{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Changes in API: Variational Inference: Bayesian Neural Networks\n",
    "\n",
    "(c) 2017 by Thomas Wiecki & Maxim Kochurov (opvi)\n",
    "\n",
    "See original blog post for old interface and more explanations of bayesian approach in Deep Learning:\n",
    "\n",
    "http://twiecki.github.io/blog/2016/06/01/bayesian-deep-learning/"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Bayesian Neural Networks in PyMC3"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Generating data\n",
    "\n",
    "First, lets generate some toy data -- a simple binary classification problem that's not linearly separable."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import theano\n",
    "floatX = theano.config.floatX\n",
    "import pymc3 as pm\n",
    "import theano.tensor as T\n",
    "import sklearn\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "from warnings import filterwarnings\n",
    "filterwarnings('ignore')\n",
    "sns.set_style('white')\n",
    "from sklearn import datasets\n",
    "from sklearn.preprocessing import scale\n",
    "from sklearn.cross_validation import train_test_split\n",
    "from sklearn.datasets import make_moons"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "X, Y = make_moons(noise=0.2, random_state=0, n_samples=1000)\n",
    "X = scale(X)\n",
    "X = pm.floatX(X)\n",
    "Y = pm.floatX(Y)\n",
    "X_train, X_test, Y_train, Y_test = train_test_split(X, Y, test_size=.5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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BbdNz8fIDeRg3uIfiOOX7p2on+doGB842svdw28rZBodf+dTwnDRMGN4LXZOs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\nNkwe+z3cMHGUJ5MQryY1sntTVJCNR2ouwOABiVUcjEHWp/T+unw5CzQ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/u+im2C2QBAxA\nKl4k2Yr8zJEn4PMt33GP7WaCLJt49w/m4bE7xvZUFjt2z/2lpeJrkchxNg84AT/7/77GnvBXal4C\nq0mVE+lPXr+RGX8rgw1EK53JVq7z5kW/ZyeuJV4VvlJg5WwXMtoucBPQJRJnMQbO8FTRCvOzJZG4\njANNbfjhGRXcHFgnuuWqSAfmTCurV1jIiiPI9MF37mSvqiq28la5LyqCKIJV0/nffoYDP/sFm0Ql\nCatJomgV++Pzh+LPH23nfsf2BNlguA6FNeHE+3BLO8JtEfTN93Pvef6iRbHKbxKX69qyMdjdygIE\npV4Cs2EVTarsuHdl/UZm/K0IBKLPL6tvP3o0/xgqrvx4G9c0KkJCRtsFTop6GPfP9h86eixP1Ye2\njggGFhegqCAH2/b2zG71h/uvn+5EW0cE/QP5wn03nZLiAtwy+RQUFeS42rN2CndgTsMZrW3Mg61q\n9a7Dh5mMalOT9X0x7z2aVyuSVVNJSyNmnDkAMK7sVPYXVdWiPEA08dOfD6sJsjSLg2O4SiZMxAkl\nP8a+5lhBm5jAMh2rFaLJcHWXl2N16el47tzrYz4a5SWIRFhQ04oV7H6ruI9VJ8O1tdHR4OZrEEWL\nW3H99dFR6rL69l648kXGNYF9NNmQIppLzNKgVvrjKlrLbjFrNXsptZiyOuPJRLSKmT+f7fdZGW1d\narSgQDzo6GUXRQE5Ri1zkTLVCScAn37K2qeiBJUMnWXJ4CtTAZwxcZS1SplAAW7ThGl4YMRU7nFv\n/tFw5ypYx66lPieIWxf/L1d69biManEecNZZrB+YUZHIFN03fSLwzDNyDfxdu5h2uCo+H4tWr6xk\nhXms+oRMTayykmkQODG2KaAFnmh651UlENnKYP+ho1HGTS4y4Z6CvGxcenYoajXtxZ41kEY648lA\ntBI7fFitepcuWLF7d+ygY5ZFFc2xjasVkcv0u+9YStippwI/+AHwm9/EthnoMRB2V5huUBh8ZQFg\nllkckm2DUzZ/iCuvm4MP/3nYdmCZdIV4bFXYT8VLUFvLN9iAmvtYtAK95x75Clq/hooKZsB5kz1j\nDe6CAlbJS++HO3ao9YnCQqBfP77R7tfP+eo4kX00RaCVtkfoK9C+fXLwh7e+5hq3/YeOelrsoH8w\nD4db2qWCEV7hRuu8VyPTfi4rY4MbT+vciunT2WD7wANqIhPGVZ/RAIr2KXNyeso38o4DJFZn2UYh\nBrO3R0m3f9cOcUGLY1XT2ioqY71IMk1tG/dB+vz8aDjw/e+L+4le1c2uW1i2ujVeg74189hjfANf\nW2udeqXidfB6pZ0iWuCJhlbaLjGvQPOPKTrpGGf8148fqawiZsWAvvl45PYL0dWtxd1VHa/Utl5B\nfb24WIOogIcKy5axdLDDh9U+zxNEmTNHvArkGWzAfs6tF9jMNzZ7j5SyOBQirbleKY9UsCzTxGS6\n1aWlsZHgKm5hWVS4TnExc8vv3MnuQ1UV0xTYvTt6fzw7m62yRdXkrPqErC27dzvrT16lvKUZGe7X\ndI9ZecxosI3oRk9FRWzYkOBxVTRRQYUDTW24/8kP8MYH25ATZ/e0F1rlaY1MQ7pvX2vFJqfs2iXf\nD8/KilVkMrZ17lz759RThRKks9zWEcH+f2yFJisQYVGIQUmlTKZCZ2V8PVDBMiuzRWm1l5ZKNeNx\nxRWx7VNRXZP9hn4/i+Zev77nGDt2sH//5Cd89Ts3fSIe/SlFtMATDRltF9jZo9aNm1Gq1AdmlAvy\nsqNkSx+7Y+zxh3vpL350/PNm4lZdyISdYia9CpUiJ01N9ip5FRUxY1tZCVx3HRtcnHLttT0DKxDd\n1pEjgbfftn9M3YC5MXIKGOV/Z724BY3BgfwP+nzMbSspOKEsy+vU+Hog5Wpsa4z0quxeV1XFrvJl\nnonnnuvJrbaqvNXUxH9v1Sq+u91Nn4hHf4pzH01VaE/bBfWNrcp71Oa6vaI8bZGbuelIO+Y8uhYH\nOataXr1tr8nIPW2VfVaVfUMzI0eyALXdu4E+fayjy0UY9+1EbRXh97PJht/PVlmhUGwUsNEFa04n\nchmZa+5PN639HSate0P4+c7ba5CzZLHwfVtZHIJ94KRmRpjd3aWlPW55872W1DkHAFRXA0uXxh7X\n+Bvedhvrt5I9fq5rWaVPyCLZve5PceyjqQoZbRfIAmDMuDVu2+ubUbNoLfe942kjZqEHD7Gb2pb2\n2AlysWsweRQVsahcO+iDa2mp/YmDmVmzoqPJjXicA8t7brK6u3Dz2t/hxxvfgl+LNSQNxSfg9adX\nYvqUM6X9zYnhTanMCNW8eVHwI8AP7DIf122AHa+dqulXVsFzTvpaBuVp98LRNnHI3HIFeX5ppS5V\ndDfi/N9/LPxMIlzU0j253oidgvdGt6uPXx/akgEDmLuch7E+sRF9304l4MiKVavEVZj0dCLVwdCi\njjQvRqI7y48VZ1whTGnTy4pabQVx3c8WyCriJRyVe11YyKRDReiBXbLjunUt89qpWt2M912VrSi7\n7eml9NIRN3GIymku/cWPPDFu+oDC0xHXiac0qRkng2LaEYmwfVSRATYHuRj3PCdOdHbO3buBn/+c\nv+daXc3/jj64ygJygkH2nt/PhF5EmCciFoaXi+LAy4uRyOruwqQvVgrveVRZ0Q7FgVwBq8wIL8/l\nKYsXW0/mrLCzx2/VH9yW5fSinGmG0ItH3sQg09vu4zJn2irQbWBxPs47dUhCpEkzCitBCtlK5LPP\nnJ2zooK9eBKQkQgLXhNJVcrSkoYNA957D2hoYJHuZ50lLzDhRmFKUeiCJ/87472lmLDhz8JDx5QV\n9UAwCIhv0Z+4EgyyYDI3qWgq0sKq/cFN+pWXJUYzAFppe0Q8VqCyAcXnA+bddG7vdlEnA9kA4vez\nvV9RtHF9PbBvn7PzGgdas6tPJXp50SIWaWxm/XpWXWn4cFbC0Mol6nTFY3OlZfRQ5Ufacf63/MlO\nxJeFN077MZ4bewMA77eC0jozwmk0vHHVbLUXLOoPtbXRn3OTfmVnK4ogo53KyAaUgcUFGDwgfoFn\nZto6IqhvbE1dd6FXyAYQTWP1eztii0sAYPWCi4rkx6+sZIZfNtCKXJGyfbuODiaKwWP5cnasSIQN\nvEa3aiAA1NSw87txcdoceI0xEv/3mhEoaW7gf1fTsOKMK9CdxXLh3W4FmfuxcrpYMhH1B7upaMbt\ni+9/Hxg8mL1GjGCv2bNZupjRoIv6wzPPsGIhKullVit/mcE31uomAJDRTghODV4qDCjGfNpbF76D\n2Y+swbPLN6GrS5Buku7IBhCfD7jkEnGQzLx51ulbkyezKG3jQLtgAYv8bm6O3ROePZt9zjxgmwfy\n+npx9LguUHLPPcCSJdFtbGlhrvfsbHcrHjsrrWNt72o5ghdWbcHDf96J/UUl3K8eKh6Ew0X9PQvo\n1PvxnQ+twktPrUJXyxFhXErSt51Ug7NUg7CMq2ZNY799SwubyO3Zw7aESkp6zjVrlrg/dHUBL77I\njKrepoULmbdHFxvKymICLgsX9nyPNwGRGfyDB5mUr2pAWiagpTC7du3SRowYoe3atSvZTXFEJNKl\n/fa1jdqMX76lTbx7uTbjl29pv31toxaJdDk6xhUOj+GG3762UZtw1/KY129f25iQ8yeF2lpNY8Oa\n/FVb2/Od1lZNq6wUf7aign2+s7PnO52d7G9Dh2paVpamBQLi7w8dyj579Gj0d/S/19drmt/P/67f\nr2k7dojbN3Qoa39rK/t/2WckdNxeI75Pra2a9tVXmjZr1vG2Nw0aoi0/fYJ2xR2vastPn8D9bsft\nNdrehiPa0fZO6bmt0Puxfq764CAtAp/WNGjI8d/laHunJ+eS0tqqaXV1lvdS0zRxPzT3O5XjWfVP\n0atPH/VnQdTeqipxv9WfB/1ZCAatrznDyfg87XgKKngpSJIM4QelQgyp4D70Gj34ZunSHvcfD2M+\nq0zwQi+9ecop0X93kt89ejSwcWPs36urgeefF39v9Wrg0kutxTRsFO7Q0fOcP92wGxNWPonzt32G\nAc2N8IUq4NOj6V9/XVi8ZMXpE/Dc2Bsw472lOGfrpyhpaURWqAJZKiUfFTD2Y6GIi0r5SzfYDfCT\n6QQEAuxezp+vfjwrQRa3VFayY4tW5qJ+axYqOukk/jF6cQEQu2Ss0Y63oEJvMHgyxbdECLokFdkA\nomM0dnbFKpwoqckIhVhbuT9WFvDtt8DYsdbts6swFQ7jpWXv4k9bjqA9hwVt5XW2o1/rQZz3ozGY\n8dEfLScm+4KDcPv0JWjPyUNeZzsGhA/iwXlXoTQkkDa1id6Pczva8etlNRjcvD/2Q/E2CnYnQ1ZG\nduRIYMsW9ePJ+qcX6Ap7IrKy+NdiZ+IrUmnLMDJ2Tzveggq9ochGWkfWuqW+3rpKl3GvVrYvN3Ys\n//huBVGM7NkjrrWtaayql0qgkDm46bPPWKCaOfju2H5r98knY+rsCfj1shrctPZ3yOruGbjXr9+B\nrtcEgUwGSloa0a/1IACgPScPkaHD0G9wP8vvqaL3436tBzFQFPAWzyhlJwF+paXyvPpvvrF3PFn/\n9AKrgDHR5MN43zO0AIhdMtJoJ0JQoTcYvFQIhEsasgFExxwVq6fghEIsaK2oiLkyX3ghNohI5fh2\nKC8XFx8Jhdj57KQI5eayoLWzzuIHQR0LasrasQN+TcPg5v2YtO4NPPaHu/HrZTV4+rlZmPfr2+Db\nae1J0IVTdLzuW3o/PtSnPxpEhUkKC1n0fzxwEuBnpXomWtXKJh/6719WJm+vEyZPBq68Uvy+qBKe\n6sS3FxcAsUtGGu1ErIJ7i8FL2cjaeCMbQIJBcTlMHU1jWuJ6dK4539nrlc/kycC//qsalQvXAAAg\nAElEQVT4vcJCtlquqWGrZ6sUIVm+tmTlOLxhOwY374cfGkqOHFAaYNoLi9CZmxfXvjVj4ihcdvFI\nbDr5fP4HWlpY9L8RJ6pwPGQTtMGDmegN75wy1bMswZ2VrUh1L8r69c4N9+DBwLRpPSp7xonfE0/w\ntQIA4FRBDI9o4mucWM6axQqcuP0degvJjYOTE6/o8aPtndqMX77FjYqe8cu3PIseTXbkt5ckJLI2\n1TBGd/v9mhYKadr06ZrW1BT7vlX0Ny8Ku7OTRVOLor5lr6ws9j1jFK65vVYR552C31IWaTx0qKZt\n2sSOY7fNgldXKKTt3bE/IX3raMMBLVJUJP9tzL+r1f1SQZaRMHSoptXUsJf5nDWCiHxZFLeb9oju\njf6aNYt9XxS1fvSopo0e3dM//H4WPd7Swu+bsj5oyjbw5HfoBWSk0da0xKYyZaTB602IBijV1DDj\ny+/vOVZdHTOAPp/949x8szjVx9xeldQhI3V1YqPs97M2i1LDeEYZ0BoL+2rdVvckEVhdW12d/ful\ngnEiYOd3rqnp+Z6on/h89g0ab4I3fbp8MnbSSdbHt7p3xr5pla4Wj9+hF5CxRrs3rYKJJOA077Wy\nMnr1EAqJV+iinNWqKvXBWdbOUIgZYPOg2dCgaWVl/O/oq1EbE5b64CBt+o3Pag1FA+THTARW19bQ\nYJ3PHq/zy87Z0KBpQ4bwPzNoEMvDd4JuOBsaWF8IhfjnCAR6PEwimprEfdnsYbLyZDjptxlCxhpt\nHVoFZyh2RC54yFZssldVlfpnjassv1/TysuZwdcHN5VrsGqncdA0utFFn9dXObIB2vRafvoEbcJd\ny4UCKk5XTraeXZWVbm2t2kpc9d7zqKuz51nRz2n1O/bpw/qL2fDx2mj8u+oWj3ml3NAQe+zqauvr\n0DS1FbSdfpth7vKMN9pEhuHVfqVMPcz80t2Xs2aJVw+BAFtJ8fb7zIOvnWuw007RhILnfrUwPt2A\n1jywVHv73Mna5Dtf1Wb88i3t2T/9Xeu67Ta20hS0W8UQRyJd2u9f+kT72Z1LtX+/7f9pP7tzqfb7\nlz6Re8kEhqIb0LoqK3vaYaUK19Tkrv+0tipPdo6f00qtzmz4mpo0bdo0TSstFU/K9L+LfvNgMHqi\nqH9X7796HIZ+75qaxKt0gCkC6teh4smw028zzF1ORpuIotd7HrzcJxMdKxDoCVybNk3T1q3rMbxW\nq/OysujVtBfXoOrKFgXEDRmiaZ9+Gr2qam2Vu3mzsjRt06ae/tRqMhim61SW/O3s1DZOmKbVBwZq\nXYDW6cvSugBtX3CgtnHCNPHERWAo9hcN0Gru++/oc8nur9v+Y9doG4+r8jsGApqWk8N/z46Xp6iI\nGX19wmb1Xav98JEj2TWoejLs9NtEbq+kAEkx2m+//bZ21113WX6OjHbi8EInPeVRneWrIorWPnCA\nuQpDoeiVTlOT+9WDnWvQJwrm1aHqwG18GVfbTU3suDfeqD6QWhg71cBQob75sVfH7TWx90xiKDp9\nWdpNM56KPpfod21qct9/rCZu5hWsWate5oK2ejnJUlB9hUJsNS1637jSFj0DlZXR99DsUZJdV6IC\nGVOAhOdpP/TQQ3j00UfRHS8NXMIR8VaISwm8rtsrKo04fz7TAd+5MzrHed489dxskbKVyjWYq0Od\ndhp7f8MG4OOPxUIXMjSt5zrKy9lx//u/xZ/X82/DYWDzZuB//of/uRUr0Ha4WU3sKByGb8UKaTN9\nK1fG3jdJnrRR2OX4uUS/a0OD+/5jJaqji6b85CexOfTZ2axCnFNJZ5nMqFv27GFCPCL27mX3x05F\nL+PvsGEDqaUdI+FGe8yYMXjwwQcTfVpCQiIU4lKCeMkkGksjWklWzp8fLR4hQmQEZPKW+jWIhFHm\nzQP693c/eOuCMaIypMEgO5c+cTjtNKmxa/7nDjWxo1274N+1U9o0/57dPfdNFyoBhIbik+FnH9dM\njxFWMpe89KL/qIrqrFolliO96irr7/NwMllTpaKCTShEYjDG+6MLqASD0Z9paYkWINIpLGTFdkSK\na8XFTMEvQ4ib0X7llVcwYcKEqNfGjRsxfvx4+Hy+eJ2WcEBv0ElXIt4yieEwW8nuFBiWXbvYak1f\nPaxfb88IRCJsJXLwIP87ekUt2aShb19WkYlHKMTUp6wmFFa0tgJ33x09cRBRUYHg9yvVJH8XL4bV\nyOGrqGBypEZPw4gRQHs7UFOD7spKRHxZ2BccdLy6GPdcPLzqPypyolZypDU10QYyEGCyuTJGxVHF\ncNIkppY2Y4b4faO+/YIF0UpwRkRepkWL+Ipr69fHGvpeTNyM9tSpU/HGG29EvUaPHh2v0xEu6A06\n6crY0d9WxeiOvvRSscRkeTlw9CgbkKxWDzwjoK+gjxzhf6ezkw30oknDzp3Avn1M1pTHlVey1ZLV\nhMKKsjJgzRq1z06ahPzioLXkbzgMvPmm0vEwb170hGHPHuDpp4H330fWxo34029ex+3Tl+B3F92E\n7qyeyYmSvLAX/UdFTtRKjnTxYvZbfvopW5Vv2wbceKP4nFVVwCefRLc9FBKvjEXo7fX7mb5+ZWX0\n9aveH1lBHtGEpaMDOHSI/x2Roe+FZKT2OBFNb9FJV0K0X+mmZrPZHS1yPx88yFzFxuIbqoOczO2u\n8+yzzCCLJg3d3WyvtLubrdTM+s7V1Wz/ORwGCgqA8ePt3IUeLroI2L1b/H5WVsx16hr35X18GNJU\nj/I+vmgdcpWqaCUlbPtBdJ/Wrwfuvx9Tb7kcl1080pmevh39ditKSoApU/jvGSdtPA103evyb/8G\nTJjA9pO7u4HZs6Pdzn36ADNnsvbm50f3/S1bxCtjHpWV7B7W1bEJwz//CXz5Zc/1h8Os1OyCBdbP\nl5OtBq9jUtKVZES/ffzxx9odd9xh+TmKHk8cIoW41nB7704Bc0trqzg/1e9nUa8iZTNjhHhDg6at\nXs3+y8OpmIvoVVvbo+88cyY/DclKh5p3vbNmyaPkKyv5albHIoW7Kiu17qys6Nxp/T5bRd77/Sw1\nTXafysqOn9uxOIs5P9uNUI8oUt2sJW8+pywav7WV3WMV1TD9WKI+KuqvqvdGRGurOBJeljkhy6HP\nkLSvpBhtVXqj0U71PGi9fUfC7b0/BcwtnZ0sP1VmRFatEqfC2BHrcCqbKno5kCO1fGVl2VO90q+r\nro4Ze6vPq7T1zTet88dF6UEy4ys6d1VVtCStsaCMHYyGVlcbE90TmUiPivHiXeeBAyyXWp/w+Hya\nlpurZoTt5K4bDbzPxyaLupCLLkD01VekRy6BjHaCSLc86EQWVElbrIyIVUUsv19s9HmDkB1xDKuX\nXvhDpmLldCKgafIVpPl9vWKZyjFvuUVukHfsYFWmVNqow1spGo2H3QlTIOCseIdZbUx0T3RFOd57\nPh9rt+w8vAmiaIIwfbp8EmBX+0D0zPz0p2oVvaz6VQZARjtBpJMRTFTp0rRGZSDXXZUyV7FsFW4W\nSvF6pe20xKaVPrX5PrmpkMYTzpAZ5VBI7tbXS0uqtkWl+pXs91fBrrdDV5Szc42y84werTZp4qGi\ncGbUK5fJ+Nq5h25rB6QxFIiWANItDzpjUsDcYBUYVV3NgqxkaUIXXaQeQasSiGWHSZOAYcOcCXVU\nV8cGz82aBdx2W2wErznXGVALqtPhBSWtXQuMHMlPS9u5Uxxd7/MBc+ZE/82qLdu3A8uWsYAuu6hE\nNNu5FzoVFUC/fuL3eTnesvNs3CgOnrQK8JIFlJWXA4891pN6V1XFAtV4iHL+RfeQ168yBDLaCSDd\njGBGpYDp8CJ0ZcgGq1CIpU7pEbOiCPEnnlCPoLVS0rLC74+NTi8sFKec8SgvZ9997DEWIfz668Dn\nn7Mo81WrgJNPjo6MF2FnAmKMotZT6844g0Uml5SwKHdVKivZfXXaFruoRDQ7OX+/fizK3855nV6n\nlWhMbi4TNxG188kno1Pv7JJJUeGKkNFOAOlmBDMqBcws+alidABmSHQxEzPmHGtRmlkwqC7WUVgI\nXH65vWszomnMyJpTcBYtYmlCOTny75eVAevW9UxAdHnUf/mX6IFZV1+TiV3IJiB+PzclDEBsat13\n37G8d1V4ue+qk6HWVuZh0Cde5eWAle6EyOA1NrI89sZGtfMbJ1yzZonFdWTndTrpsxKNuecelgZm\nZvRocU41DxUlNQIAGe2EkI5GUM+bdZTLmk6IJD/jobDEc+nZEetwIx7R3c3ydY3azgAz3tnZTJhF\nxpQpbEV11lnMSO/ZI5cy1d2aPA+GbMvg1luBb75hecU1NSwvGrDvRg4E2Mra6p6qyoqGQqxfjB/P\nlL/27AGampjLV2RwzAavrQ04/XT2/XHj2H9/8AOWOy/j1lt7Jnt33SXPgeedV79O0SSTR1YWmyDI\nRGNkv8mBA+KVvc/HJoHG36a6mv9ZL5QKexvJ3lSX0ZsC0UR50KkaPa6T6ilqrnBT9cvrimFWgTWy\nfHA3AVJWAW6hkHWEsShYqrpaHA0sigI213wOhdhx1q2zFww2a5Z1rjKvCpqoRrisLOeNN2rav/4r\na6ssolkU/X/SST1pXD6fvNKXLLBRz5MXRVLXyCukxQSnWbFpk/h+yYLlyspYlL+oRnyGRoWrQkY7\nwfRqI5hu2Knt6+V3vW6rcbJQU6Nps2fLazYHAj25xFbXsWkT+1xrK6urrTro5+ZaTxj04xoHb5Fh\nLCrStD595Of0+5mhq6pi/zWXRdXPI0p9ampi6VJ66pFqWU5dRMecp23Mvd6xQ14ac8iQnjQzPU/b\nbq6yKGpcb4ud7ANzmUwj+v2TTSL1tDnZ+yI9ggyNCleFjDaRubhRWEq0OpPsfIEAW4laGT7j67rr\n7F1HXZ14VWXnJbs3btLaQiFmHEWGIhDoMdCiFa/ZA2E0HnYU6Wpq2Ms4cSooUPvuzJnWRsvOqlS/\nDrvpfbKJp0r/Miq3yZTsMkgUxSvIaBOZjRuFpUSrM6mcT9XwGV2pqse1khF1awxUDGNOjritbnPZ\nrSYUqtevIgkqevl89qRARQbe7E0IheTeF9V7YWc7RaehQewqzyD5Ua8go01kNm720oxuQn1gjOc+\nnEpb7WqUm1dEsnvgheSpW8Po92va1Vdr2gknMANnbKtbfXarbQ0vJV/t/D76vbHjNnbbVtHEU3U7\nxc53vN5K6uWQ0SYITXO2l+bGaMvOpxKUJvuunRWx0Yhande8ehsyRNNOPtme29zKC2FlbILBnvtd\nVhYdeOXWG2C16quvt95X9/pVWakm72nuAzLlMdneOi/4TbV/yVbnVOjDM8hoE4RTnLjHZfrPTqol\n2WmXVysdvTqYTE7UbCRUr8VO1Sne/bYTIW1+zZrFn7TobSotVTuO3epoTl6yPiaLP7DyRKxbZ/37\nO+n3VOjDM8hoE4QTnKZ8yQYvrwY2PT1LtqJyu9JRTf8SleK0oqmJRWLraVQVFeJVrvEa7Bhtv58Z\nt1CIH3GuTzBUj6mvUt1MHFRfVtsMov3rQEAe9c2LQDd7YJxsKVFKl2eQ0SYIJzjZp5MZ+lBIPJjG\n07DKIqZF2En/Ul3Ji87d1MTytGXnMxamEBVgkb1EHoPrrmOpWioucWM1rM7O2Ohxr1+y+yoz2sEg\nyytXmQxYeX6cbClRSpdryGgThBOc7NPJDH1WlvfBOuZBNxCIjr4OBJhxMQuaWK2CvvpK3bhYTTjM\nbTy2T3209ai2t+GI1nG7wqpVP4fTtDQVj4ToVVrKF0Cpq9O0Tz91Fxin9wu799VqQnnllWqTAXJp\npyRktAnCKXYHNZmhj8dK23jeujrxylslb9mIHWU0q3Kdgnu4ffAwbertf9T2F5+gfg4vVeNUX59+\n2nNdbtOseK+TTuL/vaZG/nvLysGWl4vPFwpZ1xCn4LGkQtrjBOEUO7rhgFzn+sorxRW33OovFxay\nogtvvsl/f+NG/t95ZRHDYfFxAFZ4RHQvzMVZRo4EnnuOe5jKfdsw852n0f/wfvG5ysqiz2G3apkO\nr8SnCsEguxYds479zp1ibXbV448dK35fVJnOqhzs3r3iY150Efu+rCoYVd5KLsmeNciglTaRFtjZ\np5MF5MQz79tJDjPPLS87js/Hoo9F98Jm7vD+Pv20fYGB/PfLy5loh5mmJvur25Ejna2CjatdqzSr\nyspYmVXjv3nf0/XIee8ZU9942xmiftbUJF6FB4PREqyUppWSkNEmiGTAM/TxNNpOcph5+tNOB3MH\namWdgLb6pLH896uq+PfFzuREN2QHDthL06qo4IvaiPbTddER4+9t/P0F+/raV1/ZF8rh3XdzP1Pd\n1qE97ZSEjDZBeImb6Fg7g6ST89hVyaqqct9OHQcr/W5A21dUoh3KF6ycRfdFZXIyZEj0Sl313lRX\n8/O4ZSl2KitT/RhlZT2rZ9lK2+l59HOppF9RmlZKQkabILzArTCKauCPm/Po3xXpQJtfokpPTgZz\nr7TLjS+Ri1zFAJtd/1ZpWjKlMKvzudGxF7nOVa7JCjspfpSmlTKQ0SYIL3DrSlTN+/bCZSkr4GA+\n7+rVYmlKq3rVRjo77Rkg1VdZmXg/V5azLZPc3LSJRYVv2mRdJlM22bKqb61yDKOMqb4HLppY0F5z\nRkBGmyDc4kV6jMpesZdpOKqrUXNRDqcrfdH5Ro92V5lLNmlpbWXubLeTHBleFMNQOYZxkiRKuaO9\n5oyAjDZBuMWrKkZWq2gvqyUZja+qIIlTqVWryYadvG/RS88vll1nPPZlvYiytjpGU1P0RMkcge62\njCeRVpDRJgi3eJUeY2Vg4pGGoxf/mDnTukhHZaXY5exGoeurr3qu243hrq6WV6eqq7N2dzvBiy0L\nJ5r0ogInRnQZWFl6GJFWkNEmCC/wMj1Gtipyeh6rlZYdd7ndlb7qZEOfQBhLUdqVGBXdB68qqFkd\nW7TytVP21JxXLdvvtjqeaP+bXOlpCxltgvCCRKXH2D2PirFSzaGurHQutepE8nX1avuCMKJ2JCLn\nWJZ7b77/TU18I24+Rl2d+Fp9PvFEyWoSZqeOOpFSkNEmCC9J1ADIO49TIQ3VHGqne9qa5jxNzK6W\nOG/Fn0wdbdH9CgTUVvwNDWJvg9/PT3lTmYSZtyXIdZ42kNEmiHRHtppTMVZWOdTGHGWz8Q2FWFlK\nXf7SCtVJjZ43baxKZnyJFMx4RtjLAD472FGBE016ZCttgN92lUmYLACQXOcpDRUMIYh0x1yoYvt2\n9u/aWrWiD7ICE9OnA19+CTz+OJCdzV6PPw5s2ABcfz37zAsvAKedxoqBRCLythYWAsOHywughMPA\nzTcDS5YAnZ2x71dVATfcwP8ur8BGaSkQCvE/X1HB3o8HsqIbZnjFWQDWtspK/neGDAH69uV/R3S9\nOuPHiwu/iNpCpARktAkinQmHgeXL+e+tXQuUl/PfMxsrUcWy3/2Ob2DnzQOef55VsjJOFO65x/m1\n6FXARo5kxxZx8CDw0EM97c3KAgIB9nrhBVZ5yziBkE1K3FZQk6FiPHVElbMKC4HJk/nf2bsXOOus\n2MmS7HqDQXbf5syJTxUvUeUxwjuSvdSXQe5xgrDAyvU7fbo9F6iK+9pKwcuuLKZVvW/zKyurxy2s\nKqCSLB1tVU1z2d66se2q7nWrbQyv0wfjGZ1PREFGmyDSGTvCHF4ZK6cRzeaB3SgSYie9yyikYjfI\nzOtAQZVUrlmzmE663y/OhRdVLTMik5+VybJ6nT7IgyqCJQwy2gSR7qgMmF4aKycRzbJ22n2pRr7H\nM8hMZWVpVp0rK2MiNqed5szAeX2tXnkfkhmdn4GQ0SaIdCfRrl8nEc0O6mnHvAIBFlFuzjH3WiVO\nBZWJkizdi/f3YFAehR+va3U7oUvWxClDoUA0gkh39Ijuf/wD+Ppr9l892hvwPjhIFtFcWcmPxrYT\nSW1m2jRg0yZg3z5g8eKe6wKSE2QmC/7TI69ln2lp4f+9uZkFiImI17WqRPTLSFZ0foZCRpsgegvm\nwVePxh41ChgxIjaq2s15RBHNkyfzB387kdR+P4sI1yPYn38eOOUUsVFZtAioqWGR0TqBAItqd3ut\nPGQTED3y2ukkZe1a+eRKFOW/aJH9c3lFsqLzM5VkL/VlkHucIFwQz+AgJy551T1tlUIYdq41HsFn\nKmVURZ8RCcPYcSc7uaZ4qvUlKzo/AyGjTRDpjGgglu0hW+2d2qGhgWmEi4LPjJgHdiclJnlYXatK\nhSu7Bk00STBGgYs+M3OmeF87HvvwiUzHIh3zuENGmyDSEauB2ErKcvr0+J5f0+QTCl6edjwCoaw8\nDU4NWmcnM9C841dXs2uRrT4TmSJF6Vi9CjLaBJGOWA3EVsU2jLnOXp8/0UIbVtrpstWsm1Knsmj4\nUKjnmq2qf8XTnexWCIdIOchoE0S6oZoXK1IKs7N36uT8yShEYScHXL92N/nFdiqjyVD1RjjFqRAO\nkbJQ9DhBpBsq0csA0wIPBPifc5OKIzv/zp0s7YlHPAtRmKOqKyutr131PvIoLWUFO6ywuuZ4R/z3\n7cvuB4+sLH7BESKlIaNNEOmGal5sMAhUV/M/N3FifPJydWPIw00hCivMuepffgnMmMH/rJ6G5DS/\nuK0N+MEPgD17rNtl95pFFducFmJpagK6uvjvdXWx94m0gow2QaQbyc6LtTp/MoU2jCtXq5xmp/fx\nvPOA9euZk9mK8nL1a1YRbbGLEyEcIqUho00Q6YiKyEY4DKxcyf/+66+7c1WLzv/EE6kjtGGlFAfY\nFytpbGTqbKr066d+zW7c9SKcCOEQKY1P01Smi8lh9+7dGDduHFavXo1yUV1ggshkwmE2mJeWxg7A\nW7eyfdHu7tjv+f3MkA0f7t35Afb/AweyetsrVjBjU1HBDPaiRdEGM5XQr6NvX+Yy5t1PAFizBhg3\nTv24lZXMVa9iHMNhtoe9fXvse0OHskmHEyMbiTD3ejr9HoQQWmkTRDoj041OhCZ0YSEzTA880BM8\nddpp7L0NG8Qr3FQjNxdYsgQ46yx5ANjo0eLALh67d6uvkOO17aHicSDShoT+ai0tLZg7dy6OHDmC\nzs5O3HfffTj99NMT2QSCyBx0I/DEE7Hveemq1oOndPTgKYAZh3RA9RpKSoBTT2V72irYnRzpbnne\nqtgt+gSPSGsS6h5fvHgxgsEgqqursW3bNtx999147bXXhJ8n9zhBuCTertFwGDj5ZGDHjtj33Lh0\nE4nda2hrY8FomzaxCGy/n+1dNzbGfr+21tnEJRwGtm1j/z9sWOrfQyJhJHSlXV1djdzcXABAV1cX\n8vLyEnl6gsg8dNfoggXivW83qARPpfrqzu415OcD69YxI71xI3OZFxeLJ0d2iUTYdsOKFSzvPRSi\nPWjiOHHrAa+88gqWLVsW9bcFCxZg9OjRaGhowNy5c/HAAw/E6/QEQRiJl2tU3zfnBU+lSy1lp9dQ\nUgJcfHHPv72aHPWG7QYibsTNaE+dOhVTp06N+fvXX3+Nu+66C/feey/OPvvseJ2eIIhEkKh983ji\n5TW4nRxZ5WovWJAe95SIGwn1tdTV1aG2thaPP/44TjrppESemiCIeBCJsJSyQABoaWF/CwaB6dO9\nCZ5KFPEMALNDb9huIOJKQo32o48+io6ODjz88MMAgKKiIjz11FOJbAJBEDqyHG9V7rmHpUoZaW5m\nutbptP8a771/VXrDdgMRVxL6VJGBJogUwBhR7ibQqTe6cpOdFtUbthuIuJJGU2GCIDzBq0AncuXG\nh1Rx1RMpCSmiEUQm4WVRikQormUipGBGSCCjTRCZhJdFKZJdbay3I5OoJTIWmroRRCbhdaATuXIJ\nIqHQSpsgMgmvV8fkyiWIhEJPFkFkGvFYHSc76pogMgQy2gSRaaRKTjJBELYho00QmQqtjgki7aA9\nbYIgCIJIE8hoEwRBxJNwGNi61V4OPEEIIKNNEAQRDyIR4I47gFGjgBEj2H/vuIP9nSAcQnvaBEEQ\n8YDqYhNxgFbaBEEQXuOlXCxBGCCjTRAE4TVeysUShAEy2gRBEF5DxVSIOEFGmyAIwmuomAoRJygQ\njSAIIh5QMRUiDpDRJgiCiAckF0vEATLaBEEQ8YTkYgkPoT1tgiAIgkgTyGgTBEEQRJpARpsgCIIg\n0gQy2gRBEASRJpDRJgiCIIg0gYw2QRAEQaQJZLQJgiAIIk0go00QBEEQaQIZbYIgCIJIE8hoEwRB\nEESakNIypl1dXQCAffv2JbklBEEQBJE4Bg8ejOzsWBOd0ka7oaEBADBt2rQkt4QgCIIgEsfq1atR\nXl4e83efpmlaEtqjRFtbGzZv3oyBAwfC7/cnuzkEQRAEkRBEK+2UNtoEQRAEQfRAgWgEQRAEkSaQ\n0SYIgiCINIGMNkEQBEGkCWS0CYIgCCJNIKNtQUtLC2bOnInrrrsOV199NdatW5fsJmUMf/3rX3H3\n3Xcnuxm9mu7ubsybNw9XX301rr/+euzYsSPZTcoYNmzYgOuvvz7ZzcgYOjs7MXfuXFx77bWYMmUK\nVq9enewmOSKl87RTgaVLl+Lcc89FdXU1tm3bhrvvvhuvvfZaspvV63nooYfwwQcfYOTIkcluSq/m\nnXfeQUdHB15++WWsX78eCxcuxFNPPZXsZvV6nn32WaxcuRIFBQXJbkrGsHLlShQXF+O//uu/cPjw\nYUyePBnjxo1LdrNsQyttC6qrq3HNNdcAYApteXl5SW5RZjBmzBg8+OCDyW5Gr+eLL77AhRdeCACo\nqqrC5s2bk9yizCAUCmHJkiXJbkZGcfnll6O2thYAoGla2mp/0ErbwCuvvIJly5ZF/W3BggUYPXo0\nGhoaMHfuXDzwwANJal3vRHTPx48fj08++SRJrcocjhw5gqKiouP/9vv9iEQiXFEHwjsuu+wy7N69\nO9nNyCj69OkDgPX5OXPm4I477khyi5xBT6aBqVOnYurUqTF///rrr3HXXXfh3qsBxusAAAJDSURB\nVHvvxdlnn52ElvVeRPecSAxFRUVobW09/u/u7m4y2ESvpb6+HrNnz8a1116LiRMnJrs5jiD3uAV1\ndXWora3Fo48+irFjxya7OQThKWPGjMHf/vY3AMD69esxYsSIJLeIIOJDY2MjZsyYgblz52LKlCnJ\nbo5jaEptwaOPPoqOjg48/PDDANjKhAJ1iN7CpZdeig8//BDXXHMNNE3DggULkt0kgogLTz/9NJqb\nm/Hkk0/iySefBMACAvPz85PcMnuQ9jhBEARBpAnkHicIgiCINIGMNkEQBEGkCWS0CYIgCCJNIKNN\nEARBEGkCGW2CIAiCSBPIaBMEAQD45JNPcMEFF+DAgQPH//b73/8eNTU1SWwVQRBGyGgTBAEAOOec\nczBx4kT8/Oc/B8DEVl5++eXjGgUEQSQfytMmCOI4HR0dmDp1Kq666iq8+OKL+M///E+cfvrpyW4W\nQRDHIKNNEEQU//znPzFp0iTccsstaVtUgSB6K+QeJwgiir///e/o168fPvroI0QikWQ3hyAIA2S0\nCYI4Tl1dHZYsWYKXXnoJubm5pLNPECkGGW2CIAAA7e3tuPPOOzF37lxUVFRg4cKFePHFF7F+/fpk\nN40giGOQ0SYIAgCwYMECjBgxApMmTQIAlJWV4f7778fcuXOjam4TBJE8KBCNIAiCINIEWmkTBEEQ\nRJpARpsgCIIg0gQy2gRBEASRJpDRJgiCIIg0gYw2QRAEQaQJZLQJgiAIIk0go00QBEEQaQIZbYIg\nCIJIE/5//BvU8pnOEUUAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x113fde978>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()\n",
    "ax.scatter(X[Y==0, 0], X[Y==0, 1], label='Class 0')\n",
    "ax.scatter(X[Y==1, 0], X[Y==1, 1], color='r', label='Class 1')\n",
    "sns.despine(); ax.legend()\n",
    "ax.set(xlabel='X', ylabel='Y', title='Toy binary classification data set');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Model specification\n",
    "\n",
    "A neural network is quite simple. The basic unit is a [perceptron](https://en.wikipedia.org/wiki/Perceptron) which is nothing more than [logistic regression](http://pymc-devs.github.io/pymc3/notebooks/posterior_predictive.html#Prediction). We use many of these in parallel and then stack them up to get hidden layers. Here we will use 2 hidden layers with 5 neurons each which is sufficient for such a simple problem."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def construct_nn(ann_input, ann_output):\n",
    "    n_hidden = 5\n",
    "    \n",
    "    # Initialize random weights between each layer\n",
    "    init_1 = np.random.randn(X.shape[1], n_hidden)\n",
    "    init_2 = np.random.randn(n_hidden, n_hidden)\n",
    "    init_out = np.random.randn(n_hidden)\n",
    "        \n",
    "    with pm.Model() as neural_network:\n",
    "        # Weights from input to hidden layer\n",
    "        weights_in_1 = pm.Normal('w_in_1', 0, sd=1, \n",
    "                                 shape=(X.shape[1], n_hidden), \n",
    "                                 testval=init_1)\n",
    "        \n",
    "        # Weights from 1st to 2nd layer\n",
    "        weights_1_2 = pm.Normal('w_1_2', 0, sd=1, \n",
    "                                shape=(n_hidden, n_hidden), \n",
    "                                testval=init_2)\n",
    "        \n",
    "        # Weights from hidden layer to output\n",
    "        weights_2_out = pm.Normal('w_2_out', 0, sd=1, \n",
    "                                  shape=(n_hidden,), \n",
    "                                  testval=init_out)\n",
    "        \n",
    "        # Build neural-network using tanh activation function\n",
    "        act_1 = pm.math.tanh(pm.math.dot(ann_input, \n",
    "                                         weights_in_1))\n",
    "        act_2 = pm.math.tanh(pm.math.dot(act_1, \n",
    "                                         weights_1_2))\n",
    "        act_out = pm.math.sigmoid(pm.math.dot(act_2, \n",
    "                                              weights_2_out))\n",
    "        \n",
    "        # Binary classification -> Bernoulli likelihood\n",
    "        out = pm.Bernoulli('out', \n",
    "                           act_out,\n",
    "                           observed=ann_output,\n",
    "                           total_size=Y_train.shape[0] # IMPORTANT for minibatches\n",
    "                          )\n",
    "    return neural_network\n",
    "\n",
    "# Trick: Turn inputs and outputs into shared variables. \n",
    "# It's still the same thing, but we can later change the values of the shared variable \n",
    "# (to switch in the test-data later) and pymc3 will just use the new data. \n",
    "# Kind-of like a pointer we can redirect.\n",
    "# For more info, see: http://deeplearning.net/software/theano/library/compile/shared.html\n",
    "ann_input = theano.shared(X_train)\n",
    "ann_output = theano.shared(Y_train)\n",
    "neural_network = construct_nn(ann_input, ann_output)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "That's not so bad. The `Normal` priors help regularize the weights. Usually we would add a constant `b` to the inputs but I omitted it here to keep the code cleaner. Let's train the model using new ADVI implemented via [OPVI](https://arxiv.org/abs/1610.09033) framework"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from pymc3.theanof import set_tt_rng, MRG_RandomStreams\n",
    "set_tt_rng(MRG_RandomStreams(42))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Average Loss = 186.09: 100%|██████████| 20000/20000 [00:06<00:00, 3244.78it/s]\n",
      "Finished [100%]: Average Loss = 185.99\n",
      "Average Loss = 135.65: 100%|██████████| 30000/30000 [00:09<00:00, 3194.79it/s]\n",
      "Finished [100%]: Average Loss = 135.68\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 17.6 s, sys: 504 ms, total: 18.1 s\n",
      "Wall time: 19.6 s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "\n",
    "with neural_network:\n",
    "    # Run ADVI to estimate posterior means, standard deviations, and the evidence lower bound (ELBO)\n",
    "    # here is a good chance to demonstrate `cost_part_grad_scale` parameter usage\n",
    "    # the reason is described here: approximateinference.org/accepted/RoederEtAl2016.pdf\n",
    "    # to be short it is used to reduce variance of gradient on final iterations\n",
    "    s = theano.shared(pm.floatX(1))\n",
    "    inference = pm.ADVI(cost_part_grad_scale=s)\n",
    "    # ADVI has nearly converged\n",
    "    pm.fit(n=20000, method=inference)\n",
    "    # It is time to set `s` to zero\n",
    "    s.set_value(pm.floatX(0))\n",
    "    approx = pm.fit(n=30000)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's compare performance with no grad scaling"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "set_tt_rng(MRG_RandomStreams(42))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Average Loss = 136.61: 100%|██████████| 30000/30000 [00:09<00:00, 3302.62it/s]\n",
      "Finished [100%]: Average Loss = 136.62\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 9.97 s, sys: 224 ms, total: 10.2 s\n",
      "Wall time: 10.6 s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "\n",
    "with neural_network:\n",
    "    inference_no_s = pm.ADVI()\n",
    "    approx_no_s = pm.fit(n=30000, method=inference_no_s)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And using old interface. Performance is nearly the same"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Average ELBO = -175.52: 100%|██████████| 30000/30000 [00:07<00:00, 4206.95it/s]\n",
      "Finished [100%]: Average ELBO = -157.15\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 8.84 s, sys: 134 ms, total: 8.98 s\n",
      "Wall time: 8.98 s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "\n",
    "with neural_network:\n",
    "    advifit = pm.advi(n=30000)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "~ 30 sec on my laptop. That's pretty good considering that NUTS is having a really hard time. Further below we make this even faster. To make it really fly, we probably want to run the Neural Network on the GPU.\n",
    "\n",
    "As samples are more convenient to work with, we can very quickly draw samples from the variational posterior using `approx.sample_vp()` (this is just sampling from Normal distributions, so not at all the same like MCMC):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "trace = approx.sample(draws=5000)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Plotting the objective function (ELBO) we can see that the optimization slowly improves the fit over time."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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Uai+2tq5UApOvLpObAWBj45AUvSaoNtXm7fvlAGQuIai3LltjC6cLZqw3OQ74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\nMREFv4iIiIn8H854/R5GJYClAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11c909588>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(-inference.hist, label='new ADVI', alpha=.3)\n",
    "plt.plot(-approx.hist, label='new ADVI no scaling', alpha=.3)\n",
    "plt.plot(advifit.elbo_vals, label='old ADVI', alpha=.3)\n",
    "plt.legend()\n",
    "plt.ylabel('ELBO')\n",
    "plt.xlabel('iteration');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Grad scaling seemd to give no effect, but let's see difference in variance of ELBO, that's really what is expected"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(726.99405291840856, 757.69014707492715)"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "approx.hist[25000:].var(), inference_no_s.hist[25000:].var()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now that we trained our model, lets predict on the hold-out set using a posterior predictive check (PPC). \n",
    "\n",
    "1. We can use [`sample_ppc()`](http://pymc-devs.github.io/pymc3/api.html#pymc3.sampling.sample_ppc) to generate new data (in this case class predictions) from the posterior (sampled from the variational estimation).\n",
    "2. It is better to get the node directly and build theano graph using our approximation (`approx.sample_node`) , we get a lot of speed up"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "sigmoid.0"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# We can get predicted probability from model\n",
    "neural_network.out.distribution.p"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# create symbolic input\n",
    "x = T.matrix('X')\n",
    "# symbolic number of samples is supported, we build vectorized posterior on the fly\n",
    "n = T.iscalar('n')\n",
    "# Do not forget test_values or set theano.config.compute_test_value = 'off'\n",
    "x.tag.test_value = np.empty_like(X_train[:10])\n",
    "n.tag.test_value = 100\n",
    "_sample_proba = approx.sample_node(neural_network.out.distribution.p, \n",
    "                                   size=n,\n",
    "                                   more_replacements={ann_input: x})\n",
    "# It is time to compile the function\n",
    "# No updates are needed for Approximation random generator \n",
    "# Efficient vectorized form of sampling is used\n",
    "sample_proba = theano.function([x, n], _sample_proba)\n",
    "\n",
    "# Create bechmark functions\n",
    "def production_step1():\n",
    "    ann_input.set_value(X_test)\n",
    "    ann_output.set_value(Y_test)\n",
    "    with neural_network:\n",
    "        ppc = pm.sample_ppc(trace, samples=500, progressbar=False)\n",
    "\n",
    "    # Use probability of > 0.5 to assume prediction of class 1\n",
    "    pred = ppc['out'].mean(axis=0) > 0.5\n",
    "    \n",
    "def production_step2():\n",
    "    sample_proba(X_test, 500).mean(0) > 0.5"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "See the difference"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "247 ms ± 33.1 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)\n"
     ]
    }
   ],
   "source": [
    "%timeit production_step1()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "52.8 ms ± 3.71 ms per loop (mean ± std. dev. of 7 runs, 10 loops each)\n"
     ]
    }
   ],
   "source": [
    "%timeit production_step2()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "pred = sample_proba(X_test, 500).mean(0) > 0.5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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mKm14/wDqG8V5217jJC0sFotj9dpSzPvlRtz4izfw3Z+9jht/0d7Gk9cj2wpd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\noLQBALDEv+CtrwA1KLIPAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11de74278>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()\n",
    "ax.scatter(X_test[pred==0, 0], X_test[pred==0, 1])\n",
    "ax.scatter(X_test[pred==1, 0], X_test[pred==1, 1], color='r')\n",
    "sns.despine()\n",
    "ax.set(title='Predicted labels in testing set', xlabel='X', ylabel='Y');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Accuracy = 94.8%\n"
     ]
    }
   ],
   "source": [
    "print('Accuracy = {}%'.format((Y_test == pred).mean() * 100))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Hey, our neural network did all right!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Lets look at what the classifier has learned\n",
    "\n",
    "For this, we evaluate the class probability predictions on a grid over the whole input space."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "grid = pm.floatX(np.mgrid[-3:3:100j,-3:3:100j])\n",
    "grid_2d = grid.reshape(2, -1).T\n",
    "dummy_out = np.ones(grid.shape[1], dtype=np.int8)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Creater posterior predictive samples\n",
    "ppc = sample_proba(grid_2d ,500)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Probability surface"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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DLjeKEc5hpHFBqZZ5pZbb4jOUUdgxmBFpCXhr8FAZr2gUds1TsaJBTuEFFdISlFDmVbWM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98HN9xwA772ta8xnYOEGWELMTECMRaGR8hPPRbr6zcCSYBEWT+2NZAWBPStXYvGq66yvXnuYBZl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\n2QAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11df487b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "cmap = sns.diverging_palette(250, 12, s=85, l=25, as_cmap=True)\n",
    "fig, ax = plt.subplots(figsize=(16, 9))\n",
    "contour = ax.contourf(grid[0], grid[1], ppc.mean(axis=0).reshape(100, 100), cmap=cmap)\n",
    "ax.scatter(X_test[pred==0, 0], X_test[pred==0, 1])\n",
    "ax.scatter(X_test[pred==1, 0], X_test[pred==1, 1], color='r')\n",
    "cbar = plt.colorbar(contour, ax=ax)\n",
    "_ = ax.set(xlim=(-3, 3), ylim=(-3, 3), xlabel='X', ylabel='Y');\n",
    "cbar.ax.set_ylabel('Posterior predictive mean probability of class label = 0');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Uncertainty in predicted value\n",
    "\n",
    "So far, everything I showed we could have done with a non-Bayesian Neural Network. The mean of the posterior predictive for each class-label should be identical to maximum likelihood predicted values. However, we can also look at the standard deviation of the posterior predictive to get a sense for the uncertainty in our predictions. Here is what that looks like:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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QLQO8U20ysub8VB/77o4Y+iISmjLWyRFVmnJ5f7Iaq2XOcVsgAxjKyB0YzIhIk5eqTXp8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\nQAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11f43e550>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "cmap = sns.cubehelix_palette(light=1, as_cmap=True)\n",
    "fig, ax = plt.subplots(figsize=(16, 9))\n",
    "contour = ax.contourf(grid[0], grid[1], ppc.std(axis=0).reshape(100, 100), cmap=cmap)\n",
    "ax.scatter(X_test[pred==0, 0], X_test[pred==0, 1])\n",
    "ax.scatter(X_test[pred==1, 0], X_test[pred==1, 1], color='r')\n",
    "cbar = plt.colorbar(contour, ax=ax)\n",
    "_ = ax.set(xlim=(-3, 3), ylim=(-3, 3), xlabel='X', ylabel='Y');\n",
    "cbar.ax.set_ylabel('Uncertainty (posterior predictive standard deviation)');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see that very close to the decision boundary, our uncertainty as to which label to predict is highest. You can imagine that associating predictions with uncertainty is a critical property for many applications like health care. To further maximize accuracy, we might want to train the model primarily on samples from that high-uncertainty region."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Minibatch ADVI"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So far, we have trained our model on all data at once. Obviously this won't scale to something like ImageNet. Moreover, training on mini-batches of data (stochastic gradient descent) avoids local minima and can lead to faster convergence.\n",
    "\n",
    "All you need to train with minibatches is to your data with the `pm.Minibatch` class.\n",
    "The rest code should work without changes, let's see it"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Average Loss = 135.58: 100%|██████████| 40000/40000 [00:05<00:00, 6800.30it/s]\n",
      "Finished [100%]: Average Loss = 135.64\n"
     ]
    }
   ],
   "source": [
    "minibatch_x = pm.Minibatch(X_train, batch_size=50)\n",
    "minibatch_y = pm.Minibatch(Y_train, batch_size=50)\n",
    "neural_network_minibatch = construct_nn(minibatch_x, minibatch_y)\n",
    "with neural_network_minibatch:\n",
    "    approx = pm.fit(40000, method=pm.ADVI())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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9GPt+W+XDffbNWRw8V3V2v6w8hVFfV7u6f83q6nCmMaqxDm9j9MPbABdDTd+8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\nBEHA+fPnMWDAAFHO5c8//8Tu3bvh7e2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      "text/plain": [
       "<matplotlib.figure.Figure at 0x120e24be0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(inference.hist)\n",
    "plt.ylabel('ELBO')\n",
    "plt.xlabel('iteration');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It works!"
   ]
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "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"
  },
  "latex_envs": {
   "bibliofile": "biblio.bib",
   "cite_by": "apalike",
   "current_citInitial": 1,
   "eqLabelWithNumbers": true,
   "eqNumInitial": 0
  },
  "nav_menu": {},
  "toc": {
   "navigate_menu": true,
   "number_sections": true,
   "sideBar": true,
   "threshold": 6,
   "toc_cell": false,
   "toc_section_display": "block",
   "toc_window_display": false
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}
