taku-y/advi_minibatch.ipynb

## advi_minibatch.ipynb
{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import sys\n",
    "sys.path.insert(0, '/Users/taku-y/git/github/taku-y/pymc3/')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Populating the interactive namespace from numpy and matplotlib\n"
     ]
    }
   ],
   "source": [
    "%pylab inline\n",
    "import numpy as np\n",
    "from scipy import stats\n",
    "import pymc3 as pm\n",
    "import seaborn as sns\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Total sample size is 1000, 10 times larger than the full-batch example (advi.ipynb). "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "total_size = 1000\n",
    "data = np.random.randn(total_size)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To make observed variables be mini-batched, give tensors to their 'observed' arguments. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Applied log-transform to sd and added transformed sd_log to model.\n"
     ]
    }
   ],
   "source": [
    "import theano.tensor as T\n",
    "\n",
    "data_t = T.vector()\n",
    "data_t.tag.test_value=np.zeros(1,)\n",
    "\n",
    "with pm.Model() as model:\n",
    "    mu = pm.Normal('mu', mu=0, sd=1, testval=0)\n",
    "    sd = pm.HalfNormal('sd', sd=1)\n",
    "    n = pm.Normal('n', mu=mu, sd=sd, observed=data_t)\n",
    "    \n",
    "minibatch_RVs = [n]\n",
    "minibatch_tensors = [data_t]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Create a generator for mini-batches of size 100. The mini-batches are consumed in the advi function. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from copy import deepcopy\n",
    "\n",
    "def create_minibatch(data):\n",
    "    data_ = deepcopy(data)\n",
    "    \n",
    "    while True:\n",
    "        data_ = np.roll(data_, 100, axis=0)\n",
    "        yield data_[:100]\n",
    "\n",
    "minibatches = [create_minibatch(data)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false,
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Iteration 0 [0%]: ELBO = -18199.42\n",
      "Iteration 4000 [10%]: ELBO = -1589.7\n",
      "Iteration 8000 [20%]: ELBO = -1659.69\n",
      "Iteration 12000 [30%]: ELBO = -1506.56\n",
      "Iteration 16000 [40%]: ELBO = -1523.74\n",
      "Iteration 20000 [50%]: ELBO = -1515.66\n",
      "Iteration 24000 [60%]: ELBO = -1517.05\n",
      "Iteration 28000 [70%]: ELBO = -1516.15\n",
      "Iteration 32000 [80%]: ELBO = -1521.5\n",
      "Iteration 36000 [90%]: ELBO = -1525.87\n",
      "Finished [100%]: ELBO = -1471.46\n"
     ]
    }
   ],
   "source": [
    "means, sds, elbos = pm.variational.advi_minibatch(\n",
    "    model=model, n=40000, minibatch_tensors=minibatch_tensors, \n",
    "    minibatch_RVs=minibatch_RVs, minibatches=minibatches, \n",
    "    total_size=total_size\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Applied log-transform to sd and added transformed sd_log to model.\n",
      " [-----------------100%-----------------] 5000 of 5000 complete in 1.5 sec"
     ]
    }
   ],
   "source": [
    "with pm.Model():\n",
    "    mu = pm.Normal('mu', mu=0, sd=1, testval=0)\n",
    "    sd = pm.HalfNormal('sd', sd=1)\n",
    "    n = pm.Normal('n', mu=mu, sd=sd, observed=data)\n",
    "    step = pm.NUTS()\n",
    "    trace = pm.sample(5000, step)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-0.00800816920208\n",
      "0.00890622414792\n",
      "0.0323732874514\n",
      "0.0226791481698\n"
     ]
    }
   ],
   "source": [
    "print(trace['mu'].mean())\n",
    "print(trace['sd_log'].mean())\n",
    "print(trace['mu'].std())\n",
    "print(trace['sd_log'].std())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The posterior variance is smaller than the full-batch example because of the total sample size. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x153b4ce90>"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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vZvt8nQOY8zmCQT914fDUfxDTZFdnF5GBEO5KF/vGDvBn4U+c/Q+3wPTZLG+L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\nDy5FdEYDfAOGAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x153aef090>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ax = sns.distplot(trace['mu'], label='NUTS')\n",
    "xlim = ax.get_xlim()\n",
    "x = np.linspace(xlim[0], xlim[1], 100)\n",
    "y = stats.norm(means['mu'], sds['mu']).pdf(x)\n",
    "ax.plot(x, y, label='ADVI')\n",
    "ax.set_title('mu')\n",
    "ax.legend(loc=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x153fe9250>]"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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iPVqPCn4RERFpHwW/iIiIiSj4RURETETBLyIiYiIKfhERERNR8IuI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\n2vIPPLoAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x153dd7a50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "plt.plot(elbos[5000:])"
   ]
  },
  {
   "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
}