CS280.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "class CPS(object):    \n",
    "    def __init__(self, sigma, theta):\n",
    "        \n",
    "        import numpy as np\n",
    "        from itertools import permutations\n",
    "        from math import factorial\n",
    "        from scipy.stats import spearmanr, kendalltau\n",
    "\n",
    "\n",
    "        self.sigma = sigma\n",
    "        self.theta = theta \n",
    "        self.n = len(sigma)\n",
    "        # figure out better way to store this \n",
    "        self.p = np.array(list(permutations(sigma)))\n",
    "        self.idx_dict = {}\n",
    "\n",
    "\n",
    "    def compute_probabilities(self, distance_metric):\n",
    "        distance_metrics = {1: spearmanr, 2: kendalltau}\n",
    "        self.d = distance_metrics[distance_metric]\n",
    "        prob_dict = {}\n",
    "        for i, perm in enumerate(self.p):\n",
    "            self.idx_dict[i] = perm\n",
    "            prob_dict[i] = self.__cps_prob(np.array(perm))\n",
    "        # overwrite to be dictionary\n",
    "        self.p = prob_dict\n",
    "\n",
    "    def __cps_prob(self, perm):\n",
    "        num = lambda k, j: np.exp(self.theta * self.__dhat(self.__snk(perm, k, j)))\n",
    "        denom = lambda k: sum([num(k, j) for j in xrange(k, self.n)])\n",
    "        return np.prod([num(k, k) / denom(k) for k in xrange(self.n)])\n",
    "\n",
    "\n",
    "    def __snk(self, perm, k, j):\n",
    "        # todo: make this more efficient \n",
    "        lst = []\n",
    "        for arr in self.p: \n",
    "            if np.array_equal(arr[:k], perm[:k]) & (arr[j] == perm[j]): \n",
    "                lst.append(arr)\n",
    "        return lst\n",
    "                \n",
    "    def __dhat(self, snk):\n",
    "        # make this not a list comprehension :( \n",
    "        return sum([self.d(x, np.array(self.sigma)).correlation for x in snk]) / float(len(snk))\n",
    "    \n",
    "    def run_tests(): \n",
    "        # assert some stuff\n",
    "        return "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from mallows_model import mallowsfunctions as mf"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "with open('sushi3a.5000.10.order.txt', 'r') as f: \n",
    "    lst = []\n",
    "    for line in f.readlines()[1:]: \n",
    "        lst.append([int(x) for x in (line[5:]).split(' ')])\n",
    "    final = np.array(lst)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from collections import Counter"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import seaborn as sns \n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "plt.hist?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "plt.hist?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def bins_labels(bins, **kwargs):\n",
    "    bin_w = (max(bins) - min(bins)) / (len(bins) - 1)\n",
    "    plt.xticks(, ('Shrimp', 'Eel', 'Tuna-1', 'Squid', 'Urchin', 'Salmon', 'Egg', 'Tuna-2', 'Tuna-3', 'Cucumber'), **kwargs)\n",
    "    plt.xlim(bins[0], bins[-1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def plot(data): \n",
    "    plt.hist(data, align='mid', alpha = .8, edgecolor='black')\n",
    "    bins = np.arange(11)\n",
    "    bin_w = (max(bins) - min(bins)) / (len(bins) - 1)\n",
    "    plt.xticks(np.arange(min(bins)+bin_w/2, max(bins), bin_w), ('Shrimp', 'Eel', 'Tuna-1', 'Squid', 'Urchin', 'Salmon', 'Egg', 'Tuna-2', 'Tuna-3', 'Cucumber'), rotation=80)\n",
    "    plt.xlabel('Sushi Type')\n",
    "    sns.despine()\n",
    "    plt.show"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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2/5K7vxS7L05y98/Hny119x/XOoa+uPvW2HSxqE69XKYS2qOfA9YQ2oNvTfMG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\njFOiFxHJOCV6EZGM+/+UDGzfYGFDmgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x118cd9810>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(final[:,0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 104,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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KfNHdv21mn6t7uBN4CFiXfh66fURr1jzcUEy11efyXrOiUqlSrlSfUG5ea2cMV3a9rOIY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\nFxEpOCV6EZGCU6IXESm4/w/1NHLOfRByUwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x118d2fc50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(final[:,1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 105,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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Fr0rvgQPJOKnzbC+cNxD6gu8g/LzuAP6F0ByUuviZPwocFrs1HknoC/1mYHkW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\nUVIXEckRJXURkRxRUhcRyZH/D5xEt9XBE4TJAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x118d8a150>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(final[:,2])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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l7xIdbo30R8DKlOR3BN7q7v9sZiuAi9399Q0u/2Va4RhthRgqvBb4KNG82Wlm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\n9CIiOadELyKSc/8fTv2pp6SsuKUAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1186eaa50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(final[:, -1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def read_sushi(sushif): \n",
    "    '''\n",
    "        reads the sushi file dataset and returns numpy array of rankings \n",
    "    '''\n",
    "    with open(sushif, 'r') as f: \n",
    "        # skip the \n",
    "        f.next()\n",
    "        for line \n",
    "    "
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.13"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}