optimizing_ranknet_loss.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import theano\n",
    "import numpy as np\n",
    "from theano import tensor as T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "actual_y = T.vector()\n",
    "predicted_y = T.vector()\n",
    "query_id = T.vector()\n",
    "\n",
    "qi_equals_qj = T.eq(query_id[:,None], query_id[None,:])\n",
    "\n",
    "yi_lessthan_yj = actual_y[:,None] < actual_y[None,:]\n",
    "\n",
    "loss_i_j = T.exp(predicted_y[:,None] - predicted_y[None,:]) #or any other loss you think of\n",
    "\n",
    "loss = T.sum(qi_equals_qj * yi_lessthan_yj * loss_i_j)\n",
    "\n",
    "grad = T.grad(loss,predicted_y)\n",
    "\n",
    "hess = T.diagonal(T.hessian(loss,predicted_y))\n",
    "\n",
    "get_loss_and_derivatives = theano.function([predicted_y,actual_y,query_id],[loss,grad,hess])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Sanity check:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "L = 60.995\n",
      "L = 14.708\n",
      "L = 5.410\n",
      "L = 2.407\n",
      "L = 1.147\n",
      "L = 0.564\n",
      "L = 0.282\n",
      "L = 0.142\n",
      "L = 0.072\n",
      "L = 0.037\n",
      "[  1.20087573e-04   6.51633115e-02   0.00000000e+00   3.95972825e-01\n",
      "   3.95969812e-01   3.95976326e-01   7.07454456e-01   7.07450525e-01\n",
      "   1.00000000e+00   4.00683058e-02   4.78740161e-01   9.34306279e-01\n",
      "   9.75975944e-01]\n"
     ]
    }
   ],
   "source": [
    "#in action\n",
    "\n",
    "actual_y = np.array([0,0,0,1,1,1,2,2,3,0,1,2,2],'float32')\n",
    "query_id = np.array([1,1,1,1,1,1,1,1,1,2,2,2,2],'float32')\n",
    "#start with random guesses\n",
    "predicted_y = np.random.randn(len(actual_y))\n",
    "for i in range(100):\n",
    "    \n",
    "    L,dL,ddL = get_loss_and_derivatives(predicted_y,actual_y,query_id)\n",
    "    \n",
    "    if i%10==0:\n",
    "        print 'L = %.3f'%L\n",
    "    \n",
    "    predicted_y = predicted_y - 0.1 * dL / ddL\n",
    "        \n",
    "\n",
    "#convert all values into [0,1] for human readability\n",
    "humanize = lambda a: (a - a.min()) / (a.max() - a.min())\n",
    "print humanize(predicted_y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x7fc98710dbd0>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/jheuristic/anaconda2/lib/python2.7/site-packages/matplotlib/collections.py:590: FutureWarning: elementwise comparison failed; returning scalar instead, but in the future will perform elementwise comparison\n",
      "  if self._edgecolors == str('face'):\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fc98babab90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from matplotlib import pyplot as plt\n",
    "%matplotlib inline\n",
    "plt.scatter(humanize(predicted_y),humanize(actual_y),c=query_id)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Notes\n",
    "\n",
    "This implementation is __HIGHLY INEFFICIENT__ for multiple query ids. If ever use it, one is invited to split data into query IDs and use this less inefficient implementation.\n",
    "\n",
    "In fact, the one below is also \"bad\" because it computes all pairs of Qi,Qj while a more effective algorithm should only consider those of different actual_y. \n",
    "Also, computing second derivatives the proposed way is inefficient as you compute the square matrix and that take diagonal.\n",
    "\n",
    "\n",
    "But it's fucken' 2 AM and i wanna sleep, so sorry, i'm out."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "actual_y = T.vector()\n",
    "predicted_y = T.vector()\n",
    "\n",
    "yi_lessthan_yj = actual_y[:,None] < actual_y[None,:]\n",
    "loss_i_j = T.exp(predicted_y[:,None] - predicted_y[None,:])\n",
    "\n",
    "loss = T.sum(yi_lessthan_yj * loss_i_j)\n",
    "\n",
    "grad = T.grad(loss,predicted_y)\n",
    "\n",
    "hess = T.diagonal(T.hessian(loss,predicted_y))\n",
    "\n",
    "get_loss_and_derivatives_per_Qid = theano.function([predicted_y,actual_y],[loss,grad,hess])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10 loops, best of 3: 199 ms per loop\n"
     ]
    }
   ],
   "source": [
    "%%timeit -n 10\n",
    "actual_y = np.array([0,0,0,1,1,1,2,2,3,0,1,2,2]*20,'float32')\n",
    "predicted_y = np.random.randn(len(actual_y))\n",
    "\n",
    "get_loss_and_derivatives_per_Qid(predicted_y,actual_y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
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