Expected Information Gain stuff.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Populating the interactive namespace from numpy and matplotlib\n"
     ]
    }
   ],
   "source": [
    "%pylab inline\n",
    "from itertools import combinations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def calculate_uncertainty(h_list):\n",
    "    h_set = set(h_list) # make a set that includes only the unique h's\n",
    "    h_dict = {h: h_list.count(h)/len(h_list) for h in h_set} # make a dict that pairs each unique h with a p(h)\n",
    "    uncertainties = [-h_dict[h]*log2(h_dict[h]) for h in h_set] #calculate uncertainty for each h\n",
    "    return sum(uncertainties)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "I([2, 4, 6, 8, 10, 12]) = 2.584962500721156\n",
      "I([2, 4, 7, 7, 10, 12]) = 2.2516291673878226\n",
      "I([2, 2, 2, 8, 8, 8]) = 1.0\n"
     ]
    }
   ],
   "source": [
    "H1 = [2, 4, 6, 8, 10, 12]\n",
    "H2 = [2, 4, 7, 7, 10, 12]\n",
    "H3 = [2, 2, 2, 8, 8, 8]\n",
    "for H in [H1, H2, H3]:\n",
    "    print(\"I({}) = {}\".format(H, calculate_uncertainty(H)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def calculate_i_g(h_list):\n",
    "    base_u = calculate_uncertainty(h_list)\n",
    "    e_u = 0\n",
    "    for h_prime in combinations(h_list,len(h_list)-1):\n",
    "        e_u += calculate_uncertainty(h_prime)\n",
    "    e_u /= len(h_list)\n",
    "    \n",
    "    return e_u - base_u"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "I_g([2, 4, 6, 8, 10, 12]) = -0.2630344058337939\n",
      "I_g([2, 4, 7, 7, 10, 12]) = -0.19636773916712702\n",
      "I_g([2, 2, 2, 8, 8, 8]) = -0.029049405545331308\n"
     ]
    }
   ],
   "source": [
    "for H in [H1, H2, H3]:\n",
    "    print(\"I_g({}) = {}\".format(H, calculate_i_g(H)))"
   ]
  }
 ],
 "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": "3.5.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}