Population Coding.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Exerpimenting with population coding, binning and distributions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 795,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "import math\n",
    "\n",
    "from ipywidgets import interact"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1088,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "N = 100\n",
    "F_max = 1.0\n",
    "sigma = N * 0.01\n",
    "bin_size = 4\n",
    "width = ((sigma * 3.0) * bin_size) / N # https://en.wikipedia.org/wiki/68–95–99.7_rule\n",
    "scale = (1.0 - (width * 2.0))\n",
    "\n",
    "def f(v): # [0, 1]\n",
    "    v = v * scale\n",
    "    v = v + width\n",
    "    x = round(v * N)\n",
    "    return x # [0, N]\n",
    "\n",
    "def f_inv(x): # [0, N]\n",
    "    v = x / N\n",
    "    v = v - width\n",
    "    v = v / scale\n",
    "    return v # [0, 1]\n",
    "\n",
    "def bin(x):\n",
    "    return round(x / bin_size)\n",
    "\n",
    "def fill(p, v):\n",
    "    for i in range(0, N):\n",
    "        d = bin(i - f(v))\n",
    "        r = F_max * math.exp(-1.0 * ((d**2) / (2.0 * (sigma**2))))\n",
    "        p[i] = r    \n",
    "\n",
    "def vote(population):\n",
    "    num = 0.0\n",
    "    for i in range(0, N):\n",
    "        num += f_inv(i) * population[i]\n",
    "    den = 0.0\n",
    "    for i in range(0, N):\n",
    "        den += population[i]\n",
    "    return num / den"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1089,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "val 0.0 vote 0.000224513370764 expect 0.0 err 0.000224513370764\n",
      "val 0.1 vote 0.10526326262 expect 0.105263157895 err 1.04725373512e-07\n",
      "val 0.2 vote 0.197368421054 expect 0.197368421053 err 1.70932712429e-12\n",
      "val 0.3 vote 0.302631578947 expect 0.302631578947 err 2.22044604925e-16\n",
      "val 0.4 vote 0.394736842105 expect 0.394736842105 err 2.22044604925e-16\n",
      "val 0.5 vote 0.5 expect 0.5 err 2.22044604925e-16\n",
      "val 0.6 vote 0.605263157895 expect 0.605263157895 err 2.22044604925e-16\n",
      "val 0.7 vote 0.697368421053 expect 0.697368421053 err 2.22044604925e-16\n",
      "val 0.8 vote 0.802631578945 expect 0.802631578947 err 2.51731968604e-12\n",
      "val 0.9 vote 0.89473663992 expect 0.894736842105 err 2.02185518328e-07\n",
      "val 1.0 vote 0.999600508498 expect 1.0 err 0.000399491502079\n"
     ]
    }
   ],
   "source": [
    "bin_size = 4\n",
    "\n",
    "for v in np.arange(0.0, 1.1, 0.1):\n",
    "    population = np.zeros(N)\n",
    "\n",
    "    fill(population, v)\n",
    "    voted = vote(population)\n",
    "\n",
    "    expected = f_inv(f(v))\n",
    "    err = abs(expected - voted)\n",
    "    print(\"val\", v, \"vote\", voted, \"expect\", expected, \"err\", err)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1090,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[12.0, 20.0, 27.0, 35.0, 42.0, 50.0, 58.0, 65.0, 73.0, 80.0, 88.0]\n",
      "[0.0, 0.10526315789473686, 0.19736842105263161, 0.30263157894736842, 0.39473684210526316, 0.5, 0.60526315789473684, 0.69736842105263164, 0.80263157894736836, 0.89473684210526316, 1.0]\n"
     ]
    }
   ],
   "source": [
    "print([f(v) for v in np.arange(0.0, 1.1, 0.1)])\n",
    "print([f_inv(f(v)) for v in np.arange(0.0, 1.1, 0.1)])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1092,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
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    },
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     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x115146d30>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA58AAABaCAYAAAA/3OLmAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11463d588>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x115262358>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA58AAABaCAYAAAA/3OLmAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nfyqyHGuMZTrkAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x114187160>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x114b8f9b0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA58AAABaCAYAAAA/3OLmAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x115d05128>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x115f0bf28>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA58AAABaCAYAAAA/3OLmAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x114cbdb70>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA58AAABaCAYAAAA/3OLmAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nUuH+DwVQHGux3DIgAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1152192e8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA58AAABaCAYAAAA/3OLmAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nOItPSZIkSVLh/g8r+bDeKa1JNAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x115fbf7b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "for v in np.arange(0.0, 1.1, 0.1):\n",
    "    population = np.zeros(N)\n",
    "    fill(population, v)\n",
    "    df = pd.DataFrame(population)\n",
    "    df.plot(style=\".\", figsize=(16, 1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "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": "3.4.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}