{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from vowpalwabbit import pyvw\n",
    "\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Generate some count data that has poisson distribution \n",
    "# z ~ poisson(x + y), x \\in [0,10), y \\in [0,10)\n",
    "x = np.random.choice(range(0,10), 100)\n",
    "y = np.random.choice(range(0,10), 100)\n",
    "z = np.random.poisson(x + y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We will model this data in two ways\n",
    "* log transform the labels and use linear prediction (square loss)\n",
    "* model it directly using poisson loss\n",
    "\n",
    "The first model predicts mean(log(label)) the second predicts log(mean(label)). Due to [Jensen's inequality](https://en.wikipedia.org/wiki/Jensen's_inequality), the first approach produces systematic negative bias"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Train log-transform model\n",
    "training_samples = []\n",
    "logz = np.log(0.001 + z)\n",
    "vw = pyvw.vw(\"-b 2 --loss_function squared -l 0.1 --holdout_off -f vw.log.model --readable_model vw.readable.log.model\")\n",
    "for i in range(len(logz)):\n",
    "    training_samples.append(\"{label} | x:{x} y:{y}\".format(label=logz[i], x=x[i], y=y[i]))\n",
    "# Do hundred passes over the data and store the model in vw.log.model\n",
    "for iteration in range(100):\n",
    "    for i in range(len(training_samples)):\n",
    "        vw.learn(training_samples[i])\n",
    "vw.finish()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Generate predictions from the log-transform model\n",
    "vw = pyvw.vw(\"-i vw.log.model -t\")\n",
    "log_predictions = [vw.predict(sample) for sample in training_samples]\n",
    "# Measure bias in the log-domain\n",
    "log_bias = np.mean(log_predictions - logz)\n",
    "bias = np.mean(np.exp(log_predictions) - z)\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Although the model is relatively unbiased in the log-domain where we trained our model, in the original domain there is underprediction as we expected from Jensenn's inequality "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Train original domain model using poisson regression\n",
    "training_samples = []\n",
    "vw = pyvw.vw(\"-b 2 --loss_function poisson -l 0.1 --holdout_off -f vw.poisson.model --readable_model vw.readable.poisson.model\")\n",
    "for i in range(len(z)):\n",
    "    training_samples.append(\"{label} | x:{x} y:{y}\".format(label=z[i], x=x[i], y=y[i]))\n",
    "# Do hundred passes over the data and store the model in vw.log.model\n",
    "for iteration in range(100):\n",
    "    for i in range(len(training_samples)):\n",
    "        vw.learn(training_samples[i])\n",
    "vw.finish()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Generate predictions from the poisson model\n",
    "vw = pyvw.vw(\"-i vw.poisson.model\")\n",
    "poisson_predictions = [np.exp(vw.predict(sample)) for sample in training_samples]\n",
    "poisson_bias = np.mean(poisson_predictions - z)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x115741710>"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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IXrH/pwHCl9aXJdbtS5H4GNWtvujuUwndL95CdDOoTMypZ90ZEnE++rwaW6yslInT5V5H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\nRK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1133e3390>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "plt.figure(figsize=(18,6))\n",
    "# Measure bias in the log-domain\n",
    "plt.subplot(131)\n",
    "plt.plot(logz, log_predictions, '.')\n",
    "plt.plot(logz, logz, 'r')\n",
    "plt.title('Log-domain bias:%f'%(log_bias))\n",
    "plt.xlabel('label')\n",
    "plt.ylabel('prediction')\n",
    "\n",
    "plt.subplot(132)\n",
    "plt.plot(z, np.exp(log_predictions), '.')\n",
    "plt.plot(z, z, 'r')\n",
    "plt.title('Original-domain bias:%f'%(bias))\n",
    "plt.xlabel('label')\n",
    "plt.ylabel('prediction')\n",
    "\n",
    "plt.subplot(133)\n",
    "plt.plot(z, poisson_predictions, '.')\n",
    "plt.plot(z, z, 'r')\n",
    "plt.title('Poisson bias:%f'%(poisson_bias))\n",
    "plt.xlabel('label')\n",
    "plt.ylabel('prediction')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
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