Raw File
{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "MCMC and Sparse MCMC in GPflow\n",
    "--\n",
    "\n",
    "*James Hensman, 2015-16*\n",
    "\n",
    "In this notebook, we illustrate 'Exponential Regression'. The model is\n",
    "$$ \n",
    "\\theta \\sim p(\\theta)\\\\\n",
    "f \\sim \\mathcal {GP}(0, k(x, x'; \\theta))\\\\\n",
    "f_i = f(x_i)\\\\\n",
    "y_i \\sim \\mathcal {Exp} (e^{f_i})\n",
    "$$\n",
    "\n",
    "We'll use MCMC to deal with both the kernel parameters $\\theta$ and the latent function values $f$.\n",
    "\n",
    "We fit two models. In the first, we do exact inference with MCMC. In the second, sparse infrence with MCMC."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import GPflow\n",
    "\n",
    "import numpy as np\n",
    "from matplotlib import pyplot as plt\n",
    "%matplotlib inline\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "X = np.linspace(-3,3,100)\n",
    "Y = np.random.exponential(np.sin(X)**2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "#build the first model\n",
    "k = GPflow.kernels.Matern32(1,ARD=False) + GPflow.kernels.Bias(1)\n",
    "l = GPflow.likelihoods.Exponential()\n",
    "m1 = GPflow.gpmc.GPMC(X[:,None], Y[:,None], k, l)\n",
    "\n",
    "#build the second model\n",
    "k = GPflow.kernels.Matern32(1,ARD=False) + GPflow.kernels.Bias(1)\n",
    "l = GPflow.likelihoods.Exponential()\n",
    "m2 = GPflow.sgpmc.SGPMC(X[:,None], Y[:,None], k, l, Z=X[::5,None])\n",
    "\n",
    "for m in [m1, m2]:\n",
    "    m.kern.matern32.lengthscales.prior = GPflow.priors.Gamma(1., 1.)\n",
    "    m.kern.matern32.variance.prior = GPflow.priors.Gamma(1.,1.)\n",
    "    m.kern.bias.variance.prior = GPflow.priors.Gamma(1.,1.)\n",
    "    \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table id='parms' width=100%><tr><td>Name</td><td>values</td><td>prior</td><td>constriant</td></tr><tr><td>kern.matern32.variance</td><td>[ 1.]</td><td>Ga([ 1.],[ 1.])</td><td>+ve</td></tr><tr><td>kern.matern32.lengthscales</td><td>[ 1.]</td><td>Ga([ 1.],[ 1.])</td><td>+ve</td></tr><tr><td>kern.bias.variance</td><td>[ 1.]</td><td>Ga([ 1.],[ 1.])</td><td>+ve</td></tr></table>"
      ],
      "text/plain": [
       "<GPflow.kernels.Add at 0x7fa1a474a290>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Here are the two models\n",
    "m1.kern"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table id='parms' width=100%><tr><td>Name</td><td>values</td><td>prior</td><td>constriant</td></tr><tr><td>kern.matern32.variance</td><td>[ 1.]</td><td>Ga([ 1.],[ 1.])</td><td>+ve</td></tr><tr><td>kern.matern32.lengthscales</td><td>[ 1.]</td><td>Ga([ 1.],[ 1.])</td><td>+ve</td></tr><tr><td>kern.bias.variance</td><td>[ 1.]</td><td>Ga([ 1.],[ 1.])</td><td>+ve</td></tr></table>"
      ],
      "text/plain": [
       "<GPflow.kernels.Add at 0x7fa1a474a690>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "m2.kern"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "compiling tensorflow function...\n",
      "done\n",
      "optimization terminated, setting model state\n",
      "compiling tensorflow function...\n",
      "done\n",
      "optimization terminated, setting model state\n"
     ]
    }
   ],
   "source": [
    "for m in [m1, m2]:\n",
    "    r = m.optimize()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table id='parms' width=100%><tr><td>Name</td><td>values</td><td>prior</td><td>constriant</td></tr><tr><td>kern.matern32.variance</td><td>[ 10.66998732]</td><td>Ga([ 1.],[ 1.])</td><td>+ve</td></tr><tr><td>kern.matern32.lengthscales</td><td>[ 0.04422586]</td><td>Ga([ 1.],[ 1.])</td><td>+ve</td></tr><tr><td>kern.bias.variance</td><td>[ 1.35419367]</td><td>Ga([ 1.],[ 1.])</td><td>+ve</td></tr></table>"
      ],
      "text/plain": [
       "<GPflow.kernels.Add at 0x7fa1a474a290>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Now have a look at the kernel values\n",
    "m1.kern"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table id='parms' width=100%><tr><td>Name</td><td>values</td><td>prior</td><td>constriant</td></tr><tr><td>kern.matern32.variance</td><td>[ 3.23145503]</td><td>Ga([ 1.],[ 1.])</td><td>+ve</td></tr><tr><td>kern.matern32.lengthscales</td><td>[ 0.57548758]</td><td>Ga([ 1.],[ 1.])</td><td>+ve</td></tr><tr><td>kern.bias.variance</td><td>[ 1.07981782]</td><td>Ga([ 1.],[ 1.])</td><td>+ve</td></tr></table>"
      ],
      "text/plain": [
       "<GPflow.kernels.Add at 0x7fa1a474a690>"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "m2.kern"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Iteration:  100 \t Acc Rate:  88.0 %\n",
      "Iteration:  200 \t Acc Rate:  88.0 %\n",
      "Iteration:  300 \t Acc Rate:  92.0 %\n",
      "Iteration:  400 \t Acc Rate:  87.0 %\n",
      "Iteration:  500 \t Acc Rate:  86.0 %\n",
      "Iteration:  600 \t Acc Rate:  90.0 %\n",
      "Iteration:  700 \t Acc Rate:  87.0 %\n",
      "Iteration:  800 \t Acc Rate:  78.0 %\n",
      "Iteration:  900 \t Acc Rate:  86.0 %\n",
      "Iteration:  1000 \t Acc Rate:  92.0 %\n",
      "Iteration:  100 \t Acc Rate:  84.0 %\n",
      "Iteration:  200 \t Acc Rate:  91.0 %\n",
      "Iteration:  300 \t Acc Rate:  91.0 %\n",
      "Iteration:  400 \t Acc Rate:  85.0 %\n",
      "Iteration:  500 \t Acc Rate:  94.0 %\n",
      "Iteration:  600 \t Acc Rate:  92.0 %\n",
      "Iteration:  700 \t Acc Rate:  81.0 %\n",
      "Iteration:  800 \t Acc Rate:  87.0 %\n",
      "Iteration:  900 \t Acc Rate:  88.0 %\n",
      "Iteration:  1000 \t Acc Rate:  75.0 %\n"
     ]
    }
   ],
   "source": [
    "# run the sampler (why is this so slow?)\n",
    "samples = (m1.sample(1000, verbose=1, epsilon = 0.08),\n",
    "           m2.sample(1000, verbose=1, epsilon = 0.08))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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LnYbUuHmNYQu6OV6KmYOVOk8LXbfpPCRMCcrcMcvouChYFaKWHU0st6MqtYPz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wJijtt8LzXk9ZGAOtxrfeTk5AUBi2jQPQHOt/En9AaoQ/vZPMwx09txFg6kexoj5gIt/WBaFKHX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\nkYgc5xIB6ohEJCIROc7l/wEW27vZsgFtnAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fa19c278150>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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lcxsbo+kRe/Gxk9yqrfZHOeVNtYPD9pqfByYmzLxrbDSnuWhWQVNR8/PA9LS0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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fa15d032190>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#make some predictions\n",
    "for m, ss in zip([m1, m2], samples):\n",
    "    plt.figure()\n",
    "    xx = np.linspace(-4,4,100)[:,None]\n",
    "    ys = []\n",
    "    for s in ss:\n",
    "        m.set_state(s)\n",
    "        ys.append(m.predict_y(xx)[0])\n",
    "        plt.plot(xx, ys[-1], 'b', alpha=0.01, lw=2)\n",
    "    plt.plot(X, Y, 'kx', mew=2)\n",
    "    plt.ylim(0, 6)\n",
    "\n",
    "    \n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.11"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}
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