jonas-eschle/binned_chi2.ipynb

## binned_chi2.ipynb
{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This notebook tries to reproduce the plot shown in [a presention](https://indico.cern.ch/event/400895/contributions/958123) by [Alex Rogozhnikov](https://github.com/arogozhnikov) on “Reweighting distributions with gradient boosting”.\n",
    "\n",
    "Here's the plot in question:\n",
    "\n",
    "<img width=\"400px\" src=\"http://i.imgur.com/mz1mLio.png\">\n",
    "\n",
    "It shows two distributions on two quantities as histograms on the top, and the distribution of a “symmetrized binned $\\chi^{2}$” on the bottom, defined on the previous slide as $$\\chi^{2} = \\sum_{\\text{bin}} \\frac{(w_{\\text{original,bin}} - w_{\\text{target,bin}})^2} {w_{\\text{original,bin}} + w_{\\text{target,bin}}} $$.\n",
    "\n",
    "Looking at the code from the [`hep_ml` package](https://github.com/arogozhnikov/hep_ml) that the presentation is advertising, I couldn't see where this was computed (looking in the [`GBReweighter`](https://github.com/arogozhnikov/hep_ml/blob/670e184189fa3a09367e8f3b9ec3bfdcbac38b50/hep_ml/reweight.py#L180) and the [`ReweightLossFunction`](https://github.com/arogozhnikov/hep_ml/blob/670e184189fa3a09367e8f3b9ec3bfdcbac38b50/hep_ml/losses.py#L599-L605)), so I wanted to check that I understood what the $\\chi^{2}$ really meant."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "%config InlineBackend.figure_format='retina'\n",
    "\n",
    "from __future__ import division\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We'll draw a bunch of random numbers from two normal distributions, both of unit width, one centered at 1 and the other at -1. Later, we'll draw these in the range (-3, 3)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "a = np.random.normal(1, 1, 5000)\n",
    "b = np.random.normal(-1, 1, 5000)\n",
    "range = (-3, 3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "I think the ‘sum over bins’ in the $\\chi^{2}$ defintions refers to the partitions created by the split along the axis. So, compute the $\\chi^{2}$ at each possible split point as the sum of two components (one for the partition above the split value, and another for the one below). Each component is the square of the difference of the partition populations between the two samples, divided by the sum of the populations of the two samples.\n",
    "\n",
    "We are assuming unit weights here. For weighted samples, one would take ‘the population of a sample in a partition’ to be the sum of the weights."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "nx = 100\n",
    "xs = np.linspace(range[0], range[1], num=nx)\n",
    "chi2 = []\n",
    "for boundary in xs:\n",
    "    na_lt = np.sum(a < boundary)\n",
    "    na_gt = np.sum(a > boundary)\n",
    "    nb_lt = np.sum(b < boundary)\n",
    "    nb_gt = np.sum(b > boundary)\n",
    "\n",
    "    # Compute total chi^2 as sum of chi^2 for each partition\n",
    "    c = np.square(na_lt - nb_lt)/(na_lt + nb_lt)\n",
    "    c += np.square(na_gt - nb_gt)/(na_gt + nb_gt)\n",
    "    # Normalise the result by the square of the number of boundaries divide by \n",
    "    # the number of partitions\n",
    "    c /= nx*nx/2\n",
    "    chi2.append(c)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We'll also find the split that maximises the $\\chi^{2}$ function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "split = xs[np.argmax(chi2)]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally, we'll plot the two samples as histograms, and then draw the $\\chi^{2}$ values we computed at each split value."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
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giaAMAAAAAJIIygAAAAAgiaAMAAAAAJIIygAAAAAgiaAMAAAAAJIIygAAAAAgiaAMAAAA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\nSZIkSZIEGJRJkiRJkiRJAPwf5Fb9nP0UpeQAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f3e781ebd10>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 503,
       "width": 613
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(10, 8))\n",
    "ax1 = fig.add_subplot(2, 1, 1)\n",
    "ax1.hist(a, range=range, bins=25, normed=True, color='green', alpha=0.5)\n",
    "ax1.set_title('Distributions')\n",
    "ax1.hist(b, range=range, bins=25, normed=True, color='blue', alpha=0.5)\n",
    "ax2 = fig.add_subplot(2, 1, 2)\n",
    "ax2.plot(xs, chi2, color='black')\n",
    "ax2.plot([split, split], [0, 1], color='red', label=r'Maximum $\\chi^{{2}} = {0:.2f}$'.format(np.max(chi2)))\n",
    "ax2.legend()\n",
    "ax2.set_xlabel('Split value')\n",
    "ax2.set_ylabel('$\\chi^{2}$');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This looks quite similar to Alex's plot, so maybe I've got the right idea."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
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