parallelization.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Parallelization with QInfer #"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Setup ##"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We begin by enabling Python 3–style division, as is recommended for use in Python 2.7."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from __future__ import division"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next, we import the IPython parallelization library ``ipyparallel``, as well as QInfer itself and some useful things from the Python standard library."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/cgranade/anaconda/lib/python2.7/site-packages/matplotlib/__init__.py:872: UserWarning: axes.color_cycle is deprecated and replaced with axes.prop_cycle; please use the latter.\n",
      "  warnings.warn(self.msg_depr % (key, alt_key))\n"
     ]
    }
   ],
   "source": [
    "import ipyparallel as ipp\n",
    "import qinfer as qi\n",
    "from functools import partial"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We'll make some nice graphical examples later, so we also import Matplotlib and point it to the ``ggplot`` stylesheet if available. We'll also tell Matplotlib to plot inline in our notebook."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "try:\n",
    "    plt.style.use('ggplot')\n",
    "except:\n",
    "    pass"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next, we setup the parallelization client. To start a cluster running, it's convienent to use the Jupyter Notebook extension. If you're running ``ipyparallel`` 5.0 or later, you can install the Notebook extension by running:\n",
    "```\n",
    "$ ipcluster nbextension enable\n",
    "```\n",
    "Full instructions for installing the Jupyter Notebook extension are available on the [``ipyparallel`` site](https://github.com/ipython/ipyparallel). In any case, once a cluster has been started, we can make a client that connects to it by using the ``Client()`` class."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<ipyparallel.client.client.Client object at 0x7fde65b713d0>\n"
     ]
    }
   ],
   "source": [
    "client = ipp.Client()\n",
    "print(client)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Once we get a client up and running, the next step is to make a *direct view* of its engines. Since we want to use all of the engines provided by the client, we index it by a slice ``[:]``."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<DirectView [0, 1, 2, 3,...]>\n"
     ]
    }
   ],
   "source": [
    "dview = client[:]\n",
    "print(dview)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next, we'll create a simple test model to try out parallelization support."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "            <strong>BinomialModel</strong> at 0x7fde65b4f090: 1 model parameter\n",
       "        <br>\n",
       "            <p>Model chain:</p>\n",
       "            <ul><li>\n",
       "            <strong>SimplePrecessionModel</strong> at 0x7fde65b4f190: 1 model parameter\n",
       "        </li>\n",
       "            </ul>\n",
       "            "
      ],
      "text/plain": [
       "<qinfer.derived_models.BinomialModel at 0x7fde65b4f090>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "serial_model = qi.BinomialModel(qi.SimplePrecessionModel())\n",
    "serial_model"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Having made this model, we can then wrap it in ``DirectViewParallelizedModel`` to parallelize its likelihood function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "            <strong>DirectViewParallelizedModel</strong> at 0x7fde8e765890: 1 model parameter\n",
       "        <br>\n",
       "            <p>Model chain:</p>\n",
       "            <ul><li>\n",
       "            <strong>BinomialModel</strong> at 0x7fde65b4f090: 1 model parameter\n",
       "        </li>\n",
       "<li>\n",
       "            <strong>SimplePrecessionModel</strong> at 0x7fde65b4f190: 1 model parameter\n",
       "        </li>\n",
       "            </ul>\n",
       "            "
      ],
      "text/plain": [
       "<qinfer.parallel.DirectViewParallelizedModel at 0x7fde8e765890>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "parallel_model = qi.DirectViewParallelizedModel(serial_model, dview)\n",
    "parallel_model"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's try it out by making a prior and specifying an experiment design heuristic."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "prior = qi.UniformDistribution([0, 1])\n",
    "heuristic_class = partial(qi.ExpSparseHeuristic, t_field='x', other_fields={'n_meas': 20})"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The rest is handled by ``perf_test_multiple``, which will run our example many times and report on its performance. In this case, parallelizing an individual model is a bit silly, since the simple precession likelihood is fast enough that communication costs blow away the savings from parallelization. That said, it makes an illustrative example. In practice, running a parallel model makes the most sense if the model likelihood is slow to evaluate, and if you're interested in a small number of runs."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/cgranade/anaconda/lib/python2.7/site-packages/qinfer/utils.py:109: ApproximationWarning: Numerical error in covariance estimation causing positive semidefinite violation.\n",
      "  warnings.warn('Numerical error in covariance estimation causing positive semidefinite violation.', ApproximationWarning)\n",
      "/home/cgranade/anaconda/lib/python2.7/site-packages/qinfer/resamplers.py:219: ResamplerWarning: Covariance has zero norm; adding in small covariance in resampler. Consider increasing n_particles to improve covariance estimates.\n",
      "  ResamplerWarning\n",
      "/home/cgranade/anaconda/lib/python2.7/site-packages/qinfer/smc.py:264: ApproximationWarning: Extremely small n_ess encountered (1.25962954805). Resampling is likely to fail. Consider adding particles, or resampling more often.\n",
      "  ApproximationWarning\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Time elapsed: 277.54 s\n"
     ]
    }
   ],
   "source": [
    "with qi.timing() as t:\n",
    "    performance = qi.perf_test_multiple(\n",
    "        100, parallel_model, 6000, prior, 200,\n",
    "        heuristic_class, progressbar=qi.IPythonProgressBar\n",
    "    )\n",
    "print(\"Time elapsed: {:0.2f} s\".format(t.delta_t))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's plot the performance data to make sure that our test actually works."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x7fde64d10190>"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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RhHAb0myEqCHl44sx8m7MdcnoUyftjiOEW5BmI0QtqEsiod0F6LdetTuKEG5B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\nAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fde65b43710>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.semilogy(performance['loss'].mean(axis=0))\n",
    "plt.xlabel('# of Experiments')\n",
    "plt.ylabel('Bayes Risk')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that, in the above plot, we see both the exponential scaling we expect as well the errors caused by numerical precision once we get very close to the true model."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As an alternative to parallelizing over model parameters, we can parallelize over trials instead. That is, we send each trial to a different engine as they are able to handle new tasks. To do so, we'll use the ``LoadBalancedView`` offered by ``ipyparallel``. Parallelizing at the trial level instead is a much faster approach in this case, as it requires much less communication between the engines and the main process."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "lbview = client.load_balanced_view()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Time elapsed: 14.55 s\n"
     ]
    }
   ],
   "source": [
    "with qi.timing() as t:\n",
    "    performance = qi.perf_test_multiple(\n",
    "        100, serial_model, 6000, prior, 200, heuristic_class,\n",
    "        progressbar=qi.IPythonProgressBar, apply=lbview.apply\n",
    "    )\n",
    "print(\"Time elapsed: {:0.2f} s\".format(t.delta_t))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x7fde64e13bd0>"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
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cdg9s+5qDb77AoZzPMW67u0kf2abraTGppbWCg4NJTU1t9P4nvHS2bds2kpKS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\naTRCCCHc6v8A5OJa8EeDoVMAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fde647a1990>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.semilogy(performance['loss'].mean(axis=0))\n",
    "plt.xlabel('# of Experiments')\n",
    "plt.ylabel('Bayes Risk')"
   ]
  }
 ],
 "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": "3.5.1"
  },
  "widgets": {
   "state": {},
   "version": "1.1.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}