVUA/M+tvZuuZ2TWE8Rt/AzCzS8zs6azjnwbeBG42s43M7FeE6a+vZK2C\n+wCwl5kdZ2Y9zezXwLXAG+4+qVz/sLQ7//wwHfaAA2DjjZOORkRE0iDxabFxMrPjgdOBboQprye7\n+4uZfbcAvd29Z9bxXQkJxC7AHMKsllPc/cucc/6OMNbkW+BZ4Ix8l1NqcVrsRx/Bz38e7r//Pqyz\nTrLxiIhIWaV3LZVqVosJR9++cPfdcPTRcNNNSUcjIiJlpoQjCbWWcLz5JmyyCXToAJ98Aj16JB2R\niIiUWaobf0mVaFhy/ve/V7IhIiILU4UjRrVU4Xj+eairg6WWgrFjYfnlk45IREQSoAqHxMcdzjor\n3D/1VCUbIiKyKFU4YlQrFY6HHoK99oIVVoBPPw1VDhERqUmqcEg8FiyAc84J9885R8mGiIjkpwpH\njGqhwnH77XDYYbDKKqEHR4cOSUckIiIJUoVDSu/HH+G888L9wYOVbIiISGFKOKTFbroJxo2D9dYL\nVQ4REZFCdEklRtV8SWX2bFhjDfjiC7jvPth336QjEhGRFNAlFSmta64JycZmm8E++yQdjYiIpJ0q\nHDGq1grHN99Az54wYwY8/TTssEPSEYmISEqowiGl85e/hGRjhx2UbIiISHFU4YhRNVY4pkyBNdeE\nOXPg1Vdh882TjkhERFJEFQ4pjQsuCMnGvvsq2RARkeKpwhGjaqtwfPoprLsu1NfDe++F6bAiIiJZ\nVOGQ1jvvPJg/Hw4/XMmGiIhEowpHjKqpwvHOO7DRRrDYYqGF+aqrJh2RiIikkCoc0joNC7Qdf7yS\nDRERiU4VjhhVS4XjxRdhm22gY0cYOxZWXDHpiEREJKVU4ZCWcYezzgr3//QnJRsiItIyqnDEqBoq\nHI89BrvtBsstF6obSy+ddEQiIpJiqnBIdPX1cPbZ4f5ZZynZEBGRllOFI0aVXuG480445BDo0SPM\nTFliiaQjEhGRlFOFQ6KZNw/+/Odwf+BAJRsiItI6Sjgkr5tvDp1F114b+vVLOhoREal0uqQSo0q9\npPL992GBtqlT4e674YADko5IREQqhC6pSPGuuy4kGxtvDPvtl3Q0IiJSDVThiFElVji+/RZ69oTp\n0+Hxx2HnnZOOSEREKogqHFKcyy8PyUZdHey0U9LRiIhItVCFI0aVVuH4/HNYY40whuPll6FXr6Qj\nEhGRCqMKhzTvootCsrHnnko2RESktFThiFElVTjGjYN11oH58+E//4ENNkg6IhERqUCqcEjTBg4M\nzb4OPVTJhoiIlJ4qHDGqlArHe+/BL38J7drBhx/C6qsnHZGIiFQoVTiksHPOCcvQH3OMkg0REYmH\nKhwxqoQKx8svw1Zbwc9+FlqZd+2adEQiIlLBVOGQRbmHZecBTjpJyYaIiMRHFY4Ypb3C8cQTsMsu\nsOyyMHYsdOqUdEQiIlLhVOGQhdXXw9lnh/tnnqlkQ0RE4qUKR4zSXOG45x448EDo1g0++SSM4RAR\nEWmlghWOduWMQspj9OhwGzw4PB44MHytqwu3+fPh3HPDtvPOU7IhIiLxU4UjRklXOCyTZ+aGMGwY\nDBgQ1k354ANo3778sYmISFUqWOFQwhGjNCYcc+bA2mvDpElwxx1w8MHJxCYiIlVJg0YluOGGkGxs\nuCH07Zt0NCIiUitU4YhR2iocM2dCz57w9dfw6KPQp09ioYmISHVShUPgyitDsrH11rDrrklHIyIi\ntUQVjhilqcIxbVoYJDprFvzrXyHpEBERKTFNi03KoEHha8OU1KRcfHFINvr0UbIhIiLlpwpHjNJS\n4Rg/PsxM+fFHePvtMGBUREQkBhrDUcsGDw7JxsEHK9kQEZFkqMIRo7RUONq0CbcPPoA110wsHBER\nqX6qcNSy+no4+mglGyIikhxVOGKUlgrHEkuEBdq6d08sFBERqQ2apVKt5s6Fzz4LA0Nzbw3+8Acl\nGyIikixVOGJUigrH3LkwYcKiycS4ceHr5583f46vv4bOnVsVhoiISDG0eFsSikk4fvihcIVi/HiY\nOrXp12jXDlZZBVZbbdHbttuGY/QtFhGRMtEllaT88EP+CkXDbcqUpp/ftu3CCcXqqy+cVHTvHo4R\nERFJM1U4YmRmbuZNVhhyE4rcW/fuoYrRstcPX/UtFhGRMlGFIylt2sDKKxdOKFZaqeUJhYiISKXQ\nR13M5s5VQiEiIqLGXzFTsiEiIqKEQ0RERMpACYeIiIjETgmHiIiIxE4Jh4iIiMROCYeIiIjETgmH\niIiIxE4Jh4iIiMROrc1jVIrVYlti9Oh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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(1, figsize = [8, 6])\n", "plt.errorbar(min_samples_array, np.mean(min_split_scores, 1), np.std(min_split_scores, 1) / np.sqrt(5))\n", "lol_plt.prettify_axes(plt.gca())\n", "plt.ylabel('Accuracy at 10\\nminutes in game')\n", "plt.xlabel('Minimum samples for split')\n", "ax.set_xscale('log')\n", "plt.xticks(min_samples_array, rotation='vertical')\n", "ax.get_xaxis().set_major_formatter(matplotlib.ticker.ScalarFormatter())\n", "plt.ylim([0.67, 0.71]);\n", "plt.yticks(np.arange(0.67, 0.72, 0.01));" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The model gets slightly more accurate as you increase the minimum size of the split! With the default parameters, each individual tree is overfit; the bagging and randomness of the forest cannot compensate for this. By allowing for some impure splits, the algorithm reduces overfitting on each individual tree, and is better able to generalize. I could further explore this parameter, but later I'm going to do a grid search, so let's look at other parameters for now.\n", "\n", "\n", "## Sample size and model accuracy\n", "\n", "In the previous examples, I was running cross-validated models using the entire dataset of 30,000 games. It's possible that with more games, we could get better accuracy; alternatively, it might only take a handful of games to predict the winner. To test that, I ran the classifier with different numbers of input games." ] }, { "cell_type": "code", "execution_count": 26, "metadata": { "collapsed": false }, "outputs": [], "source": [ "rfc = RandomForestClassifier(n_jobs = 2, n_estimators = 25, max_features = 'sqrt',\n", " min_samples_leaf=10, min_samples_split=25)\n", "def cross_validate_df(cur_df):\n", " return cross_validation.cross_val_score(rfc, cur_df[important_col], cur_df['winner'],\n", " cv=5, n_jobs = 2)\n", "\n", "def calc_score_per_samples(timelines_df, n_samples):\n", " timelines_scores = [cross_validate_df(x.sample(min(x.shape[0], n_samples)) ) for x in timelines_df]\n", " return np.mean(timelines_scores, 1)\n", "\n", "sample_range = np.arange(1000, 20000, 3000)\n", "scores_per_samples = [ calc_score_per_samples(na_timelines_df, x) for x in sample_range]" ] }, { "cell_type": "code", "execution_count": 37, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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RAeiyBbpuhau2+xJ08gzzASpUgHbtoFMnuPRSuywwMrLov1g5kJUFn35qg4DN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\nan8kF628GzBGjVJCICIiyZVxkNvda1J/gHbAI8B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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.figure(figsize = [8, 6])\n", "for i, x in enumerate(scores_per_samples[::3]):\n", " plt.plot(time_indices, x, label = sample_range[3 * i])\n", "plt.ylim( 0.5, 1)\n", "plt.xlabel('Time (min)')\n", "plt.ylabel('Prediction accuracy')\n", "plt.xticks(time_indices)\n", "lol_plt.prettify_axes(plt.gca())\n", "plt.legend(fontsize=14, frameon=False);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The model has a similar accuracy with 1,000, or 10,000 samples! There is just more variance with the 1000 sample model. It looks like we have a lot more data than we need." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "## Grid search\n", "We could make similar plots for every parameter, but it would be nice to systematically explore parameter spaces. Scikit-learn has two tools to do that, randomized search, and grid search (there is not, unfortunately, any monte-carlo markov models in the package).\n", "\n", "Let's run a grid search over tree depth, node size, and leaf size. I will use 3-fold cross-validation as well. Note also, that I am going to stick with the default square root feature selection. I will use the dataframe for the ten minute timepoint." ] }, { "cell_type": "code", "execution_count": 32, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "GridSearchCV(cv=3, error_score='raise',\n", " estimator=RandomForestClassifier(bootstrap=True, class_weight=None, criterion='gini',\n", " max_depth=None, max_features='sqrt', max_leaf_nodes=None,\n", " min_samples_leaf=1, min_samples_split=2,\n", " min_weight_fraction_leaf=0.0, n_estimators=50, n_jobs=1,\n", " oob_score=False, random_state=None, verbose=0,\n", " warm_start=False),\n", " fit_params={}, iid=True, n_jobs=3,\n", " param_grid={'min_samples_leaf': [10, 30, 100, 300], 'min_samples_split': [30, 100, 300, 1000], 'max_depth': [5, 10, 15, 20]},\n", " pre_dispatch='2*n_jobs', refit=True, scoring=None, verbose=0)" ] }, "execution_count": 32, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from sklearn.grid_search import GridSearchCV\n", "param_dict = { 'max_depth' : list(range(5, 21, 5)), 'min_samples_leaf': [10, 30, 100, 300],\n", " 'min_samples_split': [ 30, 100, 300, 1000]}\n", "grid_forest = GridSearchCV(RandomForestClassifier( n_estimators = 50, max_features = 'sqrt'),\n", " param_grid = param_dict, cv = 3, n_jobs = 3)\n", "grid_df = na_timelines_df[1] # dataframe at 10 minutes\n", "grid_forest.fit(grid_df[important_col], grid_df['winner'])" ] }, { "cell_type": "code", "execution_count": 33, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "{'max_depth': 10, 'min_samples_leaf': 10, 'min_samples_split': 1000}" ] }, "execution_count": 33, "metadata": {}, "output_type": "execute_result" } ], "source": [ "grid_forest.best_params_" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The best forest had a maximum depth of 10, minimum leaf size of 22, and minimum node size of 50. Both the leaf and node size were at the maximum, so we could perform further grid searches. However, the accuracy gains were pretty small, so I will just use those parameters in the future." ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": true }, "outputs": [], "source": [ "better_forest = RandomForestClassifier(min_samples_leaf=20, min_samples_split=50, max_depth=10, n_estimators=25)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "\n", "# Dimensionality reduction - PCA\n", "\n", "I haven't talked much about the features, but I can tell you there is a lot of correlation between them. I should also say this section gets a little League of Legends wonky, so you can skip down to [Naive Bayes](#naivebayes)\n", "\n", "To look at the collinearity, I used a pandas function, scatter_matrix()." ] }, { "cell_type": "code", "execution_count": 41, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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kxhfLl9+SXnXkF6ELFy5gxozhtO3l2LEenGJ/x4798iSvaiHhVsf24nwGHduL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\nB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GxCrDQlwG+Ae5GP7qvIIJuOCKIBZJvroLrnw+p3O/CHSIh7MfAHyASzGUk6aCHRYGWI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\nPWeIZVnk5eWTl5fHsGFBVq9e40pOpRgwoJDS0gLKy8dx5MhWQqF4m1P40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TpCNBrF49FE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\nAiZNOo/Cwkv44IPnaWo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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "pd.tools.plotting.scatter_matrix(na_timelines_df[4][['gold_diff', 'kill_diff', 'tower_diff']], figsize = [9, 9]);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As you would expect, gold, kills, and tower differences are correlated.\n", "\n", "Random forests are pretty resilient to multicollinearity, but I wanted to see if dimensionality reduction would help the model. To do that I used PCA. First we need to load the PCA library." ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": true }, "outputs": [], "source": [ "from sklearn.decomposition import PCA\n", "from sklearn.preprocessing import StandardScaler\n", "pca = PCA(n_components=6)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "PCA only works on continous data, so we need to select those features specifically." ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "array(['blue_inhibs', 'blue_barons', 'drag_diff', 'gold_diff',\n", " 'gold_diff_diff', 'kill_diff', 'kill_diff_diff', 'red_barons',\n", " 'red_inhibs', 'tower_diff'], \n", " dtype='" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "pd.tools.plotting.scatter_matrix(pca_df[['PCA1', 'PCA2', 'PCA3']], figsize = [9, 9]);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "That is some weird blobbing of the data! The second component is highly weight by the barons and inhibs, integer data, which is creating the blobbing.\n", "\n", "Now that we have the principal components, we can try modeling again. First, let's create our list of PCA features." ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "['PCA1', 'PCA2', 'PCA3', 'PCA4', 'PCA5', 'PCA6', 'first_baron', 'first_inhib']" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "na_pca_dfs = [pca_lol_df(x, scalar_col) for x in na_timelines_df]\n", "important_col_pca = ['PCA{0}'.format(x) for x in range(1,7)]\n", "important_col_pca.extend(['first_baron', 'first_inhib'])\n", "important_col_pca" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now that we have our PCA columns, we can run the prediction." ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": false }, "outputs": [], "source": [ "def cross_validate_pca(cur_df, feature_col):\n", " return cross_validation.cross_val_score(better_forest, cur_df[feature_col], cur_df['winner'], cv=3, n_jobs = 2)\n", "pca_scores = [cross_validate_pca(x, important_col_pca) for x in na_pca_dfs]\n", "unreduced_scores = [cross_validate_pca(x, important_col) for x in na_timelines_df]" ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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MCgHVa9/l7MNdMdYCXL8Xs8ewi3KJmgUIDwJyNUDqduv+LSZsnsAXO74gOCwY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\nXEY2/0FhK8Nq4FrgaxHxZrXB1IOkgGDXYQt4fcw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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.figure(figsize = [8, 6])\n", "plt.plot(time_indices, np.mean(unreduced_scores, 1), label = 'No PCA')\n", "plt.plot(time_indices, np.mean(pca_scores, 1), label = 'PCA')\n", "plt.ylim( 0.5, 1)\n", "plt.xlabel('Time (min)')\n", "plt.ylabel('Prediction accuracy')\n", "plt.xticks(time_indices)\n", "lol_plt.prettify_axes(plt.gca())\n", "plt.legend(frameon=False, fontsize=20);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The people who said random forests are resilient to multicollinearity were right! We get the same prediction accuracy with PCA as we do without it.\n", "\n", "\n", "## Can the random forest detect champion interaction?\n", "\n", "When I parsed the game data, I recorded which champions each team were playing. I wondered if the random forest would be able to tell me if certain champions were better than others, or if combinations of champions would increase predictability. So I made a function to create features showing which champions were on each team." ] }, { "cell_type": "code", "execution_count": 57, "metadata": { "collapsed": true }, "outputs": [], "source": [ "champ_timelines_df = na_timelines_df\n", "champ_timelines_df = feature_calc.binarize_champions( champ_timelines_df )" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "There are a lot more features, so we need to create a new list of features for the model." ] }, { "cell_type": "code", "execution_count": 58, "metadata": { "collapsed": false }, "outputs": [], "source": [ "col_names = champ_timelines_df[0].columns\n", "champ_col = np.array([x for x in col_names if x not in\n", " ['winner', 'game_length', 'blue_0', 'blue_1', 'blue_2', 'blue_3', 'blue_4',\n", " 'red_0', 'red_1', 'red_2', 'red_3', 'red_4', 'matchId', 'utctimestamp'] ])\n", "num_features = np.size(champ_col)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Given the much larger number of features, I decided to make a larger forest, with both more and deeper trees. Then I ran the prediction and plotted it." ] }, { "cell_type": "code", "execution_count": 60, "metadata": { "collapsed": false }, "outputs": [], "source": [ "champ_forest = RandomForestClassifier(n_estimators=200, max_depth=30,\n", " min_samples_split=20, max_features='sqrt')\n", "\n", "def cross_validate_champ(cur_df):\n", " return cross_validation.cross_val_score(champ_forest, cur_df[champ_col],\n", " cur_df['winner'], cv=3, n_jobs = 2)\n", "\n", "champ_scores = list(map( cross_validate_champ, champ_timelines_df ))" ] }, { "cell_type": "code", "execution_count": 61, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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okcyfP7/IhvqiYk5ISJDu3buLn5+fBAUFSYcOHeTtt98WEauDSd++fR3/bzVu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\nev9SOtTpUObXVEqpK6hs5/4qsNJjUxH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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.plot(time_indices, np.mean(champ_scores, 1), label = 'With champion features')\n", "plt.plot(time_indices, np.mean(unreduced_scores, 1), label = 'Without champion features')\n", "plt.ylim( 0.5, 1)\n", "plt.xlabel('Time (min)')\n", "plt.ylabel('Prediction accuracy')\n", "plt.xticks(time_indices)\n", "lol_plt.prettify_axes(plt.gca())\n", "plt.legend(fontsize=14, frameon=False);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "There is an ever-so-slight improvement in performance based on the champion information. It looks like once the game starts, the conditions of the game matter more than which champions are playing." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "## Naive Bayes:\n", "Finally, I wanted to see how other models would perform, so I decided to look at Naive Bayes. I made a simple predictor using the \"Gaussian\" features of gold, kill, etc. differences." ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "collapsed": false }, "outputs": [], "source": [ "from sklearn.naive_bayes import GaussianNB\n", "gnb = GaussianNB()\n", "bayes_col = ['gold_diff', 'gold_diff_diff', 'kill_diff', 'tower_diff',\n", " 'square_gold_diff', 'kill_diff_diff', 'drag_diff',\n", " 'tower_diff_diff', 'red_inhibs','red_barons', 'blue_barons']\n", "def nb_score(cur_df,):\n", " gnb.fit(cur_df[bayes_col], cur_df['winner'])\n", " return gnb.score(cur_df[bayes_col], cur_df['winner'])\n", "\n", "bayes_scores = list(map(nb_score, na_timelines_df ))" ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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cKPODAqVUU+CK1npver/MFSQoECJrCA+/9fDfutVMA1y5YtvGYoFq1WwDgMBA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\nrs7TN/fWq95CJH1X0lxJ70p6PW3TuDz7NWx/lNKGLPSHpOm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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.figure(figsize = [8, 6])\n", "plt.plot(time_indices, np.mean(unreduced_scores, 1), label = 'Random Forest')\n", "plt.plot(time_indices, bayes_scores, label = 'Naive Bayes')\n", "plt.ylim( 0.5, 1)\n", "plt.xlabel('Time (min)')\n", "plt.ylabel('Prediction accuracy')\n", "plt.xticks(time_indices)\n", "lol_plt.prettify_axes(plt.gca())\n", "plt.legend(frameon=False, fontsize=18);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Naive Bayes is almost as good as random forests, and a whole lot faster! I have a feeling this dataset is a bit too simple for random forests to gain an edge of Naive Bayes.\n", "\n", "## Conclusions\n", "\n", "This will probably be my last notebook using League of Legends data for a while. It was fun learning about random forests using a game I cared about. Here are some simple take home ideas:\n", "\n", "1. Optimize your machine learning models\n", "2. Skill makes the game go faster\n", "3. Dragons don't matter" ] } ], "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": "3.4.3" } }, "nbformat": 4, "nbformat_minor": 0 }