snowhork/coin-toss.ipynb

## coin-toss.ipynb
{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import math\n",
    "\n",
    "import torch\n",
    "import torch.distributions.constraints as constraints\n",
    "\n",
    "import pyro\n",
    "from pyro.optim import Adam\n",
    "from pyro.infer import SVI, Trace_ELBO\n",
    "import pyro.distributions as dist\n",
    "\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def model(data):\n",
    "    # set prior\n",
    "    alpha0 = torch.tensor(5.0)\n",
    "    beta0 = torch.tensor(5.0)\n",
    "    prior = dist.Beta(alpha0, beta0)\n",
    "\n",
    "    # sample z from the prior\n",
    "    z = pyro.sample(\"z\", prior)\n",
    "\n",
    "    with pyro.plate(\"data_plate\"):    \n",
    "        # observe data\n",
    "        pyro.sample(\"obs\", dist.Bernoulli(z), obs=data)\n",
    "\n",
    "def posterior():\n",
    "    alpha_q = pyro.param(\"alpha_q\", torch.tensor(15.0),\n",
    "                         constraint=constraints.positive)\n",
    "    beta_q = pyro.param(\"beta_q\", torch.tensor(15.0),\n",
    "                        constraint=constraints.positive)\n",
    "\n",
    "    return dist.Beta(alpha_q, beta_q)\n",
    "\n",
    "def guide(data):\n",
    "    # sample z from the posterior\n",
    "    pyro.sample(\"z\", posterior())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def append_data(data):\n",
    "    for _ in range(6):\n",
    "        data.append(1.0)\n",
    "    for _ in range(4):\n",
    "        data.append(0.0)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "....................mean: 0.557, std: 0.093\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAW4AAAD8CAYAAABXe05zAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "....................mean: 0.569, std: 0.089\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAW4AAAD8CAYAAABXe05zAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n24cAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "....................mean: 0.573, std: 0.087\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAW4AAAD8CAYAAABXe05zAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nRK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "....................mean: 0.573, std: 0.086\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAW4AAAD8CAYAAABXe05zAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "....................mean: 0.582, std: 0.085\n"
     ]
    },
    {
     "data": {
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      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n_steps = 2000\n",
    "\n",
    "pyro.set_rng_seed(101)\n",
    "\n",
    "data = []\n",
    "\n",
    "for _ in range(5):\n",
    "    pyro.clear_param_store()\n",
    "    append_data(data)\n",
    "    # setup the optimizer\n",
    "    adam_params = {\"lr\": 0.001, \"betas\": (0.90, 0.999)}\n",
    "    optimizer = Adam(adam_params)\n",
    "\n",
    "    # setup the inference algorithm\n",
    "    svi = SVI(model, guide, optimizer, loss=Trace_ELBO())\n",
    "\n",
    "    # do gradient steps\n",
    "    for step in range(n_steps):\n",
    "        svi.step(torch.tensor(data))\n",
    "        if step % 100 == 0:\n",
    "            print('.', end='')\n",
    "\n",
    "    inferred_mean = posterior().mean\n",
    "    inferred_std = math.sqrt(posterior().variance)\n",
    "\n",
    "    print(\"mean: %.3f, std: %.3f\"% (inferred_mean, inferred_std) )\n",
    "    \n",
    "    plt.hist([posterior().sample() for _ in range(1000)], bins=20, range=(0.05,1), density=True)\n",
    "    plt.plot([0.6, 0.6], [0, 5])\n",
    "    plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Python [default]",
   "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": 1
}