ForwardBackward.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import torch"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 125,
   "metadata": {},
   "outputs": [],
   "source": [
    "T = 10\n",
    "V = 2\n",
    "\n",
    "# log potentials\n",
    "unary = torch.rand(T, V)\n",
    "binary = torch.rand(T, V, V)\n",
    "\n",
    "unary.fill_(1)\n",
    "\n",
    "# psi^T_t (ignoring the timestep)\n",
    "binary[:, 0, 0] = 1\n",
    "binary[:, 1, 1] = 1\n",
    "binary[:, 1, 0] = 0.1\n",
    "binary[:, 0, 1] = 0.1\n",
    "\n",
    "# Fix two values. \n",
    "unary[2][0] = 100\n",
    "unary[8][1] = 100"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 126,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Forward\n",
    "m_f = torch.Tensor(T, V) \n",
    "bel_f = torch.Tensor(T, V) \n",
    "bel_f[0] = 1 / 2.\n",
    "for t in range(1, T):\n",
    "    m_f[t] = torch.mm(binary[t], bel_f[t-1].unsqueeze(1))\n",
    "    bel_f[t] = unary[t] * m_f[t]\n",
    "    bel_f[t] = bel_f[t] / bel_f[t].sum()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 127,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Backward\n",
    "m_b = torch.Tensor(T, V) \n",
    "bel = torch.Tensor(T, V) \n",
    "bel[T-1] = 1 /2.\n",
    "for t in range(T-2, -1, -1):\n",
    "    m_b[t] = torch.mm(binary[t].transpose(0, 1), \n",
    "            (unary[t+1] * bel[t+1]).unsqueeze(1))\n",
    "    bel[t] = m_b[t] * bel_f[t]\n",
    "    bel[t] = bel[t] / bel[t].sum()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 128,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x7f8594319c88>"
      ]
     },
     "execution_count": 128,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAW4AAABlCAYAAABtEgn4AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nnTHcktSZfwPLpj7sp/ml6QAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f859466bd30>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Draw\n",
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "plt.imshow(unary.numpy().T)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 129,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x7f8594270ef0>"
      ]
     },
     "execution_count": 129,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAW4AAABlCAYAAABtEgn4AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f85942ab400>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.imshow(bel.numpy().T)"
   ]
  }
 ],
 "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": "3.5.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}