{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Empirical Approximation overview\n",
    "\n",
    "For most models we use sampling MCMC algorithms like Metropolis or NUTS. In pymc3 we got used to store traces of MC samples and then do analysis using them. As new VI interface was implememted it needed a lot of approximation types. \n",
    "\n",
    "One of them was so-called *Empirical*. This type of approximation stores particles for SVGD sampler. But there is no difference between independent SVGD particles and MCMC trace. So the idea was pretty simple to understand and realize: make *Empirical* be a bridge between MCMC sampling output and full-fledged VI utils like `apply_replacements` or `sample_node`. For the interface description, see [variational_api_quickstart](variational_api_quickstart.ipynb). Here I will just focus on Emprical and give an overview of specific things for *Empirical* approximation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "import theano\n",
    "import numpy as np\n",
    "import pymc3 as pm\n",
    "np.random.seed(42)\n",
    "pm.set_tt_rng(42)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Multimodal density\n",
    "Let's recall the problem from [variational_api_quickstart](variational_api_quickstart.ipynb) where we first got a NUTS trace"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "WARNING (theano.gof.compilelock): Overriding existing lock by dead process '26463' (I am process '27017')\n",
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "100%|██████████| 50500/50500 [00:25<00:00, 2015.98it/s]\n"
     ]
    }
   ],
   "source": [
    "w = pm.floatX([.2, .8])\n",
    "mu = pm.floatX([-.3, .5])\n",
    "sd = pm.floatX([.1, .1])\n",
    "\n",
    "with pm.Model() as model:\n",
    "    x = pm.NormalMixture('x', w=w, mu=mu, sd=sd, dtype=theano.config.floatX)\n",
    "    trace = pm.sample(50000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
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c2flcMEqfHJ/MlESuXFrCrPx0zp0zsg/ROXPyAyZXAGfPyhtMjsYaNGBG3tAm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\nJSIiIiIi0iAaYImIiIiIiDTIP82gxfzVFNWNAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x118b68e80>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pm.traceplot(trace);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Great. First having a trace we can create `Empirical` approx"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Single Group Full Rank Approximation\n"
     ]
    }
   ],
   "source": [
    "print(pm.Empirical.__doc__)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "with model:\n",
    "    approx = pm.Empirical(trace)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<pymc3.variational.approximations.Empirical at 0x1193a41d0>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "approx"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This type of approximation has it's own underlying storage for samples that is `theano.shared` itself"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "histogram"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "approx.histogram"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-0.28495539],\n",
       "       [-0.27002112],\n",
       "       [-0.27578667],\n",
       "       [-0.36169251],\n",
       "       [-0.43738686],\n",
       "       [-0.479884  ],\n",
       "       [-0.3633637 ],\n",
       "       [-0.31469654],\n",
       "       [-0.36427262],\n",
       "       [-0.36479427]])"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "approx.histogram.get_value()[:10]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(50000, 1)"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "approx.histogram.get_value().shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It has exactly the same number of samples that you had in trace before. In our particular case it is 50k.  Another thing to notice is thet if you have multitrace with **more than one chain** you'll get much **more samples** stored at once. We flatten all the trace for creating `Empirical`.\n",
    "\n",
    "This *histogram* is about *how* we store samples. The structure is pretty simple: `(n_samples, n_dim)` The order of these variables is stored internally in the class and in most cases will not be needed for end user"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<pymc3.blocking.ArrayOrdering at 0x1190be390>"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "approx.ordering"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Sampling from posterior is done uniformly with replacements. Call `approx.sample(1000)` and you'll get again the trace but the order is not determined. There is no way now to reconstruct the underlying trace again with `approx.sample`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "new_trace = approx.sample(50000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.54 s ± 24.3 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)\n"
     ]
    }
   ],
   "source": [
    "%timeit new_trace = approx.sample(50000)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "After sampling function is compiled sampling bacomes really fast"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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L5/1mLdOz4vjHjYt1Yk4/EZGNxpjCQbw+Esg1xuwewrCGxVCcy17aWoaj00lydHi37lsi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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1191c1d30>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pm.traceplot(new_trace);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You see there is no order any more but reconstructed density is the same.\n",
    "\n",
    "## 2d density"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "100%|██████████| 1500/1500 [00:02<00:00, 677.32it/s]\n"
     ]
    }
   ],
   "source": [
    "mu = pm.floatX([0., 0.])\n",
    "cov = pm.floatX([[1, .5], [.5, 1.]])\n",
    "with pm.Model() as model:\n",
    "    pm.MvNormal('x', mu=mu, cov=cov, shape=2)\n",
    "    trace = pm.sample(1000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "with model:\n",
    "    approx = pm.Empirical(trace)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[<matplotlib.axes._subplots.AxesSubplot object at 0x11839eac8>,\n",
       "        <matplotlib.axes._subplots.AxesSubplot object at 0x118631160>]], dtype=object)"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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em9ensXjtJBR9zUaT4ihf+8U2gickIvlmexXZIZdT7MU402KbW5Zm34e5Po1I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\nGGaI/w9sNwjW1ba+BwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11839eba8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pm.traceplot(approx.sample(10000))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import seaborn as sns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x118a29240>"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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h/bkjfBR+Dp43dK+GqFVqPJ3c8XRyp6t/OK8s/wd74g9ipbHkqYlzb4pnwoqi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\n/wAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x118a32f60>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.kdeplot(approx.sample(1000)['x'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Previously we had a `trace_cov` function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 1.03635135  0.56102585]\n",
      " [ 0.56102585  1.03247922]]\n"
     ]
    }
   ],
   "source": [
    "with model:\n",
    "    print(pm.trace_cov(trace))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we can estimate the same covariance using `Empirical`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Elemwise{true_div,no_inplace}.0\n"
     ]
    }
   ],
   "source": [
    "print(approx.cov)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "That's a tensor itself"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 1.035315    0.56046482]\n",
      " [ 0.56046482  1.03144674]]\n"
     ]
    }
   ],
   "source": [
    "print(approx.cov.eval())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Estimations are very close and differ due to precision error. We can get the mean in the same way"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 0.03685694 -0.01467962]\n"
     ]
    }
   ],
   "source": [
    "print(approx.mean.eval())"
   ]
  }
 ],
 "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": "3.6.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
