Latent Ability Models.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 0.  0.  1.]\n",
      " [ 1.  0.  1.]\n",
      " [ 0.  0.  0.]]\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "\n",
    "def sigmoid(t):\n",
    "    return np.exp(t)/(1+np.exp(t))\n",
    "\n",
    "\n",
    "\n",
    "x_true = np.array([19, 23, 15])\n",
    "N = len(x_true)\n",
    "beta = 0.05\n",
    "\n",
    "R = np.zeros((N,N))\n",
    "\n",
    "for i in range(N):\n",
    "    for j in range(N):\n",
    "        if i > j:\n",
    "            delta = x_true[i] - x_true[j]\n",
    "            p = sigmoid(beta*delta)\n",
    "            r = np.random.choice([0,1],p=[1-p, p])\n",
    "            R[i,j] = r\n",
    "            R[j, i] = 1-r\n",
    "                        \n",
    "print(R)\n",
    "\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Plot the histograms x_samp for each player apart from player 0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
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      "5\n",
      "14\n",
      "49\n",
      "68\n",
      "46\n",
      "41\n",
      "3\n",
      "41\n",
      "83\n",
      "24\n",
      "3\n",
      "4\n",
      "22\n",
      "0\n",
      "10\n",
      "4\n",
      "27\n",
      "9\n",
      "29\n",
      "52\n",
      "23\n",
      "33\n",
      "37\n",
      "14\n",
      "13\n",
      "3\n",
      "27\n",
      "50\n",
      "27\n",
      "13\n",
      "7\n",
      "28\n",
      "49\n",
      "14\n",
      "12\n",
      "4\n",
      "2\n",
      "58\n",
      "29\n",
      "45\n",
      "38\n",
      "66\n",
      "41\n",
      "0\n",
      "8\n",
      "33\n",
      "16\n",
      "26\n",
      "10\n",
      "55\n",
      "7\n",
      "23\n",
      "21\n",
      "17\n",
      "30\n",
      "62\n",
      "25\n",
      "16\n"
     ]
    }
   ],
   "source": [
    "EPOCH = 1000\n",
    "x = np.array([19, 89, 27])\n",
    "\n",
    "\n",
    "for epoch in range(EPOCH):\n",
    "    for j in range(1,N):\n",
    "        x1 = np.arange(0, 100)\n",
    "        LL = np.zeros((len(x1)))\n",
    "\n",
    "        for i in range(N):\n",
    "            if i != j:\n",
    "                delta = x1 - x[i]\n",
    "                lp = np.log(sigmoid(delta*beta))\n",
    "                lp0 = np.log(1-sigmoid(delta*beta))\n",
    "                LL += R[j,i]*lp + R[i,j]*lp0\n",
    "\n",
    "        pp = np.exp(LL - np.max(LL))\n",
    "        pp = pp/np.sum(pp)\n",
    "        x_samp = np.random.choice(range(0,100),p=pp)\n",
    "        x[j] = x_samp\n",
    "\n",
    "        if j==2:\n",
    "            print(x_samp)\n",
    "        "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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wJnAY8FG9c7zvTeto4OfAgcAawJHAkRFx0MwTvOfzrTN54cGBwP9M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\nAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1105ab4a8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pylab as plt\n",
    "\n",
    "plt.plot(np.exp(LL))\n",
    "plt.show()"
   ]
  }
 ],
 "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": "3.5.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}