{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Variational API quickstart\n",
    "\n",
    "The variational inference (VI) API is focused on approximating posterior distributions for Bayesian models. Common use cases to which this module can be applied include:\n",
    "\n",
    "* Sampling from model posterior and computing arbitrary expressions\n",
    "* Conduct Monte Carlo approximation of expectation, variance, and other statistics\n",
    "* Remove symbolic dependence on PyMC3 random nodes and evaluate expressions (using `eval`)\n",
    "* Provide a bridge to arbitrary Theano code\n",
    "\n",
    "Sounds good, doesn't it?\n",
    "\n",
    "The module provides an interface to a variety of inference methods, so you are free to choose what is most appropriate for the problem."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "import pymc3 as pm\n",
    "import theano\n",
    "import numpy as np\n",
    "\n",
    "np.random.seed(42)\n",
    "pm.set_tt_rng(42)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Basic setup\n",
    "\n",
    "We do not need complex models to play with the VI API; let's begin with a simple mixture model:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "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",
    "    x2 = x ** 2\n",
    "    sin_x = pm.math.sin(x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can't compute analytical expectations for this model. However, we can obtain an approximation using Markov chain Monte Carlo methods; let's use NUTS first. \n",
    "\n",
    "To allow samples of the expressions to be saved, we need to wrap them in `Deterministic` objects:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "with model:\n",
    "    pm.Deterministic('x2', x2)\n",
    "    pm.Deterministic('sin_x', sin_x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "100%|██████████| 50500/50500 [00:40<00:00, 1248.15it/s]\n"
     ]
    }
   ],
   "source": [
    "with model:\n",
    "    trace = pm.sample(50000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
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Exc1C7Kmd1T67FQaDJlhKqYjy89cP09Vn56uXB6csPSkjiTsvmsGLe0+z6UjkrpWizhKR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\n23ooSLMMG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Ioc5helDw4ZdDUgh7tyfgGryrOH9OikuZ2/YXHRkKPr7uYVOpKmxSUeEsZh\n94txDofylCDkjTHMb1FJBhfOymVFWdZgQpyXluhxfw5PospzUrhpSTE3LikefOy5FWf3qzdDS+cV\nplGanTyYyF6zsHDMHtXY2LOvfPhcJU8HAdxdNi9/yBDPG5c4PgfuwwevW1w02Ms42ff2VHn6urfE\nx44Ynur6nLjfJzslgXMrckhJiCMxLoalzuG0mckJEx4y596jMzMvlWWlmaxdVkJpdjLZKQmsXVYy\npeHD2SkJfukdmuPhYIn7LrXEx7JmZg7zCtNZu6yE6TnJJMbFsqIsa0hvtTsR4eqFhSwoTuf8mbmD\nCVwgePsuzAX2i8grIrLOdRrrAeI4NPQYcMAY8+BUA1VKRZcdVa3sqWnjrgsqwqpstIjwqTVl7K1p\nZ+ep1mCHEzFEpExEvgn8FkfRpW8GOSS/i4uJodCtISQiZA0bSuY+tGy0oTLDTebj5PoMunqDxlKa\nnczCYkdy4anhc/WCQq5eUEhiXOxgguFy05Liwd6N8T73F8/JG/L4tcvGn+adkhg3pHF4/eJCbl5a\nPOKxKYlxYw6v9DR0zjibg0kJsaxdVsIM52s/Z3oWq8qzmZaVzPJREsrl07MGh5O5ephcDevZBanE\niJCTkjjk9pxhCVhuauLg/zbObb8sKE7ngmEHqWJiZEjDPXVY5chL5+Zz5fwC4GzCMi0reXBYaKwI\niXGxXLuoiJl5qVjiY8lIiucK52O85alnxMW1P9Mt8UN6+mJjHJ+DKxcUkJwQR7mzh2ZBcTrnVuRM\naLhlICyZNnTuoesAyfkzc4cMZSzMsHDlggJiYoTc1AQqclNYWZY1YljpRBRm+K4gjiuOWJFJfYeM\npSgjyeN3hStpHWsfxMXGDBlKHCq8HUD7vUls+wLg08AeEdnpvO7bxpj1k9iWUirKPL7xBGmWOD56\nTvjVxvnw8hIeWH+ApzZXjdqgUt4TkS1APPB74GPGmONBDikgDOP3gF40O4/nd9YAcPm8Arr7rbx9\neOh85gVF6aRZ4tlS2URZTgp2L3tW18zIGZLQeZPAuMzKT2VWvqPBtK926JS54cPm3MXECOdWZFPd\n0jOpyf1LpmWS4GWiCVOfqL9mRg6nWnqobuke0TPh4kpKXAmba0hTVvLZ15cQF8PMvFSKMix09lnZ\ndKxpsOpibmoiNy0txm43WO125hQMbYiW5yZT197DdGePUlefjRl5KZxo6gIcCVn2OEPyhu8F930/\nrzCNPTVtxMcK84vSyUiKJ3+UHhCLc9/Hxgg3Linm9QNnAM/DyS6clUtKYhwt3f3jBjbaXLCrFpxN\n6GJjxKcJxWQNT6iGWzotg9KspDF7okVkcDtNnWPsn3GMlcCGkvlFnnvE0hLjyEiK99gbPOR+lnjW\nzMhh0/EmIPjzr8DLBMsY87aIlAGzjTGviUgyMOZ/zRjzLmMNAlZKqVHUtfXy0p7T3H1BeUiXZh9N\namIcH1pewnPbq/nOjfN9Pt8gCt1hjDkU7CCCITkhjjRL3IjJ8sPNyk8lIS6GhLgE5hamcaiuY3C+\n0WxnY8OVIO2oavFq+GpMjPhkuFVxZhK1rT3j39HJEh87mJxNlL+rBU7LSqKtZ2Dwcn66hfx0CyvK\nvD+QUpBu4ZqFhUOGS7okJ8SRnBDH6orsEUU9YmJksGdw+GMun3c20XDNUbl0Tj47qlooSLdgt3v+\nf09kELPgeD+MNhxroob3wI0XzLkVOZMq3hFoReMkeXGxMaMmqGPx5oCLS0VuCnML00ZN+qcikAPf\nY2Jk3GI+Lq7Xmp4Uz/wglep351XLRUQ+B9wLZAMzcZRb/zlwhf9CU0pFq6c2n8QWJqXZR/Op88r4\nzZYqnttezWcvmhHscMJatCZX4BjO59549mR4z9LcgjSykhNGXS8r0Ec+x5tjM57EuFjmjVLMAuD6\nxUU+eU0LizNG9LYNt6LMN5PkPSVX7nwxVyQjOd4n1fSKM5M4fKaD8tyJD8MqzLBwtL5zQr2KY20r\nlIXajFtvkquJTBMO9ZH66UlxlGYnT/rgjK95e2j4S8BqnGXWjTFHRCS4NTCVUhGpd8DG01uruHJ+\ngddrhoSi+UXprCzL4jdbqrjngooRc02U8sZk50v5ag2sUHDtorFrbPmqqMGs/FRyUhKwRVFxmnNn\nZFPZ0DVmOXRLfOxg0ZCJWlCUzsy8VL/0pIwl1KoKrpmZE7DRGN6+fYWJJYWuJDnNEpqjSkQkpBbm\n9vYd2GeMGRwEKiJxhF6yrpSKAC/sqqW5q5+7w6g0+2g+dV4ZlY1dvHesMdihKDVh0XhIICslYVKL\n9IardEs8S0u9K1k/GSIybm+dP1jiY4mPjRm1FzfQ8tMso67j5A9TKYwxmnRLPBfMymWRh2GqaiRv\nE6y3ReTbQJKIXAU8C7zgv7CUUtHIVZp9TkHqkHLM4eq6xYVkpyTw1OaTwQ4lrIlIsoh8R0QedV6e\nLSI3BjuuSDWRuR7BsLgkgzVerNWkAs9V4dAXic1UOxKTE2IJxMCB3gEbjZ19/n+iEJCbmqijMbzk\nbYL1D0ADsAf4PLAe+Cd/BaWUik7bTrawr7adu84Pr9Lso0mMi+VjK6fx2oF66tp6gx1OOPsV0Aes\ncV6uAf41eOEEhj9HqoV2CjW2GXmpkyoSEM0C9XUaEyNcOb9gQkU/xupt8UdPjK+9daiB946eHaUQ\nAT9d4wqH/0uweZVgGWPsxphHjTEfM8bc4jwfzt/PSqkQ9Ph7J8hIiudDy4uDHYrPfHJ1GXZjeGZr\nVbBDCWczjTH/AQwAGGO6iZIRbP5oyETCwQsVulIS4ya8OC74t+e0s886aiXFqeqz2gDPpeh9KRRb\n3ZoKjM6rBEtEKkXk+PCTv4NTSkWP2tYeXt5Xx22rSsOyNPtopuckc8mcPH77fhUDNnuwwwlX/SKS\nhLPjRURm4ujRmjIRuVZEDonIURH5Bw+3J4rI75y3bxGRcl88r1IqMAZsdl4/cIYPTrV4/Zh+q53e\nAZsfo/Kep+MhdW29vLj7NPUdvh8ZMdGkSZMsz7wdIrgSWOU8XQT8GHjKX0EppaLPrzefxBjDp9eU\nBTsUn/vUuWWcae/jtf1ngh1KuPou8DJQKiK/AV4HvjnVjYpILPBT4DpgAXC7iCwYdrfPAC3GmFnA\nfwM/nOrzKqXG54tmuwFszp6rhg5Hrbb23oER9+voHRhyAOy1A2d4ZV+dYxvG0NY98jGB0uNM9Grc\n1pLbUtmE1W5n07GmEfefyH7z1Gu4blct7xxu4FRz9+B1o/VHvn6gnvV76ibwjNHD2yGCTW6nGmPM\n/wA3+Dk2pVSU6Oyz8tTmk1y7qJBpWeFbmn00l83LpyQziae2aLGLyTDGvAp8BLgLeAZYaYx5yweb\nXg0cNcYcd1bK/S2wdth91gJPOM8/B1whOsZOhbFoefeKCGfaezl8pmPwupNNXbx5sJ76dkfPz6nm\nbpq7+nnjYD3r95weXBDbPdk61tDJW4frae7qxxu+Htbb7lzY2j3hcecpyfLqf+x2n94BG8/vrBmc\nK9zS3e/VguRd/VasdjtvHqyns88KOHr/1u2qpaEjOgp/jMbbIYLnuJ1WisgX8H4NLaWUGtMzW6ro\n6LXy+YtnBjsUv4iNEW5fXcp7R5s43tAZ7HDChvtvD1AGnAZqgenO66aqBDjldrnaeZ3H+xhjrEAb\nMKKEnYjcKyLbRGRbQ0ODD0IDux+H3hgDPf02v81LUaElmo8JVDZ2AY65UgfrHMmWKxnYUdXChiNn\nP6/vn2ge8fg2Z4LT3W8d83n89Uly/es6+6yDiaE7XwwTdCVxrn3lsv90u3eP7x1ga6Uj0Wvt6ccY\nw5H6jiH3aeseoLPPijGG/bXebTeceZsk/ZfbeStwArjV59EopaJOv9XOY+9WsmZGDktLM4Mdjt98\nfNV0Hnr9CL/efJLv3rQw2OGEi/8a4zYDXB6oQMZjjHkEeARg5cqVU25ruRpSxxo6WVCcPtXNDSGA\n1W7nr/vrmJaVTENHL4unZVKSmTT0flHcKFeB4/42e35nDXlpiZw/M3fEbb4w0XlVta09NHU6eq6M\nAbvd8OKe08wvSmdWfuqQ+7ru50+bjjexdtnwY0BnBXPeWEevlVf21TEz7+x+6bfaae7qpzDDwluH\n6wHISk6gpdv/+yrYvEqwjDGX+TsQpVR0Wrerlrr2Xh746OJgh+JXeWmJ3LC4iGe3VfO3V80hzRIf\n7JBCXgB+e2qAUrfL05zXebpPtYjEARnAyDE5PtTTb2PTccdT+KsXyzUvpbrFMexo24lmSsZouKnI\nUdPaw6KS0Fss1vVWb+joo99qp7W7nwI/lePv7LOOOuTO/frhPVov7K4FYF9tGxW5KUOqJZ5u6yFY\nmjr72H6yZXC+1mSN10vnMlri2ztg45jbKI2X9p4GYG5h2uB10ZBcgZcJloj87Vi3G2Me9E04Sqlo\nYrcbHn77GPMK07hkTl6ww/G7ey6s4M87a3l2WzX3XFgR7HDChohYgC8CF+LoudoA/NwYM9WxMe8D\ns0WkAkcidRvwiWH3WQfcCWwCbgHe8PcyJUFftFRHDUa0UKmON9wZt6Furoa5t/OePGkdoyFf2dhF\nJV0eb9tR5V21wb/srvXYm+Tvjt8WD/vkXbd1uLzVO2Cjo9dKV5+VPqtjzplr6ORUuN5f7nOwDtV1\njHb3iOXtEEFXFcF1zss3AVuBI/4ISikVHd48VM+R+k7+5+PLomI40pJpmawsy+LxjSe48/zySa0V\nE6WeBDqAnzgvfwL4NfCxqWzUGGMVkS8DrwCxwC+NMftE5H5gmzFmHfAY8GsROQo040jCItKp5m6v\nG5dK+ZqnRrg/5yFOlKfPRk9/IJLVob8T7xzxzRzPjl5HMvX+iWYS4rwtKq685W2CNQ04xxjTASAi\n3wNeNMZ8yl+BKaUi38NvH6ckM4kblhQFO5SAuefCCr74mx28fuAMVy8sDHY44WKRMca9fPqbIrLf\nFxs2xqwH1g+77p/dzvcyxUQuXAxvQFrtum6b8r/69tF7bEMov/Lor/vDv0R5W88ACbETS7D6reN/\nN0TLXKvReLtHCwD3vdTvvE4ppSZl07Emtp5o5rMXVRA/wS/3cHb1ggJKMpP45XuVwQ4lnOwQkfNc\nF0TkXGBbEOPxq6pR5ob4iuvItVKhwBfD0tTU9NsmdjDlmBfVcKM5uQLve7CeBLaKyJ+clz/E2XVB\nlFJqQowx/PdrhylIT+T21dODHU5AxcXGcMeaMn7w0kH21baxsDj0JpuHoBXARhGpcl6eDhwSkT2A\nMcYsCV5ovufvOVhNXdG9Po0KLW090d0QV5HJ24WG/w24G2hxnu42xvy7PwNTSkWu9442sbWymS9d\nNgtLfGywwwm421ZNJyk+ll+9dyLYoYSLa4EK4BLnqcJ53Y045gQrpSJQKM3BCidnPKyXpQJrIuNy\nkoF2Y8xDOMrVagkspdSEGWN48NVDFGVY+Piq0vEfEIEykuO5ZcU01u2spa5NfwjHY4w5CbTjKJGe\n4zoZY046b1N+IGgRFhUI+j4by2TqP/l62KW/09xILHLlVYIlIt8F/h74lvOqeOApfwWllIpcbx9u\nYEdVK1++fBaJcdHXe+XyuYtmYDOGRzccD3YoIU9Evg/sBn6MY/Hh/wL+M6hBKaV8os8ammXjQ4Wf\nV4VQfuJtD9aHgZvBsWiAMaYWSBvrASLySxGpF5G9UwtRKRUpHL1Xh5mWlcTHVkRn75XL9Jxk1i4t\n5uktVVNa6yVK3ArMNMZcaoy5zHm6PNhBKaWUv2l+FZ68TbD6nQsrGgARSfHiMY/jGCOvlFIAvHag\nnt3VbXz18tm67gbwxctm0mu18ct3taLgOPYCmcEOQimlAi0URs+FQAhhx9sWzu9F5GEgU0Q+B7wG\nPDrWA4wx7+BYlFEppei32vnBSweYkZvCh88pCXY4IWFWfhrXLizkiY0naOsZCHY4oewHwAci8oqI\nrHOdgh2UUkr5W3VLT7BDUJPgVZl2Y8x/ishVOCYZzwX+2Rjzqi8CEJF7gXsBpk+PrnLNSkWTJzed\n4HhDF4/duTKq1r0az5cum8VLe+v49aYTfPny2cEOJ1Q9AfwQ2APo6rcBEgpHzpVSKhyNm2CJSCzw\nmjHmMsAnSZU7Y8wjwCMAK1eu1JGmAdLVZ2X/6XaO1Xdyuq2Xlu5+Bmx2QEi3xJGbmkhpdjILi9OZ\nlpUUkRVeVOA0dfbx0OtHuHhOHpfPyw92OCFlUUkGl83N47F3K7nnwgqSE7xdnjCqdBtjfhzsIJRS\nKhpp43zixv0lN8bYRMQuIhnGmLZABKV8zxjDvtp2XtlXx1uHGth/uh2b/exHJiMpnoS4GIwxdPRa\n6bOePUhckJ7IyvJszqvI5tpFReSlJQbjJagw9uCrh+nut/GdG+Zrsu7Bly+fxUd/tolfbzrJ5y+Z\nGexwQtEGEfkBsA4YXCXXGLMjeCEppXwhPjbGeYBXqcjh7aHSTmCPiLyKs5IggDHmq36JSvlMR+8A\nz++s5ektVew/3U6MwMqybL546UyWlWYyOz+NokzLiCFbbT0DnGjsYnd1K9tOtrDtRAsv7j7Nd9ft\n44JZuaxdVsL1iwv1aLsa14HT7TyztYo71pQzu2DM4qNRa0VZNpfOzeOnbx7l46tKyUxOCHZIoWa5\n8+95btcZQCsJKhXmLPGaYEW7SCxF723r+I/Ok9dE5BngUiBXRKqB7xpjHptYeGqymjr7ePid4zy1\n+STd/TbmFabx/bULuXFJMVkp4zfeMpLiWVqaydLSTD69phyAw2c6WLezlud31fD1Z3fxry/u547z\nyrjj/HJyU7VXS41kjOH+F/aTnhTPfVfq/KKxfOu6+Vz30Dv87xtH+acbFwQ7nJDiHKKuAux0a69+\ntyul1CSMmWCJyHRjTJUx5omJbtgYc/vkw1KT1drdzyPvHOfxjSfoHbBx89Ji7jy/nGWlmVMemjWn\nII2vXzOXv7t6Du+faOHRDcf5yZtHefid49y6spSvXDGL/DSLj16JigR/3FHDpuNNfP9Di7RXZhxz\nC9O4ZcU0ntx0kjvPL6c0OznYIYUUEbkBWAgMfskYY+4PXkSRzxaBR5WVUhPn74H99gj8qhmvB+vP\nwDkAIvIHY8xH/R+Smgyb3fD01ir+85VDtPUMcOOSIu67cjaz8n0/JEtEWF2RzeqKbI41dPLoO8d5\nZmsVf9hRzecumsHnLp5BaqIOHYx2jZ19fP/F/awoy+KTq7VCqDf+9qq5+H4FTwAAG0BJREFUrNtV\ny49eOcSPb18+/gOihIj8HEgGLgN+AdwCbA1qUFFAZ0uqQBB9p0W9rj4rGUnxwQ7Dp8arlez+rp/h\nz0DU5O2oamHtT9/lO3/ey/yiNNZ/9SL+9xPn+CW5Gm5mXioPfHQJr/7tJVw6N4+HXj/CpT96k+e2\nV0fkmFrlHWMM331+H919Nh74yGJiYvQH1BuFGRY+d9EM1u2qZXd1a7DDCSXnG2PuAFqMMf8CrAHm\nBDmmiKf1aFQgFGboyJdQ5+/WXCSuAzlegmVGOa9CQE+/je+t28dH/m8jDR19/Pj25TzzufNYUJwe\n8FgqclP4v0+u4E9fPJ/p2cl8/dldfPzhzRw+0xHwWFTwPb+zlhf3nOb/XTlbC1tM0OcvmUlOSgL/\n+uIBPUhxlmulzW4RKQYGgKIgxhMVtGdBBUKk9VyoiYvEn7rxEqylItIuIh3AEuf5dhHpEJH2QASo\nPNt+soXrf7yBxzee4K7zy3n97y7l5qXFQS+BvXx6Fs994Xwe+MhiDtd3cP1DG/iPlw/SO2ALalwq\ncGpae/jO83tZUZbFF7Tk+ISlJsbx9WvmsrWymT/uqAl2OKHiLyKSCfwI2AGcAJ4OakRRQHuwlFJq\ncsacKGOMiQ1UIMo7fVYb//PaER5++xhFGUk8/dlzOX9WbrDDGiImRrht9XSuXljID9Yf4P/eOsZf\n95/hR7csYfn0rGCHp/xowGbnK0/vwBh48NalxOrQwEn5+MpSnttezb+tP8Dl8/K9qvwZyYwx33ee\n/YOI/AWw6LqMSikVGUwEDpIbrwdLhZC9NW3c/JP3+Nlbx7h1ZSkv33dRyCVX7rJTEvjRx5byxD2r\n6eqz8tGfbeQHLx3Q3qwI9h8vH2RHVSsPfHQxZTkpwQ4nbMXECP/24UW09Qzw/Rf3BzucoBGRVSJS\n6Hb5DuD3wPdFJDt4kUWHGO3CUkrh/4I36ZbIGyaqCVYYGLDZeei1I3zop+/R0t3Pr+5axQMfXUJa\nmLwhL5mTxytfu5iPryrl4bePc8OPN7CjqiXYYSkfe35nDY9uqOSONWXcuKQ42OGEvXmF6Xzx0pn8\ncUcNf91XF+xwguVhoB9ARC4GHgCeBNqAR4IYV1SI0RaCCgDN48eWkxL8tegir3/J//TrM8QdOdPB\nR/5vI//92mFuWFLEX792MZfNyw92WBOWbonnBx9ZwpP3rKan38YtP9vIv6/X3qxIsfNUK998bjer\ny7P5pxt0kVxf+crls1lYnM63/7SHxs6+YIcTDLHGmGbn+Y8Djxhj/mCM+Q4wK4hxBUww59VqkQsV\nCAW6fuaYoqHKYjQWuVBBYrMbHnnnGDf85F1qWnv4v0+ew0O3LQ/7xVovHuzNms4j7xzn+h9vYPtJ\n7c0KZyebuvjsE9vIS0vkZ586h4Q4/VrxlYS4GB68dRntvVa+9rud2CNxNcaxxYqIa67wFcAbbrdN\nabE9EckWkVdF5Ijzr8cJoiJiE5GdztO6qTxnuMlKDo9REmpiQm1ubKQt4+H7obWh972fFK8lGsaj\nLaEQdKyhk1sf3sS/rz/IpXPyeOW+i7l+ceRUJE6zxPODjyzmqc+cS9+AnVt+vpHvrdtHZ5812KGp\nCapv7+XTj23FZrfz+N2ryEkN/lCGSDO3MI3v3bSQDUca+embR4MdTqA9A7wtIs/jKNW+AUBEZuEY\nJjgV/wC8boyZDbzuvOxJjzFmmfN08xSfM6zkp0f+kfNolKvf034ViAQ2JWFKx5emrDgzyafb0yIX\nyq9cvVbXP7SBo/WdPHjrUh7+9Ary0iLzy/DC2bm88rWL+fR5ZTyx6QRXPfg2r+0/E+ywlJfq23u5\n/dHNNHb28au7VwdkYetodfvqUj60rJgHXzvM6wei5zNijPk34O+Ax4ELzdmFwWKAr0xx82uBJ5zn\nnwA+NMXt+UwoTPi+dG74DUVX3skM4Z7JdB+uiZUQG7lN3HPKxq7IvLA4I0CR+EZKYnATRn+I3Hdf\nmDla38EtP9/Iv68/yMVz8nj1axfzkXOmBX1dK39LTYzj/rWLeO4L55NuieezT27jb57azpn23mCH\npsZQ09rDbY9spq6tl8fvXs2y0sxghxTRRIQffGQJi4oz+MozH7C/NnqWITTGbDbG/MkY0+V23WFj\nzI4pbrrAGHPaeb4OKBjlfhYR2SYim0Vk1CRMRO513m9bQ0PDlAJLTjg7/Mbfi03PK/S8MH26JfIa\nPMphbggv/n6OD5dyGS/JWFaaycryyRUjjRtWAcafyVxC7MjheMN7ydzn5p8zPYtZ+al+iwegPNe3\nVYKD3SPnD5pgBVmf1cZP3zzK9T9+l8rGLh66bRmPfHpF1A3NWFGWxV++eiHfuGYubxys58r/eptf\nvlvJgM0e7NDUMPtr2/nwT9+joaOPJ+5ZzeoKrZYdCEkJsfzizpVkJMVz16+2cqKxa/wHRTkReU1E\n9no4rXW/n7NnbLRMpswYsxL4BPA/IuJx9WxjzCPGmJXGmJV5eXlTinv59CxKs5MBWDMzZ0rbGsva\nZSXMLRzZ2E6Kj434g3vRLJT/txnDerCGX56I+LiRr9N97lBGUjwlmUmkDus9uXBWLjeNUQm3Ijdl\n1MIT/pibVJqdxIqyrME5+HmpiWQkxQ9+dofH7/ruGM/iksn3cqUmxnH94iIWFmdw6Rzt7fYk8lLG\nMPLWoXr+5YX9VDZ2cd2iQu5fuyhihwN6Iz42hi9dNosbFhfxnef3cv9f9vPU5pN86/r5XDk/P6R/\nFKLFS3tO8/Vnd5FmiefZv1kz6tFv5R8F6RaeuGc1H394E5/8xRZ+9/nzmJbl3Y9pNDLGXDnabSJy\nRkSKjDGnRaQIqB9lGzXOv8dF5C1gOXDMH/G6JMTFcM70LJ8ezXdXlJHE6baeUW9fNl17pCPR9YuL\nsIVooZxL5+bT0z+0qnBOSiILiif/G+Pe+XvejBw2H28iPjaGHmf1YlfCEufW+7S6ItvjXOK5hWmk\nW+J5/0QzZdkppFnimF+Uxs5TrTR0+LfCq4gwLSt5xHd9SWYSh+o6EJlcD9DwXrDCdAt1Exg9FB8b\n43VPWV5aot/3U6jRHqwgOFrfyeee3MZdv3ofAZ64ZzU/+1TkzrWaqPLcFJ68ZzW/umsVIvC5J7dx\n2yOb2Xy8KdihRa0+q41/e3E/f/ObHcwuSOPPX7pAk6sgmVOQxq8/cy7tvQN87OebOHKmI9ghhat1\nwJ3O83cCzw+/g4hkiUii83wucAEQ9is/ryzL4tpFhaPeHonDdZSjQWwJ0epvGUnxg71Cl8zJY83M\nHC6cnUt2yuQrJ7vP68lPS6QiN4WV5SMPWriG4V4yJ4+iDM/FG/JSEynOTGLtshIykuOJiRGSE+JY\nWOToBYp3JmllOb4dOjcW91R5MoU1hieScR6GOQ4fCjmaZaWZQ+ZtDp9LV5hu4bwZOdy0pNjjOplJ\nCaH5vpwKTbACqLqlm288u4ur//ttNh5t5O+vncfL913MJXOmNpwkEokIl83L5+X7Lub+tQs53tjF\nbY9s5uMPb2LjsUa/z0tQZ+2rbeNDP93Ioxsq+dR50/nd58+LinU5Qtmikgx+d+8arHbDLT/fxHtH\nG4MdUjh6ALhKRI4AVzovIyIrReQXzvvMB7aJyC7gTeABY0zYJ1gxMUJi3OgNmkiccK7CR2ZyAvk+\nWBsrIyl+8GCBiLBkWiZpHgrIuJKisRr54yUasbHCzUuLPQ65DZRL5+Zz9YLRD5wMl5oYx9plJYOX\nZ+SmTHouWVlOChlJ8cSI47tlobPn0bU/CjMsFKRbiImREcng+TNzJ/WcoU6/RQPgeEMnj71bybPb\nqkHg7gsq+OKlM7WktRfiY2O4Y005t64s5ZmtVfzsrWN84tEtLCpJ58415dy0tDhkj8iFu9bufn7y\nxlEe33iCrOR4fnHHSq5cMFodABVoC4rT+cMXzuczT7zPpx/bwjevnce9F82IuDVl/MUY04Rjba3h\n128DPus8vxFYHODQgsa9saVUJLhsXr7Hudx5bu2vitwUKsYo2jC/KJ0MLyovBnoag+vZYp3J32Tn\nq12zsJAYERLiYjh/Vi7VLd0cre+c1LZuWFyEiGNfXL2gkKSE2DFHu0Tyd44mWH5ijGFLZTO/2FDJ\n6wfPEB8Tw0dXlPCVy2f7fP2AaGCJj+XuCyq4ffV0nttezRMbT/CN53bz7+sP8LGVpXx4eQnzi3TI\nmi909A7wy3dP8IsNx+nst3Lbqun8w7XzvPqBUYE1PSeZP33pAr7x7C4eeOkgbx6s50e3LGV6js7L\nUt6bkZtKmlYNVBEoNkaIjRl6EPbqBYUkxI3fU5OTkkhTVx+lITrPNc0Sz/yi9CnHZxlW+CMjKQO7\n3TE14Ez7xOZNuR/gG2/Yny96KUOZhNJQq5UrV5pt27YFO4wpqWnt4Y/bq3luRzUnm7rJSo7n0+eV\n8ek15TrHyoeMMWw61sTjG0/wxsF6rHbDvMI01i4r4eqFBczITdGiGBN0qrmb3287xa83n6S1e4Br\nFxbytavmBHXIg/KOMYZnt1Vz/1/202+zc+9FM/j8JTM8DocJFhHZ7qzGF/Ei4bdMqWg3YLPT0t0/\nZiLQ1j3AW4fryUiKj8i14zYebaShs48blxT7dAFlm90QI6Fd0XI03v6WaYI1RcYYjjV08tf9Z3ht\n/xk+ONWKMbBmRg63rJjG9YuLInLyXihp6uzjxT2n+fMHNeyoagWgLCeZy+flc/HsPFaUZ4XEwp2h\nqKN3gLcONfD7bad41zmP5/K5+dx35RwWTwuvhQoV1LX18sOXD/KnD2pIt8Rx1/nlfPK8MgpCYNkH\nTbCUUpGmd8DGK/vqWFCUzuwQXl9ssgZsdrr6rIMVF5UmWH5jjKGquZutlc1sqWxmS2UTp5od5W4X\nl2Rw1YICPry8xOt1CJRv1bT28MbBet44cIaNx5ros9qJEccY6lXl2SwqyWBRSTqz8lI9VsyJdFab\nnYN1HWypbOaNg2fYWtnMgM1QlGHh1pWl3LqqlBIdwhr29ta08ePXj/DX/WeIjREumZPHVQsKuGJe\nftDW2NMESykViaw2e1S2J6JVSCRYInIt8BAQC/zCGPPAWPcPpR8lu91Q39HHiaYuqpq6OXSmg/21\n7ew/3U5bzwAAmcnxrC7P5qLZuVy5oGDU8p4qOHr6bXxwqoWtlc1srWzmg6rWwfUvEuNiqMhNoTwn\nhbLcZCpyUijLSWFaVhK5qYlh3+tojKGxs5/Kxi6O1ndyrKGTPTVt7KluG9wHs/NTuXx+PlfMK2BF\nWZZPu/9VaDjZ1MXTW6t4cfdpqlscB4KWTMtgeWmm82BDBjPyUsasKOcrmmAppZQKd0FPsEQkFjgM\nXAVUA+8Dt49V4nYqP0o2u6GuvRebzWC127Ebg9VusNoMNrvjvM1uGLDZ6eyz0t1vpbPPRneflY5e\nK01dfTR09NHQ2U9jRx8NnX30W89WnkmMi2FeUToLitJZWOzoDZmdn6oVu8KIzW6obOxiX20be2va\nON7Q5Uigm7sZsA39HKQmxpGXlkheaiJZKfGkWeJJTYwjzRJHamIcqc6/yQlxxMc6qu8kxMaQEBdD\nvPNvQqzjfIwAAoI4quvgGHcsQIzzChFHUu96zw7Y7M73rJ0Bm+O6fpud7n4rXX1WuvpsdPVb6exz\nXG7vsVLf0cuZdsf7uL6jd8hrssTHMLcwnXOmZ7J8ehbnTM/UBWqjiDGGQ2c6eG3/Gd453Mi+2ja6\n3Bb1zEtLpCQziaIMC+mWeNIscaRZ4rHEO97DNy4pmnLPlyZYSimlwp23v2X+LBu0GjhqjDnuDOi3\nwFr8tEhjc1c/FzzwxqQeGyOQnZJIXloiuakJzMxNIS8tkdLsZMpykinLTqE406JdwGEuNkaYlZ/K\nrPzUIaVBbXZDbWsPJ5q6ON3WS0NHH42dzoS7o4/Kxi66+mx09A7Q2WfFHjqjagHH60qzxJGflkh+\nmoUZeSnkp1koSE9kRl4qM/NSKM5I0oMBUUxEmFeYzrzCdL58+WzsdsNx58GGE43d1Lb2UNPaw5H6\nTjp6B+jotdLtloAtm54ZtKGFSimlVLjxZ4JVApxyu1wNnDv8TiJyL3Cv82KniBzyY0wAucCIVTkr\n/fykPuQx/jCi8QeXxh9cYRn/ih8Onp1K/GU+CSYMbN++vVFETk5xM2H5XvEz3SdD6f4YSvfHSLpP\nhvLF/vDqtyzoC18YYx4BHgnU84nItnAepqLxB5fGH1waf3CFe/yBYozJm+o2dF+PpPtkKN0fQ+n+\nGEn3yVCB3B/+HPNWA5S6XZ7mvE4ppZRSSimlIpI/E6z3gdkiUiEiCcBtwDo/Pp9SSimllFJKBZXf\nhggaY6z/v73zj9mqLOP45xs/KyBAUklgwAYrZg2JOVyapoJEDdpqRZOJxWqT1WquNZ1b68df1nTp\ncLOmTnGZlIkxtfHDYGzOF9DkN/FTZi+StAyMtYzy6o/7euvw8jzvc57xcM55nuf6bGfPfa5zPy/f\nc3Ff5zr3ue9zP5K+AawlLdP+iJntuVD/XhMUNh3xAhH6yyX0l0voL5d2199OhK/PJXxyNuGPswl/\nnEv45GyKeyWpSj80HARBEARBEARB0M7EuuNBEARBEARBEAQtIjpYQRAEQRAEQRAELaLjO1iSxkpa\nL+mgf46pU2+SpHWS9knaK2lysUprk1e/1x0lqVfSiiI1DkQe/ZJmSnpJ0h5JOyV9qQyt/TTNl7Rf\n0iFJd9Q4PkzSKj++pSrtpY8c+m/3dr5T0guSKvUbRY30Z+p9XpJJqtQytHn0S/qi/x/skfRE0RoH\nIkf7mSRpo6RXvQ0tKENnp5K3/bcjkh6RdELS7oytZp5Q4n73w05JszLfWer1D0pamrF/XNIu/879\nkir9C+uSJnos9V0LvuX2rvSJpOGStkra4f74gduneK495Ll3qNvr5mJJd7p9v6SbMva2iy9Jg/x6\n+6zvd7s/jnqb3i7pZbdVK2bMrKM34MfAHV6+A7i7Tr1NwFwvjwDeV7b2ZvT78fuAJ4AVZetuRj8w\nHZjm5Q8Bx4HRJWoeBBwGpgJDgR3AjH51lgMPenkxsKpsXzep/1N9bRy4rd30e72RwGagB5hdtu4m\n/T8NeBUY4/sXl627Sf0/B27z8gzgaNm6O2XL2/7bdQM+CcwCdmdsNfMEsAD4HSBgDrDF7WOBI/45\nxst9sbTV68q/++myz7mBP8YDs7w8EjjgMdWVPnGNI7w8BNji2n8FLHb7g5nrT81c7D7cAQwDpnhM\nDWrX+AJuJ93fPev73e6Po8C4frZKxUzHj2ABi4DHvPwY8Ln+FSTNAAab2XoAMzttZv8oTuKANNQP\nqbcNXAKsK0hXXhrqN7MDZnbQy28AJ4Dz/qHO8+BK4JCZHTGzfwFPks4jS/a8ngJuqNBTwYb6zWxj\npo33kH6nrirk8T/Aj4C7gX8WKS4HefR/DXjAzP4GYGYnCtY4EHn0GzDKyx8A3ihQX6eTt/23JWa2\nGXirn7lenlgErLREDzBa0njgJmC9mb3lMbQemO/HRplZj6W7pJXUyZlVwcyOm9kfvPx3YB9wGV3q\nEz+v0747xDcDriflWjjXH7Vy8SLgSTN7x8xeAw6RYqvt4kvSBOAzwEO+L7rYHwNQqZjphg7WJWZ2\n3Mt/JnVC+jMdOCnpaR+C/YmkQcVJHJCG+iW9B7gH+E6RwnKSx///Q9KVpKcohy+0sAG4DPhTZr/X\nbTXrmNm/gVPARYWoa0we/VmWkZ7QVIWG+n2If6KZPVeksJzk8f90YLqkFyX1SJpfmLrG5NH/fWCJ\npF7geeCbxUjrCpqN306gXp6o54uB7L017G2BT+e6gjRq07U+8elw20kPW9eT7gdOeq6Fs8+hXi5u\n1k9V5qfAd4F3ff8iutsfkDrd6yS9IunrbqtUzFyw38EqEkkbgEtrHLoru2NmJqnWuvSDgWtIF7bX\ngVXArcDDrVVamxboXw48b2a9ZQyitEB/398ZDzwOLDWzd+vVC1qHpCXAbODasrXkxR8o3EuK0XZl\nMGma4HWk0cPNkj5qZidLVZWfLwOPmtk9kq4CHpd0ecRtcL40yhOdiqQRwG+Ab5vZ29lc3m0+MbP/\nADMljQZWAx8uWVJpSPoscMLMXpF0Xdl6KsTVZnZM0sXAekl/zB6sQsx0RAfLzG6sd0zSm5LGm9lx\nv4GvNRWnF9huZkf8O8+Q5l4W0sFqgf6rgGskLSe9PzZU0mkzK+RlxRboR9Io4DngLh/CLZNjwMTM\n/gS31arTK2kwaZrUX4uR15A8+pF0I6kTfK2ZvVOQtjw00j8SuBzY5DchlwJrJC00s5cLU1mfPP7v\nJc0DPwO8JukAqcO1rRiJA5JH/zJgPoCZvSRpODCOOvEdNEWu+O0w6uWJer44Rno4kbVvcvuEGvUr\njaQhpM7VL8zsaTd3tU8AzOykpI2ke5zRkgb7qEz2HOrl4oHiqJ3i6xPAQqWFhIaTpmbfR/f6AwAz\nO+afJyStJk11rFTMdMMUwTVA38ogS4Hf1qizjdRY+977uR7YW4C2PDTUb2Y3m9kkM5tMmia4sqjO\nVQ4a6lda/WY1SfdT/Y+XwDZgmtIqPUNJL4qu6Vcne15fAH7vc3WrQEP9kq4AfgYsrNj7P9BAv5md\nMrNxZjbZ23wP6Tyq0LmCfO3nGfzCLmkcacrgkSJFDkAe/a8DNwBI+ggp8f+lUJWdSx7/dxr18sQa\n4BYl5gCnfArQWmCepDFKK4XNA9b6sbclzfH3Tm6hds6vDK7zYWCfmd2bOdSVPpH0QR+5QtJ7gbmk\n99I2knItnOuPWrl4DbBYaVW9KaQHWFtps/gyszvNbILnusWk87uZLvUHgKT3SxrZVya19d1ULWas\nAquBXMiNNPf0BeAgsAEY6/bZwEOZenOBncAu4FFgaNnam9GfqX8r1VpFsKF+YAlwBtie2WaWrHsB\naTWnw6RRNYAfkm7kId1Q/pr0ouhWYGrZvm5S/wbgzYy/15StuRn9/epuokKrCOb0v0jTHPf6NWdx\n2Zqb1D8DeJG04tR2YF7Zmjtpq+X/TtmAX5JWij1DGsldNkCeEPCA+2FXNs6Br/r19xDwlYx9Nulm\n6zCwAlDZ59zAH1eT3ifZmbkeL+hWnwAfI62wutM1f8/tUz3XHiLl3mFur5uLSTM0DgP7yawC167x\nRXoo17eKYNf6w899h297+H+OqlTMyP9QEARBEARBEARBcJ50wxTBIAiCIAiCIAiCQogOVhAEQRAE\nQRAEQYuIDlYQBEEQBEEQBEGLiA5WEARBEARBEARBi4gOVhAEQRAEQRAEQYuIDlYQBEEQBEEQBEGL\niA5WEARBEARBEARBi/gvEcCkV5+hjC4AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10f7109e8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pm.traceplot(trace);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Above are traces for $x^2$ and $sin(x)$. We can see there is clear multi-modality in this model. One drawback, is that you need to know in advance what exactly you want to see in trace and wrap it with `Deterministic`.\n",
    "\n",
    "The VI API takes an alternate approach: You obtain inference from model, then calculate expressions based on this model afterwards. \n",
    "\n",
    "Let's use the same model:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "with pm.Model() as model:\n",
    "    \n",
    "    x = pm.NormalMixture('x', w=w, mu=mu, sd=sd, dtype=theano.config.floatX)\n",
    "    x2 = x ** 2\n",
    "    sin_x = pm.math.sin(x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here we will use automatic differentiation variational inference (ADVI)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Average Loss = 2.2413: 100%|██████████| 10000/10000 [00:02<00:00, 4653.71it/s]\n",
      "Finished [100%]: Average Loss = 2.2687\n"
     ]
    }
   ],
   "source": [
    "with model:\n",
    "    mean_field = pm.fit(method='advi')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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drrAwVq1aRYfbhnL4D3MBh7BLOxM7ZjSuBmeu+uA4Dng8OB4POfn5hLrdGGPY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\nrKJgEhERqyiYRETEKv8f0dIaVSUPQ24AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x111f8a278>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pm.plot_posterior(mean_field.sample(1000), color='LightSeaGreen');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Notice that ADVI has failed to approximate the multimodal distribution, since it uses a Gaussian distribution that has a single mode.\n",
    "\n",
    "## Checking convergence"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Help on class CheckParametersConvergence in module pymc3.variational.callbacks:\n",
      "\n",
      "class CheckParametersConvergence(Callback)\n",
      " |  Convergence stopping check\n",
      " |  \n",
      " |  Parameters\n",
      " |  ----------\n",
      " |  every : int\n",
      " |      check frequency\n",
      " |  tolerance : float\n",
      " |      if diff norm < tolerance : break\n",
      " |  diff : str\n",
      " |      difference type one of {'absolute', 'relative'}\n",
      " |  ord : {non-zero int, inf, -inf, 'fro', 'nuc'}, optional\n",
      " |      see more info in :func:`numpy.linalg.norm`\n",
      " |  \n",
      " |  Examples\n",
      " |  --------\n",
      " |  >>> with model:\n",
      " |  ...     approx = pm.fit(\n",
      " |  ...         n=10000, callbacks=[\n",
      " |  ...             CheckParametersConvergence(\n",
      " |  ...                 every=50, diff='absolute',\n",
      " |  ...                 tolerance=1e-4)\n",
      " |  ...         ]\n",
      " |  ...     )\n",
      " |  \n",
      " |  Method resolution order:\n",
      " |      CheckParametersConvergence\n",
      " |      Callback\n",
      " |      builtins.object\n",
      " |  \n",
      " |  Methods defined here:\n",
      " |  \n",
      " |  __call__(self, approx, _, i)\n",
      " |      Call self as a function.\n",
      " |  \n",
      " |  __init__(self, every=100, tolerance=0.001, diff='relative', ord=inf)\n",
      " |      Initialize self.  See help(type(self)) for accurate signature.\n",
      " |  \n",
      " |  ----------------------------------------------------------------------\n",
      " |  Static methods defined here:\n",
      " |  \n",
      " |  flatten_shared(shared_list)\n",
      " |  \n",
      " |  ----------------------------------------------------------------------\n",
      " |  Data descriptors inherited from Callback:\n",
      " |  \n",
      " |  __dict__\n",
      " |      dictionary for instance variables (if defined)\n",
      " |  \n",
      " |  __weakref__\n",
      " |      list of weak references to the object (if defined)\n",
      "\n"
     ]
    }
   ],
   "source": [
    "help(pm.callbacks.CheckParametersConvergence)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's use the default arguments for `CheckParametersConvergence` as they seem to be reasonable."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Average Loss = 2.2559: 100%|██████████| 10000/10000 [00:01<00:00, 7581.25it/s]\n",
      "Finished [100%]: Average Loss = 2.2763\n"
     ]
    }
   ],
   "source": [
    "from pymc3.variational.callbacks import CheckParametersConvergence\n",
    "\n",
    "with model:\n",
    "    mean_field = pm.fit(method='advi', callbacks=[CheckParametersConvergence()])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can access inference history via `.hist` attribute."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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JjA8PdAzgbsfy7hAw1u7ah2c/2YH9Dc0cZoDIBjeqbiYAuMw8/geAzwD83oXtkA/ZubT9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\nAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10fe377b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(mean_field.hist);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is not a good convergence plot, despite the fact that we ran many iterations. The reason is that the mean of the ADVI approximation is close to zero, and therefore taking the relative difference (the default method) is unstable for checking convergence."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Average Loss = 3.1313:  47%|████▋     | 4688/10000 [00:00<00:00, 7060.06it/s]\n",
      "Convergence archived at 4700\n",
      "Interrupted at 4,700 [47%]: Average Loss = 4.7995\n"
     ]
    }
   ],
   "source": [
    "with model:\n",
    "    mean_field = pm.fit(method='advi', callbacks=[pm.callbacks.CheckParametersConvergence(diff='absolute')])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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2mXjwfKC/9IllGPcX4wPpjbUF3d7Hc2exc+iEq4ttaffuuB7BfNDndU5hNZ78ZHePm+Fu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\n8jkGeiIin2OgJyLyOQZ6IiKf+39kX08TFzLcLAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1120758d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(mean_field.hist);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "That's much better! We've reached convergence after less than 5000 iterations."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Tracking parameters"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Another usefull callback allows users to track parameters. It allows for the tracking of arbitrary statistics during inference, though it can be memory-hungry. Using the `fit` function, we do not have direct access to the approximation before inference. However, tracking parameters requires access to the approximation. We can get around this constraint by using the object-oriented (OO) API for inference."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "with model:\n",
    "    advi = pm.ADVI()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<pymc3.variational.approximations.MeanField at 0x1113ffef0>"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "advi.approx"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Different approximations have different hyperparameters. In mean-field ADVI, we have $\\rho$ and $\\mu$ (inspired by [Bayes by BackProp](https://arxiv.org/abs/1505.05424))."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'mu': mu, 'rho': rho}"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "advi.approx.shared_params"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There are convenient shortcuts to relevant statistics associated with the approximation. This can be useful, for example, when specifying a mass matrix for NUTS sampling:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([ 0.34], dtype=float32), array([ 0.69314718], dtype=float32))"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "advi.approx.mean.eval(), advi.approx.std.eval()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can roll these statistics into the `Tracker` callback."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "tracker = pm.callbacks.Tracker(\n",
    "    mean=advi.approx.mean.eval,  # callable that returns mean\n",
    "    std=advi.approx.std.eval  # callable that returns std\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, calling `advi.fit` will record the mean and standard deviation of the approximation as it runs."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Average Loss = 1.9568: 100%|██████████| 20000/20000 [00:03<00:00, 6098.12it/s]\n",
      "Finished [100%]: Average Loss = 1.9589\n"
     ]
    }
   ],
   "source": [
    "approx = advi.fit(20000, callbacks=[tracker])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can now plot both the evidence lower bound and parameter traces:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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YLWY208ymAn2JVCgmOK8F0C/XMjsVgRFmNh2YSmSE9+VC/WQJqlm5PAD/GDU/jLcXERGR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\nc/NrXbfvMYfq7V+nlY/1sn7H3vJE+P8u7qnf9606vktJqas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AAACAeiCR9YEl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dKkRbx22u0T8M/3bcG+5skBRbITuGSuO9aZuPOZ258NX82ONeB682g3Tsv7BV86qH/xAEjfADeU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\nQeQV/wdrLVjUqv6JUQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x112850208>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(16, 9))\n",
    "mu_ax = fig.add_subplot(221)\n",
    "std_ax = fig.add_subplot(222)\n",
    "hist_ax = fig.add_subplot(212)\n",
    "mu_ax.plot(tracker['mean'])\n",
    "mu_ax.set_title('Mean track')\n",
    "std_ax.plot(tracker['std'])\n",
    "std_ax.set_title('Std track')\n",
    "hist_ax.plot(advi.hist)\n",
    "hist_ax.set_title('Negative ELBO track');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Notice that there are convergence issues with the mean, and that lack of convergence does not seem to change the ELBO trajectory significantly. As we are using the OO API, we can run the approximation longer until convergence is achieved."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Average Loss = 1.8638: 100%|██████████| 100000/100000 [00:16<00:00, 6032.70it/s]\n",
      "Finished [100%]: Average Loss = 1.8422\n"
     ]
    }
   ],
   "source": [
    "advi.refine(100000)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's take a look:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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Oe0iKfWxwBfl5bC2ryNTlRUREGkUqJfOCWVTXACPdfV1MHfdt7n5Qk3Y6UJifR4dWBazb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\n2bptTdI3yQ4DerT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dZDTo/SV1r21NJpWfbLj/t0+aR8eYKfVA1cjn90IZwFP16LtL+Sim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8fraIVEn8JvvLgV33hxa2IbYSPStTJ/by3udooQi0XP+gufHcW8PbXYWtoa8nrHgAfri2NbRoUI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\nIqn4f/9yEJcrogKNAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1112075f8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(16, 9))\n",
    "mu_ax = fig.add_subplot(221)\n",
    "std_ax = fig.add_subplot(222)\n",
    "hist_ax = fig.add_subplot(212)\n",
    "mu_ax.plot(tracker['mean'])\n",
    "mu_ax.set_title('Mean track')\n",
    "std_ax.plot(tracker['std'])\n",
    "std_ax.set_title('Std track')\n",
    "hist_ax.plot(advi.hist)\n",
    "hist_ax.set_title('Negative ELBO track');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We still see evidence for lack of convergence, as the mean has devolved into a random walk. This could be the result of choosing a poor algorithm for inference. At any rate, it is unstable and can produce very different results even using different random seeds.\n",
    "\n",
    "Let's compare results with the NUTS output:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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vfvUrXn75ZUwmE2vWrGHp0qVkZ2fHpOFCiPhyuMIhHL2esFajxmrW9byXEKmm3+HoSy65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\nSfJ/w+X7scnlvsYAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x112520e80>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import seaborn as sns\n",
    "ax = sns.kdeplot(trace['x'], label='NUTS');\n",
    "sns.kdeplot(approx.sample(10000)['x'], label='ADVI');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Again, we see that ADVI is not able to cope with multimodality; we can instead use SVGD, which generates an approximation based on a large number of particles."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 300/300 [00:47<00:00,  6.62it/s]\n"
     ]
    }
   ],
   "source": [
    "with model:\n",
    "    svgd_approx = pm.fit(300, method='svgd', inf_kwargs=dict(n_particles=1000), \n",
    "                         obj_optimizer=pm.sgd(learning_rate=0.01))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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b23uAR/c/QYe/E5vRxpnly1lSsgi7ycZgaJAPeg/wfu8+frT9XmqNS0Gpx+Qd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\nYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1163c7f98>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ax = sns.kdeplot(trace['x'], label='NUTS');\n",
    "sns.kdeplot(approx.sample(10000)['x'], label='ADVI');\n",
    "sns.kdeplot(svgd_approx.sample(2000)['x'], label='SVGD');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "That did the trick, as we now have a multimodal approximation using SVGD. \n",
    "\n",
    "With this, it is possible to calculate arbitrary functions of the parameters with this variational approximation. For example we can calculate $x^2$ and $sin(x)$, as with the NUTS model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# recall x ~ NormalMixture\n",
    "a = x**2\n",
    "b = pm.math.sin(x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To evaluate these expressions with the approximation, we need `approx.sample_node`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Help on method sample_node in module pymc3.variational.opvi:\n",
      "\n",
      "sample_node(node, size=None, deterministic=False, more_replacements=None) method of pymc3.variational.approximations.Empirical instance\n",
      "    Samples given node or nodes over shared posterior\n",
      "    \n",
      "    Parameters\n",
      "    ----------\n",
      "    node : Theano Variables (or Theano expressions)\n",
      "    size : None or scalar\n",
      "        number of samples\n",
      "    more_replacements : `dict`\n",
      "        add custom replacements to graph, e.g. change input source\n",
      "    deterministic : bool\n",
      "        whether to use zeros as initial distribution\n",
      "        if True - zero initial point will produce constant latent variables\n",
      "    \n",
      "    Returns\n",
      "    -------\n",
      "    sampled node(s) with replacements\n",
      "\n"
     ]
    }
   ],
   "source": [
    "help(svgd_approx.sample_node)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array(0.03916390240192413, dtype=float32)"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a_sample = svgd_approx.sample_node(a)\n",
    "a_sample.eval()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array(0.08051037788391113, dtype=float32)"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a_sample.eval()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array(0.2376987785100937, dtype=float32)"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a_sample.eval()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Every call yields a different value from the same theano node. This is because it is **stochastic**. \n",
    "\n",
    "By applying replacements, we are now free of the dependence on the PyMC3 model; instead, we now depend on the approximation. Changing it will change the distribution for stochastic nodes:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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iF8KFUPUGnZgl9d+wg9YwAMB/kQvhoeyWVcRJSgCAIEUvhHtnOw+tO7rQEj7IDGkAQAAi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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x115a37cc0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.kdeplot(np.array([a_sample.eval() for _ in range(2000)]));\n",
    "plt.title('$x^2$ distribution');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There is a more convinient way to get lots of samples at once: `sample_node`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "a_samples = svgd_approx.sample_node(a, size=1000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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v2ONNndok2x47FWR/Jqepk1rU1tZa0fMnt8YkSc2tcbUd19zIpo0LlZ43DMZ5qx3nrnac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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x111538c88>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.kdeplot(a_samples.eval());\n",
    "plt.title('$x^2$ distribution');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The `sample_node` function includes an additional dimension, so taking expectations or calculating variance is specified by `axis=0`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array(0.13250988721847534, dtype=float32)"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a_samples.var(0).eval()  # variance"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array(0.23787158727645874, dtype=float32)"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a_samples.mean(0).eval()  # mean"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A symbolic sample size can also be specified:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "i = theano.tensor.iscalar('i')\n",
    "i.tag.test_value = 1\n",
    "a_samples_i = svgd_approx.sample_node(a, size=i)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(100,)"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a_samples_i.eval({i: 100}).shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(10000,)"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a_samples_i.eval({i: 10000}).shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Unfortunately the size must be a scalar value."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Converting a Trace to an Approximation\n",
    "\n",
    "We can convert a MCMC trace into an Approximation. It will have the same API as approximations above with same `sample_node` methods:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<pymc3.variational.approximations.Empirical at 0x113f401d0>"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "trace_approx = pm.Empirical(trace, model=model)\n",
    "trace_approx"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can then draw samples from the `Emipirical` object:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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NAAAwXnBRZ4yKcig42O7PWgrldEaW2rYDBT2gBxI9kOiBRA8keiDRg4sVOdCkpGT4s45C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\nAADGI9AAAADj/X8B924ReXUzqgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x114489a20>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pm.plot_posterior(trace_approx.sample(10000));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Multilabel logistic regression\n",
    "\n",
    "Let's illustrate the use of `Tracker` with the famous Iris dataset. We'll attempy multi-label classification and compute the expected accuracy score as a diagnostic."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from sklearn.datasets import load_iris\n",
    "from sklearn.model_selection import train_test_split\n",
    "import theano.tensor as tt\n",
    "import pandas as pd\n",
    "\n",
    "X, y = load_iris(True)\n",
    "X_train, X_test, y_train, y_test = train_test_split(X, y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![](http://5047-presscdn.pagely.netdna-cdn.com/wp-content/uploads/2015/04/iris_petal_sepal.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A relatively simple model will be sufficient here because the classes are roughly linearly separable; we are going to fit multinomial logistic regression."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "Xt = theano.shared(X_train)\n",
    "yt = theano.shared(y_train)\n",
    "\n",
    "with pm.Model() as iris_model:\n",
    "    \n",
    "    # Coefficients for features\n",
    "    β = pm.Normal('β', 0, sd=1e2, shape=(4, 3))\n",
    "    # Transoform to unit interval\n",
    "    a = pm.Flat('a', shape=(3,))\n",
    "    p = tt.nnet.softmax(Xt.dot(β) + a)\n",
    "    \n",
    "    observed = pm.Categorical('obs', p=p, observed=yt)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Applying replacements in practice\n",
    "PyMC3 models have symbolic inputs for latent variables. To evaluate an espression that requires knowledge of latent variables, one needs to provide fixed values. We can use values approximated by VI for this purpose. The function `sample_node` removes the symbolic dependenices. \n",
    "\n",
    "`sample_node` will use the whole distribution at each step, so we will use it here. We can apply more replacements in single function call using the `more_replacements` keyword argument in both replacement functions.\n",
    "\n",
    "> **HINT:** You can use `more_replacements` argument when calling `fit` too:\n",
    ">   * `pm.fit(more_replacements={full_data: minibatch_data})`\n",
    ">   * `inference.fit(more_replacements={full_data: minibatch_data})`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "with iris_model:\n",
    "    \n",
    "    # We'll use SVGD\n",
    "    inference = pm.SVGD(n_particles=500, jitter=1)\n",
    "    \n",
    "    # Local reference to approximation\n",
    "    approx = inference.approx\n",
    "    \n",
    "    # Here we need `more_replacements` to change train_set to test_set\n",
    "    test_probs = approx.sample_node(p, more_replacements={Xt: X_test}, size=100)\n",
    "    \n",
    "    # For train set no more replacements needed\n",
    "    train_probs = approx.sample_node(p)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "By applying the code above, we now have 100 sampled probabilities (default number for `sample_node` is `None`) for each observation."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next we create symbolic expressions for sampled accuracy scores:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "test_ok = tt.eq(test_probs.argmax(-1), y_test)\n",
    "train_ok = tt.eq(train_probs.argmax(-1), y_train)\n",
    "test_accuracy = test_ok.mean(-1)\n",
    "train_accuracy = train_ok.mean(-1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Tracker expects callables so we can pass `.eval` method of theano node that is function itself. \n",
    "\n",
    "Calls to this function are cached so they can be reused."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "eval_tracker = pm.callbacks.Tracker(\n",
    "    test_accuracy=test_accuracy.eval,\n",
    "    train_accuracy=train_accuracy.eval\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 100/100 [00:10<00:00,  9.93it/s]\n"
     ]
    }
   ],
   "source": [
    "inference.fit(100, callbacks=[eval_tracker]);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x115bd2828>"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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sqJv2aYYprUmkMGgh4RctF6iyIDZdav1+8aSFQjVhUwgTqCZstyOtNX2zgdTF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\nRBE0woQQQogi/g8CUfW+LWwzAQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x114479198>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import seaborn as sns\n",
    "\n",
    "sns.tsplot(np.asarray(eval_tracker['test_accuracy']).T, color='red')\n",
    "sns.tsplot(np.asarray(eval_tracker['train_accuracy']).T, color='blue')\n",
    "plt.legend(['test_accuracy', 'train_accuracy'])\n",
    "plt.title('Training Progress')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Training does not seem to be working here. Let's use a different optimizer and boost the learning rate."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 400/400 [00:40<00:00,  8.76it/s]\n"
     ]
    }
   ],
   "source": [
    "inference.fit(400, obj_optimizer=pm.adamax(learning_rate=0.1), callbacks=[eval_tracker]);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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LWl9kblkfe4JL2R87jdar5jHw3ALw+zEXL0U7fIhDixYhpUAvDGJaItlIwLKP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\nEAwaw+8bXVZnp0YwaB913jShv9+qaywGfn+Y3t5kub29yTK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qpwvVYk0pamjEarJubMK1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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11188fe10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.tsplot(np.asarray(eval_tracker['test_accuracy']).T, color='red', alpha=.5)\n",
    "sns.tsplot(np.asarray(eval_tracker['train_accuracy']).T, color='blue', alpha=.5)\n",
    "plt.legend(['test_accuracy', 'train_accuracy'])\n",
    "plt.title('Training Progress');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is much better! \n",
    "\n",
    "So, `Tracker` allows us to monitor our approximation and choose good training schedule."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Minibatches\n",
    "When dealing with large datasets, using minibatch training can drastically speed up and improve approximation performance. Large datasets impose a hefty cost on the computation of gradients. \n",
    "\n",
    "There is a nice API in pymc3 to handle these cases, which is avaliable through the `pm.Minibatch` class. The minibatch is just a highly specialized Theano tensor:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "issubclass(pm.Minibatch, theano.tensor.TensorVariable)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To demonstrate, let's simulate a large quantity of data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Raw values\n",
    "data = np.random.rand(40000, 100) \n",
    "# Scaled values\n",
    "data *= np.random.randint(1, 10, size=(100,))\n",
    "# Shifted values\n",
    "data += np.random.rand(100) * 10    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For comparison, let's fit a model without minibatch processing:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "with pm.Model() as model:\n",
    "    mu = pm.Flat('mu', shape=(100,))\n",
    "    sd = pm.HalfNormal('sd', shape=(100,))\n",
    "    lik = pm.Normal('lik', mu, sd, observed=data)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Just for fun, let's create a custom special purpose callback to halt slow optimization. Here we define a callback that causes a hard stop when approximation runs too slowly:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def stop_after_10(approx, loss_history, i):\n",
    "    if (i > 0) and (i % 10) == 0:\n",
    "        raise StopIteration('I was slow, sorry')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Average Loss = 4.2374e+08:   0%|          | 10/10000 [00:02<36:08,  4.61it/s]\n",
      "I was slow, sorry\n",
      "Interrupted at 10 [0%]: Average Loss = 4.6469e+08\n"
     ]
    }
   ],
   "source": [
    "with model:\n",
    "    advifit = pm.fit(callbacks=[stop_after_10])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Inference is too slow, taking several seconds per iteration; fitting the approximation would have taken hours!\n",
    "\n",
    "Now let's use minibatches. At every iteration, we will draw 500 random values:\n",
    "\n",
    "> Remember to set `total_size` in observed"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "X = pm.Minibatch(data, batch_size=500)\n",
    "\n",
    "with pm.Model() as model:\n",
    "    \n",
    "    mu = pm.Flat('mu', shape=(100,))\n",
    "    sd = pm.HalfNormal('sd', shape=(100,))\n",
    "    likelihood = pm.Normal('likelihood', mu, sd, observed=X, total_size=data.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Average Loss = 1.1379e+07: 100%|██████████| 10000/10000 [01:40<00:00, 99.73it/s]\n",
      "Finished [100%]: Average Loss = 1.1374e+07\n"
     ]
    }
   ],
   "source": [
    "with model:\n",
    "    advifit = pm.fit()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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3asqUKbrnnntkGIZuvfVWnXvuuRozZowmT56sMWPGKCwsTHPmzGmOulvd/qMFmr7oW/3y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\n8v22CQlO5eQU1Ln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      "text/plain": [
       "<matplotlib.figure.Figure at 0x11ba63b70>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(advifit.hist);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Minibatch inference is dramatically faster. Multidimensional minibatches may be needed for some corner cases where you do matrix factorization or model is very wide.\n",
    "\n",
    "Here is the docstring for `Minibatch` to illustrate how it can be customized."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Multidimensional minibatch that is pure TensorVariable\n",
      "\n",
      "    Parameters\n",
      "    ----------\n",
      "    data : :class:`ndarray`\n",
      "        initial data\n",
      "    batch_size : `int` or `List[int|tuple(size, random_seed)]`\n",
      "        batch size for inference, random seed is needed \n",
      "        for child random generators\n",
      "    dtype : `str`\n",
      "        cast data to specific type\n",
      "    broadcastable : tuple[bool]\n",
      "        change broadcastable pattern that defaults to `(False, ) * ndim`\n",
      "    name : `str`\n",
      "        name for tensor, defaults to \"Minibatch\"\n",
      "    random_seed : `int`\n",
      "        random seed that is used by default\n",
      "    update_shared_f : `callable`\n",
      "        returns :class:`ndarray` that will be carefully \n",
      "        stored to underlying shared variable\n",
      "        you can use it to change source of \n",
      "        minibatches programmatically \n",
      "    in_memory_size : `int` or `List[int|slice|Ellipsis]`\n",
      "        data size for storing in theano.shared\n",
      "\n",
      "    Attributes\n",
      "    ----------\n",
      "    shared : shared tensor\n",
      "        Used for storing data\n",
      "    minibatch : minibatch tensor\n",
      "        Used for training\n",
      "\n",
      "    Examples\n",
      "    --------\n",
      "    Consider we have data\n",
      "    >>> data = np.random.rand(100, 100)\n",
      "\n",
      "    if we want 1d slice of size 10 we do\n",
      "    >>> x = Minibatch(data, batch_size=10)\n",
      "\n",
      "    Note, that your data is cast to `floatX` if it is not integer type\n",
      "    But you still can add `dtype` kwarg for :class:`Minibatch` \n",
      "\n",
      "    in case we want 10 sampled rows and columns\n",
      "    `[(size, seed), (size, seed)]` it is\n",
      "    >>> x = Minibatch(data, batch_size=[(10, 42), (10, 42)], dtype='int32')\n",
      "    >>> assert str(x.dtype) == 'int32'\n",
      "\n",
      "    or simpler with default random seed = 42\n",
      "    `[size, size]`\n",
      "    >>> x = Minibatch(data, batch_size=[10, 10])\n",
      "\n",
      "    x is a regular :class:`TensorVariable` that supports any math\n",
      "    >>> assert x.eval().shape == (10, 10)\n",
      "\n",
      "    You can pass it to your desired model\n",
      "    >>> with pm.Model() as model:\n",
      "    ...     mu = pm.Flat('mu')\n",
      "    ...     sd = pm.HalfNormal('sd')\n",
      "    ...     lik = pm.Normal('lik', mu, sd, observed=x, total_size=(100, 100))\n",
      "\n",
      "    Then you can perform regular Variational Inference out of the box\n",
      "    >>> with model:\n",
      "    ...     approx = pm.fit()\n",
      "\n",
      "    Notable thing is that :class:`Minibatch` has `shared`, `minibatch`, attributes\n",
      "    you can call later\n",
      "    >>> x.set_value(np.random.laplace(size=(100, 100)))\n",
      "\n",
      "    and minibatches will be then from new storage\n",
      "    it directly affects `x.shared`.\n",
      "    the same thing would be but less convenient\n",
      "    >>> x.shared.set_value(pm.floatX(np.random.laplace(size=(100, 100))))\n",
      "\n",
      "    programmatic way to change storage is as follows\n",
      "    I import `partial` for simplicity\n",
      "    >>> from functools import partial\n",
      "    >>> datagen = partial(np.random.laplace, size=(100, 100))\n",
      "    >>> x = Minibatch(datagen(), batch_size=10, update_shared_f=datagen)\n",
      "    >>> x.update_shared()\n",
      "\n",
      "    To be more concrete about how we get minibatch, here is a demo\n",
      "    1) create shared variable \n",
      "    >>> shared = theano.shared(data)\n",
      "\n",
      "    2) create random slice of size 10\n",
      "    >>> ridx = pm.tt_rng().uniform(size=(10,), low=0, high=data.shape[0]-1e-10).astype('int64')\n",
      "\n",
      "    3) take that slice\n",
      "    >>> minibatch = shared[ridx]\n",
      "\n",
      "    That's done. Next you can use this minibatch somewhere else. \n",
      "    You can see that implementation does not require fixed shape\n",
      "    for shared variable. Feel free to use that if needed.\n",
      "\n",
      "    Suppose you need some replacements in the graph, e.g. change minibatch to testdata\n",
      "    >>> node = x ** 2  # arbitrary expressions on minibatch `x`\n",
      "    >>> testdata = pm.floatX(np.random.laplace(size=(1000, 10)))\n",
      "\n",
      "    Then you should create a dict with replacements\n",
      "    >>> replacements = {x: testdata}\n",
      "    >>> rnode = theano.clone(node, replacements)\n",
      "    >>> assert (testdata ** 2 == rnode.eval()).all()\n",
      "\n",
      "    To replace minibatch with it's shared variable you should do\n",
      "    the same things. Minibatch variable is accessible as an attribute\n",
      "    as well as shared, associated with minibatch\n",
      "    >>> replacements = {x.minibatch: x.shared}\n",
      "    >>> rnode = theano.clone(node, replacements)\n",
      "\n",
      "    For more complex slices some more code is needed that can seem not so clear\n",
      "    >>> moredata = np.random.rand(10, 20, 30, 40, 50)\n",
      "\n",
      "    default `total_size` that can be passed to `PyMC3` random node\n",
      "    is then `(10, 20, 30, 40, 50)` but can be less verbose in some cases\n",
      "\n",
      "    1) Advanced indexing, `total_size = (10, Ellipsis, 50)`\n",
      "    >>> x = Minibatch(moredata, [2, Ellipsis, 10])\n",
      "\n",
      "    We take slice only for the first and last dimension\n",
      "    >>> assert x.eval().shape == (2, 20, 30, 40, 10)\n",
      "\n",
      "    2) Skipping particular dimension, `total_size = (10, None, 30)` \n",
      "    >>> x = Minibatch(moredata, [2, None, 20])\n",
      "    >>> assert x.eval().shape == (2, 20, 20, 40, 50)\n",
      "\n",
      "    3) Mixing that all, `total_size = (10, None, 30, Ellipsis, 50)`\n",
      "    >>> x = Minibatch(moredata, [2, None, 20, Ellipsis, 10])\n",
      "    >>> assert x.eval().shape == (2, 20, 20, 40, 10)\n",
      "    \n"
     ]
    }
   ],
   "source": [
    "print(pm.Minibatch.__doc__)"
   ]
  }
 ],
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