pruning.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "id": "6dY4sYN5BhnF"
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import find_split as fs\n",
    "import evaluation as ev\n",
    "import matplotlib.pyplot as plt\n",
    "from trees import binarySearchTree"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[-59. -53. -51. -54. -45. -79. -87.   4.]\n",
      " [-66. -53. -59. -62. -69. -81. -79.   1.]\n",
      " [-41. -57. -63. -40. -73. -66. -65.   2.]\n",
      " [-62. -58. -52. -63. -50. -87. -88.   4.]\n",
      " [-63. -58. -64. -67. -74. -87. -87.   4.]]\n"
     ]
    }
   ],
   "source": [
    "#using the noisy dataset so we can see the effects of pruning\n",
    "data = np.loadtxt('noisy_dataset.txt')\n",
    "print(data[:5])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "max depth: 18\n",
      "---RESULT METRICS---\n",
      "Precisions:   [0.71929825 0.79166667 0.8        0.8       ]\n",
      "Recalls:      [0.78846154 0.71698113 0.8        0.8       ]\n",
      "F1 Score:     [0.75229358 0.75247525 0.8        0.8       ]\n",
      "Avg Accuracy: 0.775\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Library/Frameworks/Python.framework/Versions/3.7/lib/python3.7/site-packages/matplotlib/figure.py:459: UserWarning: matplotlib is currently using a non-GUI backend, so cannot show the figure\n",
      "  \"matplotlib is currently using a non-GUI backend, \"\n"
     ]
    },
    {
     "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": [
    "#first, create a train and test set \n",
    "#evaluate on the test set to see pre-pruning results\n",
    "\n",
    "data2=data.copy()\n",
    "#shuffle data\n",
    "np.random.shuffle(data2)\n",
    "t_split=0.8\n",
    "v_split=0.9\n",
    "train=data2[:int(len(data2)*t_split)]\n",
    "validation=data2[int(len(data2)*t_split):(int(len(data2)*v_split))]\n",
    "test=data2[int(len(data2)*v_split):]\n",
    "\n",
    "model=binarySearchTree(train)\n",
    "print('max depth:',model.get_max_depth())\n",
    "y_pred=model.predict(test[:,:-1])\n",
    "#evaluate\n",
    "cm=ev.confusion_matrix(test[:,-1],y_pred,plot=True)\n",
    "i=ev.get_metrics(test[:,-1], y_pred, printout=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "current f1: 0.7803122995915888\n",
      "new f1 score: 0.7803122995915888\n",
      "pruned 1!\n",
      "current f1: 0.7803122995915888\n",
      "new f1 score: 0.7803122995915888\n",
      "pruned 1!\n",
      "current f1: 0.7803122995915888\n",
      "new f1 score: 0.7803122995915888\n",
      "pruned 1!\n",
      "current f1: 0.7803122995915888\n",
      "new f1 score: 0.7803122995915888\n",
      "pruned 1!\n",
      "current f1: 0.7803122995915888\n",
      "new f1 score: 0.7803122995915888\n",
      "pruned 1!\n",
      "current f1: 0.7803122995915888\n",
      "new f1 score: 0.7803122995915888\n",
      "pruned 1!\n",
      "current f1: 0.7803122995915888\n",
      "new f1 score: 0.7803122995915888\n",
      "pruned 1!\n",
      "current f1: 0.7803122995915888\n",
      "new f1 score: 0.7803122995915888\n",
      "pruned 1!\n",
      "current f1: 0.7803122995915888\n",
      "new f1 score: 0.7803122995915888\n",
      "pruned 1!\n",
      "current f1: 0.7803122995915888\n",
      "new f1 score: 0.7798732436634769\n",
      "did not prune\n",
      "current f1: 0.7803122995915888\n",
      "new f1 score: 0.7798732436634769\n",
      "did not prune\n",
      "current f1: 0.7803122995915888\n",
      "new f1 score: 0.7803122995915888\n",
      "pruned 1!\n",
      "current f1: 0.7803122995915888\n",
      "new f1 score: 0.784895182508945\n",
      "pruned 1!\n",
      "current f1: 0.784895182508945\n",
      "new f1 score: 0.784895182508945\n",
      "pruned 1!\n",
      "current f1: 0.784895182508945\n",
      "new f1 score: 0.784895182508945\n",
      "pruned 1!\n",
      "current f1: 0.784895182508945\n",
      "new f1 score: 0.784895182508945\n",
      "pruned 1!\n",
      "current f1: 0.784895182508945\n",
      "new f1 score: 0.784895182508945\n",
      "pruned 1!\n",
      "current f1: 0.784895182508945\n",
      "new f1 score: 0.784895182508945\n",
      "pruned 1!\n",
      "current f1: 0.784895182508945\n",
      "new f1 score: 0.784895182508945\n",
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      "new f1 score: 0.8279953453210854\n",
      "did not prune\n",
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      "new f1 score: 0.855124576146248\n",
      "pruned 1!\n",
      "current f1: 0.855124576146248\n",
      "new f1 score: 0.855124576146248\n",
      "pruned 1!\n",
      "current f1: 0.855124576146248\n",
      "new f1 score: 0.855124576146248\n",
      "pruned 1!\n",
      "current f1: 0.855124576146248\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "new f1 score: 0.855124576146248\n",
      "pruned 1!\n",
      "current f1: 0.855124576146248\n",
      "new f1 score: 0.855124576146248\n",
      "pruned 1!\n",
      "current f1: 0.855124576146248\n",
      "new f1 score: 0.855124576146248\n",
      "pruned 1!\n",
      "current f1: 0.855124576146248\n",
      "new f1 score: 0.855124576146248\n",
      "pruned 1!\n",
      "current f1: 0.855124576146248\n",
      "new f1 score: 0.855124576146248\n",
      "pruned 1!\n",
      "current f1: 0.855124576146248\n",
      "new f1 score: 0.8596697788427112\n",
      "pruned 1!\n",
      "current f1: 0.8596697788427112\n",
      "new f1 score: 0.8596697788427112\n",
      "pruned 1!\n",
      "current f1: 0.8596697788427112\n",
      "new f1 score: 0.8596697788427112\n",
      "pruned 1!\n",
      "current f1: 0.8596697788427112\n",
      "new f1 score: 0.8596697788427112\n",
      "pruned 1!\n",
      "current f1: 0.8596697788427112\n",
      "new f1 score: 0.8594533773105202\n",
      "did not prune\n",
      "current f1: 0.8596697788427112\n",
      "new f1 score: 0.8596697788427112\n",
      "pruned 1!\n",
      "current f1: 0.8596697788427112\n",
      "new f1 score: 0.8596697788427112\n",
      "pruned 1!\n",
      "current f1: 0.8596697788427112\n",
      "new f1 score: 0.8596697788427112\n",
      "pruned 1!\n",
      "current f1: 0.8596697788427112\n",
      "new f1 score: 0.8596697788427112\n",
      "pruned 1!\n",
      "current f1: 0.8596697788427112\n",
      "new f1 score: 0.8596697788427112\n",
      "pruned 1!\n",
      "current f1: 0.8596697788427112\n",
      "new f1 score: 0.8596697788427112\n",
      "pruned 1!\n",
      "current f1: 0.8596697788427112\n",
      "new f1 score: 0.8596697788427112\n",
      "pruned 1!\n",
      "current f1: 0.8596697788427112\n",
      "new f1 score: 0.8553231637482578\n",
      "did not prune\n",
      "current f1: 0.8596697788427112\n",
      "new f1 score: 0.8596697788427112\n",
      "pruned 1!\n",
      "current f1: 0.8596697788427112\n",
      "new f1 score: 0.8596697788427112\n",
      "pruned 1!\n",
      "current f1: 0.8596697788427112\n",
      "new f1 score: 0.8596697788427112\n",
      "pruned 1!\n",
      "current f1: 0.8596697788427112\n",
      "new f1 score: 0.8596697788427112\n",
      "pruned 1!\n",
      "current f1: 0.8596697788427112\n",
      "new f1 score: 0.8596697788427112\n",
      "pruned 1!\n",
      "current f1: 0.8596697788427112\n",
      "new f1 score: 0.8742201353185335\n",
      "pruned 1!\n",
      "current f1: 0.8742201353185335\n",
      "new f1 score: 0.8742201353185335\n",
      "pruned 1!\n",
      "current f1: 0.8742201353185335\n",
      "new f1 score: 0.8742201353185335\n",
      "pruned 1!\n",
      "current f1: 0.8742201353185335\n",
      "new f1 score: 0.8742201353185335\n",
      "pruned 1!\n",
      "current f1: 0.8742201353185335\n",
      "new f1 score: 0.8742201353185335\n",
      "pruned 1!\n"
     ]
    }
   ],
   "source": [
    "#now prune the model\n",
    "#use print_path=False to not print\n",
    "model.prune_tree(validation,print_path=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "---RESULT METRICS---\n",
      "Precisions:   [0.85185185 0.97727273 0.89130435 0.82142857]\n",
      "Recalls:      [0.88461538 0.81132075 0.91111111 0.92      ]\n",
      "F1 Score:     [0.86792453 0.88659794 0.9010989  0.86792453]\n",
      "Avg Accuracy: 0.88\n"
     ]
    },
    {
     "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": [
    "#now use the pruned model on the test set again\n",
    "\n",
    "y_pred=model.predict(test[:,:-1])\n",
    "#evaluate\n",
    "cm=ev.confusion_matrix(test[:,-1],y_pred,plot=True)\n",
    "i=ev.get_metrics(test[:,-1], y_pred, printout=True)"
   ]
  }
 ],
 "metadata": {
  "colab": {
   "collapsed_sections": [],
   "name": "Copy of trees.ipynb",
   "provenance": []
  },
  "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": "3.7.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}