Raw File
{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import sys\n",
    "import numpy as np\n",
    "import numpy.random as rnd\n",
    "import time\n",
    "import GPflow\n",
    "import tensorflow as tf\n",
    "import matplotlib\n",
    "import matplotlib.pyplot as plt\n",
    "plt.style.use('ggplot')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "M = 50"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Create a dataset and initialise model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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hPvh4vnjU/jyFODvGVbeEnJDTzlL0Zk/FSmwM5t/+jLl5g3hc3hCB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\nQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11074e250>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def func(x):\n",
    "    return np.sin(x * 3*3.14) + 0.3*np.cos(x * 9*3.14) + 0.5 * np.sin(x * 7*3.14)\n",
    "X = rnd.rand(10000, 1) * 2 - 1\n",
    "Y = func(X) + rnd.randn(10000, 1) * 0.2\n",
    "plt.plot(X, Y, 'x')\n",
    "D = X.shape[1]\n",
    "Xt = np.linspace(-1.1, 1.1, 100)[:, None]\n",
    "Yt = func(Xt)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def init():\n",
    "    kern = GPflow.kernels.RBF(D, 1)\n",
    "    Z = X[:M, :].copy()\n",
    "    m = GPflow.svgp.SVGP(X, Y, kern, GPflow.likelihoods.Gaussian(), Z, minibatch_size=len(X))\n",
    "    return m\n",
    "m = init()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Stochastically calculate bound and show noise\n",
    "The minibatch estimate should be an unbiased estimator of the `ground_truth`. Here we show a histogram of the value from different evaluations, together with its mean and the ground truth. The small difference between the mean of the minibatch estimations and the ground truth shows that the minibatch estimator is working as expected."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "ground_truth = m.compute_log_likelihood()\n",
    "m.X.minibatch_size = 100\n",
    "m.Y.minibatch_size = 100\n",
    "evals = [m.compute_log_likelihood() for _ in range(100)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.lines.Line2D at 0x1114d9b10>"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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3b9bcuXMlSdeuXdNrr72mzs5O+Xw+rVq1Sl//+tclSZ2dndq9e7eGhoZUU1OjVatWpddp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\nDwiFI2rIwwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1114d9b50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(evals)\n",
    "plt.axvline(ground_truth)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Show that minibatches speed up computation\n",
    "The use of using minibatches is that it decreases the time needed to make an optimisation step, since estmating the objective is cheaper. Here we plot the change in time required with the size of the minibatch. We see that smaller minibatches result in a cheaper estimate of the objective."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "mbps = np.logspace(-2, 0, 10)\n",
    "times = []\n",
    "objs = []\n",
    "for mbp in mbps:\n",
    "    m.X.minibatch_size = m.Y.minibatch_size = int(len(X) * mbp)\n",
    "    start_time = time.time()\n",
    "    objs.append([m.compute_log_likelihood() for _ in range(20)])\n",
    "#    plt.hist(objs, bins = 100)\n",
    "#    plt.axvline(ground_truth, color='r')\n",
    "    times.append(time.time() - start_time)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x103e335d0>"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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1uE3tkEgF0dHRlxzTarX1HiciIvIUFr1EROQ24mwVxL/WQuRmQ3ooBtLghyC14FsNERER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\niIiIiIjkLXV6RUREREREJG/9A9d7ebBWiN99AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x111837f90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "f, (ax1, ax2) = plt.subplots(1, 2, figsize=(16, 6))\n",
    "ax1.plot(mbps, times, 'x-')\n",
    "ax1.set_xlabel(\"Minibatch proportion\")\n",
    "ax1.set_ylabel(\"Time taken\")\n",
    "\n",
    "ax2.plot(mbps, np.array(objs), 'kx')\n",
    "ax2.set_xlabel(\"Minibatch proportion\")\n",
    "ax2.set_ylabel(\"ELBO estimates\")\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Show actual stochastic optimization"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x11146b7d0>"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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gf6TLkQPwy89itotp59s+liDftgsKlvtDtwS0c5Up7OshenRLuO0esQlWx7wy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\nvh03PU0qsQ4bhZr7hgj+S68UmXPDLb41hck+KKt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CH0kyeepMcpko2JFeCbjJSHGR1OH+\naXZhhTEqnGtqBDtdQrIEZZZgryspV86B+nrI//kA8vsbXIqj2QLeBXng+Yct1aMGx5k4jAGniqEZ\nMjRwgXI/w9IzSX9q/Vpg9j0kk2GsoQyrSdPIr2/NYIvywG/f1Aho1ICDFp8usUzMcmw8UFnh5EBO\n7Rc/36JskDQplbKUrO9iXeWnjQzszjspFay4CNKiR6hfwYLlXp8qOI19cxMZd72BAq6XjiYp1ZYW\nkiTtO5iq9jqS0jW6qALtDLilMXOYnlYpegPYDVm08vk0G7Csfrx6KPxFYT5NROWnPQuceoouDMgc\nTzpA6RnAH562TJJuuN6qz9KOruhH4GyFW/57po+gIP7u7fS5TA4CykyiWoFRl4GFhQePe01huMlI\nhVZLVkIaO7G1aGjYaOBvayF/tR3Y9hHw2EvApR7ER7gM/HCQVGS9mCRtE/M//txaxdrxkaQnNXqs\nokHSDqXQg+H5tAu0c5ORanG8JDiNPUABOZOJUvvyD5EP32Qkf+/JIsqcqbeszJnkn16bvhBuoAep\nzwByI2zfBDZ3MdjgFJvUcsBvJHssgmjSw78jrRB/oA2jCTwyCmzBMsoG6dnbMxfa+Srg/FkaSzfG\nT87ZDb73S8qEMjkJ2nOZJuXBqdDY6fVfdBTmW6R5DdS5Sa0Be+hZsLGTSLrjw38A/ZLAwvUki+FJ\nhlraSEpLrPEwfRNodcn17k8TuuMjgdx9YJNnKB4kbS+FHgzPp03OxD6V1kuCzEK2g0lUrGFuoQdV\nbwBOHadArX3mDJe9F3PyBfsuOvYBXrWGrqf6HDB6HFCQZ5mdDUBxka2zUFD5hK1Km4DnCojuENud\ninbMZuDYz+D//AtlUZ0qJl+x3uBaiM3KgCQaSxfIObvBd26j+yXMQDtDR6g1FGA8UeTmB+qa2LJ0\nCvPB0kZQNlh8T0sTGz2pQDbUga97FkjP8CxDLf8QuVj+/S7knN2eXZi1bWB5qeMJxtpUJi6eKuYV\npn3nr2B8Pn2ZgILb2LdvpWaqo0i8K8GuziC2B+WYW3cUkooKVKJiyYXT2AAMTiXp5SumAkDbIpch\naUEVBGzTk7b8NHU7UoqEPsD02WAz7gAmTwdKjlN5+ifvAEuepMK2BcvdS5cdMAQwGcln787YMYs8\nRUwsHObXM0bfWWw3SNfd4sEH67qw9EzKCLNbNVoNPy6bSDGzbR8C0bHu92gNN1DCRO/+4EXu9x/g\nh3MgH9gDmJtpcecovVC2tKicerMiUgltriEYM3Gs12Zplu7rTiO4jX1HuErR6yzOlZNv3hBBapsR\nERRXiLVkCUTH0aro9nvA16+FfGCPbeVsC/wEaxAwKso7UayOkFTA+XOUOguANTYCDz4D/PsdsPuf\nhGpYBhn6zRsBd7Rvin+mDKqqCpf6NVLmBLB5D9AYFzspsOO8tUVmKGK/akxKpZiISk26LLJskXNy\nw+DX1dL9b4gAGhqpr/PHb7t8GW9soJTqyjPk1nNWxVtWSsF9peMp7Tt/BbKavT3t+mh7S9cz9sFG\n8lCwbj2ASTeSkmBxIbD0KUseMAeLjKaKux0fg1dVtAn8BGMQkOnCyGevRLepiCgKUMf3pIyYxgaw\nKdPB9u22Fa3IlWcojzihH2XpAM4NC+fkS751vlurO1Z6ArjpDtJQcoYk0ecOhoe7k2mvAgkOQKMB\nm3GnRW6Eua8XVVcLHN5P3/v6tSRa6Or900ZS79zyUtJncoZOBxzap/iK+4IxQOCq2dvTPnjsLcLY\n+8LQUcDpEvADe4CDe8hgzLqbOtbfvQSoqwVvbLB10+LPPRA0gR9HsPRMSnHtNxgIj/Ct2KzBBFwy\njFJnJ08Hyk5duFV++zXKI04ZRtWcgy5xblgkCcgcT2XrTh5Ea962HBtvyfBwUTmr0QIHvgVP7Ifm\nA3u8/MAXAYX5JBUxLYskxuct9cxKWCWv930FpKa7VeXK9BHk4tOEOZfw7dWHamOGjwm5Sdk+eOwt\nwth7S3Q3oPYccNdiYP/XJI3wyGqwqgqwmXNJmnnhw5CiYmwpU0EZ+OkAKTkN7NcPAb0SfVMAlTmt\n1K6bBfycB9Z/8AVbZWnBMkhRMSQZ8cTLlswqJyv7pKFA8lDqLZyzm4KwHfmGk1Ihv78BeO9vVIzX\n1Oj4vLpwcg+eqwL/6wtQXTLM+8/cxbFvzM3uXgJseY/6PrRvouEMsxnQaqgNqMnocvK09RlwpVFf\nWw3cswKstiYoVtydSRsZBy8JrLH3RGwpmIiIBCADcT3oYZh9DwX3unVvI6Iknau0+duCMfDjDL5z\nKzBqLD203iKbaTW2ewfQo5ctIGiPdatse3hrzjnfTRTkAds/An9/A/iuraRk2UFhGtNHkB44GAXN\nO6zKtBj/5kaKtxhrgSFpkPytzR/EtAlUjhpLAdpefUjHyBNqaoAzpZDXv+Jy8uSJ/cj1U3rCcXA2\nXA/0SAC2vNel20V6Q/vgsbcE1thXnw3o23uFWk35/b37k4+x7yCorr6BNMOzN0D+NNvmj6Z+p0Ec\n+HFEUip9N//dbNcD0wti44GyEtrWG40uJzi+aysZF6cdszhV3BprAVmm0n/73qJ2q3wpcwLp4Rz7\nycEEYhFxk2WSDkgdDml65whcBS129yvTR7TKiHuiRRMWTro6/90EXHU9zD8dcXo437mV0mPByfXX\nEfUm4LKJYOOnBPez4w8USLsEAm3suyIpwymQd+IXICoG0vV2qXoW+WX7FXxHKVPBEvhxBNNHkK9d\nNsOnW8Qs00oteSjpArl4SFm/wfTQ11YDaaOcn7u5EdDpIX/ydqv4Vjv5CW4yUpqnWtOaJdUea0FX\n9wT/99HtAlwQqDxWQDvwpkZSyXSHhnqqVL5tIfDu31yu7Fn/wZSJM8zFM3Fwj01AMJToKHjsDYE1\n9gbv+0gGBEMkbTVLjgGXjgK78trWL8GqGW7RQO8SK3gnSFExlGFk1cmJiHL+go6oIZU+ae5i0sp3\nRweo8gw1ij/5C5XxO5I+7t6LtJNy90HuoLydm4yQ179CE/OAZKodaH8uxlqlfGUZuGU+6bP4o6is\nK2MyUn2DJ5Wxkgp4/+/AvKUuV/ZS5gTKnz/wrWOlzZhuvu0yuzA2kTgf8cnY7927F8uXL8dtt92G\nX375xfMTdFNej9ovMIlWhxoN+ZRPnwS7Zmab5hbBnLrlFUmp9PDFxlOMwuikVaEjVCrgvfXgpjq3\nJj6mC4O04neUytojgdL4HNVVVJSRQWluBN55vU2Wk03BcM4i4IcDJLWh1V54Ls4pmNizNxVV/XcT\nMHWmS+MUKnCTkWIkE6+jzmTuNraRJNox9UgA/rqavs9257V3t3GTkQw5kzpQ2rSYqPp6YEBS0KjE\ndirBkGffr18/rFixAkOHDvXuBKXH4bRFXLCgUgFDRwLnz9IENfse8E1vBX2Q1Vu4pUIVA4YAC5e3\nahB5ClMBg1PB/7yKDL6Lic86YUqZE4Cb7yJj7yrnPiwCuGIq5LdfoxW+pdoQBXnkgpg5lwyPsx6o\n8T3BHvs9rVyPFVzc2jieYPUVNzYC9z9J9RKWanCnyDIARrvgO+5Fw7t/ayvrvWkjeGMD3Wcfvw35\nk7cpGaDDXZzlXAzkkgsSldjOJCjy7BMTE5GQkOD9CXRhCOpmnyo1XaMuDDi8j9q3JQ2FNHYiEWMS\nrgAAGxpJREFUpAXLukRWjVdYOttLWfOBL7cCl0/2/BwqNdAtnoqZFiz3WKGQHT1ETU2cpX62NFG2\nUNGPQGQU+LpnwRP70Qp/6kzwXduAV1Y6ljRWqWm12tIEpjdAWvSI4mX4XRlbc50p06mD1C3zKPHA\nLd89Jxfato8Q/j8PXqgmmTaSfjdqLLBnJ9WmhDsaew7owiD95omgrlHxJ10/z374r0igKlgxt1Cx\nTV0t9YvVhoHdkEWBQKBL++SdYdVNQWE+MOoyYPc261/cO4FKRUHZGXeATZgC6VylxwqFbMp0ytF3\nVdR16gRNCHkHgYgo8F1baYX/aTbFGYw1rZW57TG3AMPHgF15Xet32lXdbv6kMJ9qJf7v90CiVZXS\nxb2gCwdy9wKjx0E+eYx2X48vBPoPbs30mXkn2FfbabdwtoJkzR1RV+tSHuNiRok8exeNP4FVq1ah\nurpVeIxzDsYYZs+ejYyMDLffKC8vD3l5rc0BsrKyoNHp0BysXhxJRdt/Yw3CH3ga5l9+gmrgEJi/\n3ALdrLmQTx6j7X5PH3Y2CqLVahEZqWzA2zxkKGofnEtCZtXnnUsE28H6DETYNTdBd/lVXr2vXGeE\n6f0NkOtqXcsfcxkoPQGW0BeSVgdUlkN+6XFK/2uot8QbnDRFP7QPurSR0M69D+afjkAzaqxfxrIr\nI48YA9P/Pg9p1jw0ffoe+eQ5J/0kR6qYjfWAVgfpx0NQjf4V8MrTUI+dCHaiCOHSNZAMEWj++QeY\nBySh4c0/UTC+vNTxRRgioT5RBMOk6/3zIYMYuc6Ihk/fQ9jc+2w1INnZ2ba/p6WlIS0tzeV5GOe+\nlEgSzz77LObOnYtBgwZ59LqTDy8gP5wX+td+h0lkSAyRwC3zbE3Bra3Tgm0FGBkZidpaJ0bNC/jh\nHMilJ4CtHwDX3Qp8+KaDIxlt7WvOUa/d5hZg6HBIt9/j1babH86BfPQgkPM1UFMNl64+tZoa3AxO\nIT12K9YJ2xFMAnr3BbThUD3+ku3X/hjLroy96qJ57W+BH4+0Ph/OUKtphd9gAi7NgPQ/D1CXrLdf\nA5uzCHzHx9SMSBdGqcwqVdvOc1b0EXSOkWMh3eVeH4OLifaql4mJTvooOyGwbpxb5tPqq7PpSNFR\nsjz4VreBNgzIGEdNw/+7iar80MUzbDyEpWdCde0s8rl/+KaTbAyLMR44hNpGTrsVqDnv9babpWdC\nGjoS7PE1JHzlit4DgeIiYMdmyqfXR5BEgjNDr1KRJ6KmGmyh963eQgH7BhqoM9Iq3J3+ES0tlowq\nMxAeDm6qoxTc62aBv/wkLQ44A04ep+M7MvQAueFmzgW697wo3aauCIo8+3379uG+++5DQUEBXnzx\nRbzwwgsevZ6VlQC9+vpyCY6xj+zb/5sxS2DPLhikj6Asm+oaStHT6Ggb2thIbQ77JYH/eDgk077k\nyjOk85OSbumpq4HNX2ufKVNXA/xqInDbAuCHA9RJShfmdVN1lp5JIlqLHnF9cPHPpMPT2EgG5opr\nyAfsDLOZZBQyx5MypsAptqK12++hLnKSSw8w0T2Bnr/c78BXrwCPjAJefxmYeC1lt9UbXesvqVRg\nGeOhmjUvZBZa/kARN463nNr2MeQvtpArp/qcf97EEEWGSK2hrAy1hm4uLgMqDW39o2OprP9UMXD5\nJGDi9cBbf6Uy+1l3g2WMB3/7NUs7t+DcQvrFjWMtTLp8ErD+FWq6UldLKXjlp2krHxZOlaeGSGDq\nzcDeL4GOdIG8HDfzmseAgqPuHazW0g7N3EIrd2cKigBd/8O/gyq5rb9TuHEuhB/OAU/sB/7WX2hx\nlH+I7gVXMEZJDk2NZPTNLcDQEfRz6UmgZ6LzrlOx8bT77zcwpLNx7OmSbhyWnkmVcxxkdJUmbRQZ\nekMEGfpwA/2/RwLlAkdFAzGxYFNnApXlwIw5UM1dDKlbd6B3P2D4ZcDeneBbsoPa0PuNwnzaPr+/\nAfjVFeSXnziNxip1ODUor6+jXZGkAr77EmzJSsqwUKCpuvnkMaDQg/ZzLU0kk2xucW3oAZqo/vV/\nF2f6rMKw9Eyw0hOkTXP9ra0tJF2pYXJO30X6GPpeGCOf//FCWmS5ai9Ycx6YfCMgqUM6G0cJAmrs\nuckIZpaBeUuAXxTuKRmup+DP8DHkZ+w3mHzOix4BKk4DN95O0q2SRLrdix+HlNgPcuUZyOtfAZuW\nBTYik1b75tAs02bpmWAH9oA9/AJU8x8E+/Uy4It/A9OySK4g9zsgYzwwMIm6C0VEg+kNyjVt3vgq\ndY+K9EKqwRWXpFv63uohb/1A+fNfhLD0TGo08sEGYMBg6j3gKK3VHkmiOpUrLXUTspkM/+mTrl8b\nHQcU/Qh212JRA+EjgQ3QFubT6vDDf1BbP6C1p6s3WFcZIy8nSdbLrybp1FnzqGR+9gJyzyxbBVZb\nTR2McvdRZ6mNr0KOjadmGjPngm/JBi/6kfJaVZqQXVVIM+ZAiu9p0+RnT60DcnZTdeSAJLBZdwM6\nPfUtjekG+cAexZo2s8k30q6stsaxRo4VlYdSzOcqgF8/RGqKQVzXF2zwvIMU/I7vSdLH7jyvskzf\n365trb9z13t8thyIiaNdhfDX+0TA3Tis9AS5cMIjqCuOO1F+R9SbgKQ04OC3wFXTaFW+5EnKAJi3\nFHjtJWDBMkj1Jppktn4IrPgdVe/deR/w8m+peOTzLQADyefG96RK0oK8kN3uyzm7ST5hSBpYt+7A\nVdfTRN27P/iWbLC0EZBuv4e6Te34GJg6UxHtfilzApDYlwLmrnoPe7L70miBs1XAn1YBvfq0VS4V\nOIXpwkjw77pbaGVutmjauCqy8rZ3dJgeaKgXhl4BAi9xnJRKJfXzlgCb/wUke6mzI0nkRzxZBKSO\nAAp+ALv3UWpovew5YNtHtCr98j+Us1p6AtKCZVD1HQhpziLgpceBBcuAlx4HS0ppo5Pe1RUsFYED\nGDgEcvYG8rOOHg/s3QmYm6l5uj6CahGWrLRltygxbmz2Pcrfpc1N5N/XhYGNvjz0YjE+0CYN0NxC\ncRyVGn7bHkVFg2WM98+5Q4zAG/vCfEgLlgGHcqjp8PFCCqC6gzX1LyqGUu8kFRl6BrDFTwDbN0Gu\nPAP21XZIy56D1HegTdPGWqRgLUNmT60DPniT/l9cdOFbhVB+fXukzAmQsuaDb8mmlNTjhWDTbiWh\nNHWr+8SaLmk/Tj6P27ECysjwB8lDyQct8JzCfEjLnwemzKCJ0x+oNa0S1AKfCbixt60UevUmIzv4\nEtI0Vzvx0WrDYOt4H9ONIva9+1PmTX0d5XiXnqBV5TefO+wUZcsdnjqT/NFLVpLQ09SZF6/ImZcw\nfQRYUgqw/2uwuxaDP/cApBuyIN063287Hm4ygh/KoQboShMbD6jUkN/fIL5nL6Bq8jpg13bPulh5\nQksz0HeQCMwqRMCNvRVWVUEpXbXVlJLV0kKpce3pPdCix8HJD3++ilbzVWeAgZcA3XtRRohVLnfG\nHMc681YJV8vEIFn8zLaJIpTdNu3gJiNQXAT21Drwja/S/7dvAuBH8bDCfArcJ19KuzhJodtVFw4s\nWUlGqrk5ZIPvvsBNRsq579YduPYW3xIrHMEY8NMPtup1gW8EjbGXZsyB6uobgMkzgLo6SrdrqKfI\nvz2njgEGA6lQvvcGZdKcLadjtVqwaVlur8ptEq52fkj7n0PVbdOeQO2AWHom2OBUStUblmnRSVfi\nxAysrITiMsMzxcrRGwrzwcZPAZu3FDi4l6QMlIZz4IqposJZIYLG2AOWvPviIuDeRyjdLiKKyt7t\ntWy0OiBpKGVoZE4APvsE6DPQlvqHYwViVa40AdwBMV0YaSiVHlfupE2N4Ds+Ac87GJI9TZXAJoN9\nrIAaxFeeoboFJTFEkkxyCDYs8QdBZexRmA+e0Ad46y9U9GQNwLY0teZZa8PopjLVUru02O5goy8n\nhcXhmdShCEKXXEkCuQNi6ZnAvl2URx8W5jrf3h1iYqk/rkAZigtJ515SOe4h6ymSRD778VPEwk0h\ngsvYJ6UCh/YBQ4YBcfFUpakLo2AtAzAsg1w4R3OBhQ+DHdgDKWs+ZVQU5tMqTazqLzpYv8FkoCNj\nfavDAMiINNSDrXihTQ9hgXcwXRhww21kmKNiO+gh6yXheppADu0TK3uFCC5jX5hPreFuuoMKnmqr\n6QvvnwyM+BVwugQ4U0puneJCW/cjayolENopkhcrTBdGLe7MLeTH9WX1KMvAdbcIP7CCSJdNJOmE\n0mLlArX6COCKa0iLRyzeFCGojL3NLVB6giR1K8rArrgG0tKVYLPmUeR/0g1AUgqQs7ttT0tRGHPR\nwtIzKf0yXE9xGkc9Zd06GQO+/VysFhWCNzZAfvt18t2H633feQFk6C2ZeEwXJhZvChFUxt5GUiqY\nJJEuTXGRremB9JvHobr9HirNj4pRRmxL0CWQktNIjsFY456ipSO0OgAMcrbIr1cCljaSRPA0WuUa\nEZmMwJBLgQN7xKSsIEFn7K1pfmzmna36Km+/Rnor9kZdpQG7e4nPYluCrgFLzwTGTSFte2+rKuN7\nAgOSgGtuAksbIdwDCsD0EZQtVX7afXEzV2h1wO4dYHMWiYWcggSdsbel+dllfUgLltl8rNbJQMqa\nD2n8FJ/FtgRdiOJCQK8HtB0U27mDqQ5s3gOQomJEyqWS7NtFblclkCxNZ268TcRVFCbojH1H/Rbb\nBF07mAxEBs7FCz+cAzlnN9VgVFUA9z7qpRYLoxXjsQJh5BWEm4xAbS2518L1Hfd39gTZTBXTBXnC\nhaMwQWfsXeFyMhBcXCSlgh/NJR97t+7AO69b5DI8hQPmFmqvJ3aBisHzDlJatC5MuQBtUwPYnEVi\nx64wXc7YC0ILpo8AGzqCdNN3/gc4eZwamkTFeHoman4dEyd2gQpi1beH2uJ+0Whctyp0hkYLVJ8X\nlfB+QBh7QdDD0kaSXHpxEQAOxPeiVpNun4BRC8qYWKhmzRO7QAWx7bRHXEaSxHoDNRHylmGjgUHJ\nlHIpduyKokDtuUDQCTAAPRKBnonkz/Wo8xEDBiZBmrvYX1cX8qjGT4G5fxLwwgrLbxig07rXo9ZK\nRBQVSz61TmTh+AGxshcENdxkpJaIKg3YvY8CR/aTGyeuh8Vd4KIdHkCaOi1myP8RjcX9BTcZgS+2\nAMlp9IuByUCzBxOySkW7tb6D/HOBAmHsBUFOYT7Y0BFgN2SBf74FyBhH7oKISMracNUOT60ht0Lh\nUWqQI/ALPO8gjXNZCUlbFBeSH793f/dOYDYDY68i7SLhp/cLwo0jCGpYeiZgLbRLG0G/nDUP/L31\nllV+FAAO1NV28GJGqXz6CECtEbr1foQ3NgClxWCPrAavNwF5BylrypPYypH9kJ5/Vbhw/IRY2QuC\nH0tthZQ5gYqhSk9QNk58L0Cnc16mL8vk558xRxh7P8KqKsCWPk29Dg7sAR54inZf56vcO4EkAU1N\nQsbCjwhjLwh6LqitSEoFzlWBPfgMEB1DwVomkW/eHl0YtarU6ISglp+RZsyBFE/dqtiU6cC3X3iW\nc9+rN0mbJ6WA7/jET1cZ2ghjL+hyWCU0+Bt/AE4co4YmBgPQ0NB6UFw80GcAoNUAYycCBXlixdiZ\nNJiA+no36yEYUHYKuG4mWHERTRYCxfHJZ79x40Z8//33UKvV6NmzJ37zm99Ar/ehoEIgcBNuqgMq\nTtOqft5SYOOrrX+MiaOAX0QUlfGfOdVaoCNW935HPrCHJuE+/YHjhdQv+sQvFEPpUCyNU8+Kd/8G\ntvx54bP3Ez6t7NPT07F27VqsWbMGCQkJ2Lx5s1LXJRA4he/aCqQOBx5ZDWS/QX2IAdK/UaupjeGp\nYiAmDqzfYFGg04mwqgrg6hsAXTiQlEpGZtY8x6qYegPp4fdPFobej/hs7CWJTpGcnIyqKjeDMQKB\nD3CTEayhgfoOHz0EXHEtcLyADEpTI1BZDqgkIC4ebNTlov1gJ8OmTAc7XQLpN4+D/XoZ5MYG4ON/\ndXxwQj/KsY+MBspPCVebH1HMZ//ll19i5MiRSp1OIHCMnfIpHzUW+Go7cO3NwOefAJcMo2MqyoAZ\nd4gMnEBg9/0wvQFSYl/qLqbVtqpiShK52cpOUoHc0JHAZVcJ8TM/4tJnv2rVKlRXV9t+5pyDMYbZ\ns2cjIyMDAPDRRx9BpVJh/Pjx/rtSgcCC1R3DTUZg01vA/b8F3vwzaaEXFwKpI4CS48CfV0F+eDW8\nbHUi8BJ7d5m89QOwijJyueUfol8aoqjtoLmZXDtNjWA33UEptSK24jcY5761l9m5cyc+//xzPPXU\nU9BoNA6Py8vLQ15enu3nrKws1NZ2UAgj8AqtVoumJm+kf7suzQf2QHXJMJh/OoKWk8VofOc1sO4J\n0E67FebCfMgVZWBaHQwPPg3J4L4vOBTH0h/IdUbUb3wVqCiDHBEFXlUO+XghWGQ0+NkKqFKGgcV0\ng1xzHrrJ06G7/KpAX3KXIDIyEtnZ2baf09LSkJaW5vJ1Phn73Nxc/POf/8Szzz6LyMhIj19fWlrq\n7VsL2hEZGRmykyc3GSGvfwVIGwX8fBT4/mvqX6w3gOcd9DjHPpTHUkn44RzwxH5gb/0FclU52KJH\nwf/9DnDke3LhcA722O/B9IbWVqQiQOuSxMREr17nk7FfunQpWlpabIY+OTkZCxYscPv1wtgrR6ga\nKPuexQBINK25GdBoIN063yvjEapj6Q/44RxomxrR8P23wP6vgV9NBHokAP9+B7j5brCzFbbvDoX5\nImPKDQJi7H1FGHvlCFUDxQ/n2NrX2Rt9nncQKMjzarUYqmPpL7RH9qP+u69IOiFcTwVUdy0Gtn5I\nTcVLTwgj7wHeGntRQSvo0tikFNpkgESQho7odBRwuMmIliP7qYPVjDlA7nckjfDtF2BzFgHbN4le\ns52EMPaCiwLRmzhIKcxH+J33gU3LAta/Aix9CjhzChicQqJpYkLuNISxFwgEfsM22W7fBHb/k8Cf\nngNb+DBYcREVx4kJudMQxl4gEPgV809HgKkzga+2U5bUV9vpZ7Gi71SEsRcIBH5FdckwWtnPvBPM\n6roRvvpORxh7gUDgV8w/HWmTFcX0EcJXHwCEsRcIBH5FM2qsCJ4HAcLYCwQCQQggjL1AIBCEAMLY\nCwQCQQggjL1AIBCEAMLYCwQCQQggjL1AIBCEAMLYCwQCQQggjL1AIBCEAMLYCwQCQQggjL1AIBCE\nAMLYCwQCQQggjL1AIBCEAMLYCwQCQQggjL1AIBCEAMLYCwQCQQggjL1AIBCEAMLYCwQCQQggjL1A\nIBCEAOpAvvlvdxQH8u0vKlQqNczmlkBfxkWBGEtlEeOpLBvuTvTqdWJlLxAIBCEA45zzQL15aWlp\noN76oiMyMhK1tbWBvoyLAjGWyiLGU1kSE71b2fvkxnnvvfewf/9+MMYQHR2NxYsXIyYmxpdTCgQC\ngcAP+LSyb2hoQFhYGABg69atKCkpwcKFC91+vVjZK4dYPSmHGEtlEeOpLN6u7H3y2VsNPQA0NjaC\nMebL6QQCgUDgJ3zOxnn33Xexa9cuGAwGPP3000pck0AgEAgUxqUbZ9WqVaiurrb9zDkHYwyzZ89G\nRkaG7febN29GU1MTsrKy3H5z4cZRDrFVVg4xlsoixlNZvHXjKJaNU1lZidWrV2Pt2rUd/j0vLw95\neXm2nz2ZFAQCgUDQSnZ2tu3faWlpSEtLc/kan9w4ZWVl6NWrFwAgJycHvXv3dnhs+wvKzs4WBl9B\nxHgqhxhLZRHjqSzejqdPxv5f//oXTp8+DcYYunfv7lEmjkAgEAg6D5+M/fLly5W6DoFAIBD4kYDJ\nJbjjYxK4jxhP5RBjqSxiPJXF2/EMqFyCQCAQCDoHIYQmEAgEIYAw9gKBQBACdJqe/d69e/H++++j\npKQEq1evxqBBgzo8Ljc3F2+++SY457jqqqtw0003ddYldimMRiP++Mc/oqKiAj169MBDDz0EvV5/\nwXGLFy+GXq8HYwwqlQqrV68OwNUGJ+7ca3//+9+Rm5sLnU6HxYsXY8CAAZ1/oV0EV+N59OhRvPTS\nS+jZsycAYMyYMZg1a1YgLjXoefXVV3HgwAFER0fj5Zdf7vAYj+9N3kmcOnWKl5aW8meeeYYXFRV1\neIzZbOb3338/Ly8v583NzXzFihW8pKSksy6xS/HWW2/xzZs3c84537RpE9+4cWOHxy1evJjX1tZ2\n5qV1Cdy51w4cOMBfeOEFzjnnBQUF/IknngjEpXYJ3BnPvLw8/uKLLwboCrsW+fn5/NixY3z58uUd\n/t2be7PT3DiJiYlISEhwekxhYSESEhLQvXt3qNVqjBs3Djk5OZ10hV2L/fv348orrwQATJw40eE4\ncc7BRQz+Aty513JycmxjnJycDJPJhPPnzwficoMed59dcS+6R0pKCgwGg8O/e3NvBpXP/uzZs+jW\nrZvt57i4OJw9ezaAVxS8VFdX23oHxMTEtNEvsocxhueffx6PP/44Pvvss868xKDGnXtN3I/u4+5Y\n/fzzz3j44YexevVqlJSUdOYlXlR4c28q6rN3VzRN4B7OxrM9juSlV61ahdjYWNTU1GDVqlXo06cP\nUlJS/HbNAoEjBg0ahL/+9a/Q6XQ4ePAg1qxZg3Xr1gX6skIGRY39ypUrfXp9XFwcKisrbT+fPXsW\ncXFxvl5Wl8XZeMbExOD8+fO2/0dHR3d4XGxsLAAgKioKY8aMQWFhoTD2cO9ei4uLQ1VVle3nqqqq\nkL4fneHOeNr3vxg5ciTWr18Po9GIiIiITrvOiwVv7s2gcuMkJSWhrKwMFRUVaGlpwTfffCN2BA4Y\nPXo0du7cCQDYuXNnh+PU2NiIhoYGANRV7PDhw+jbt29nXmbQ4s69lpGRgV27dgEACgoKYDAYRNtN\nB7gznvY+5cLCQgAQht4JzuJt3tybnVZBu2/fPmzYsAE1NTUwGAwYMGAAnnjiCZw7dw6vvfYaHnvs\nMQCUvrVhwwZwzjFp0iSReukAo9GIP/zhD6isrET37t3x0EMPwWAwtBnP8vJyrFmzBowxmM1mTJgw\nQYynHR3dazt27ABjDJMnTwYAvPHGG8jNzUVYWBjuu+8+hynDAtfjuW3bNuzYsQMqlQparRZ33303\nkpOTA33ZQcm6detw9OhR1NbWIjo6GllZWWhpafHp3hRyCQKBQBACBJUbRyAQCAT+QRh7gUAgCAGE\nsRcIBIIQQBh7gUAgCAGEsRcIBIIQQBh7gUAgCAGEsRcIBIIQQBh7gUAgCAH+H6IJPsBdBdx/AAAA\nAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x111df7e10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def plot():\n",
    "    pX = np.linspace(-1, 1, 100)[:, None]\n",
    "    pY, pYv = m.predict_y(pX)\n",
    "    plt.plot(X, Y, 'x')\n",
    "    line, = plt.plot(pX, pY, lw=1.5)\n",
    "    col = line.get_color()\n",
    "    plt.plot(pX, pY+2*pYv**0.5, col, lw=1.5)\n",
    "    plt.plot(pX, pY-2*pYv**0.5, col, lw=1.5)\n",
    "    plt.plot(m.Z.value, np.zeros(m.Z.value.shape), 'k|', mew=2)\n",
    "\n",
    "plot()\n",
    "plt.title(\"Predictions before training\")\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "st = time.time()\n",
    "logt = []\n",
    "logx = []\n",
    "logf = []\n",
    "def logger(x):\n",
    "    if (logger.i % 10) == 0:\n",
    "        logx.append(x)\n",
    "        logf.append(m._objective(x)[0])\n",
    "        logt.append(time.time() - st)\n",
    "    logger.i+=1\n",
    "logger.i = 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "compiling tensorflow function...\n",
      "done\n",
      "Caught KeyboardInterrupt, setting model                  with most recent state.\n"
     ]
    }
   ],
   "source": [
    "m.X.minibatch_size = 100\n",
    "m.Y.minibatch_size = 100\n",
    "\n",
    "m.Z.fixed = True\n",
    "m.optimize(method=tf.train.AdamOptimizer(), max_iters=np.inf, callback=logger)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x11626de50>"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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p19vf2Nsi7Z1RFOoVf9UByKjz211wLmG5iVg0PKbFUMAijcIb6oETx8Hfew3i\n+69rj+UdBf9C6qbO//Ox48DJn6XXijLwb/ZLK8J+6jRNkTrAVV+UgpL6F3S9o8cW3/aG6kPtr3Jn\nCzlg2RogvrPOUc2oFmZvx1CVJvjrL+tlV6Iu+ZTozyLB6+uljg5eVrNVzq9QrdekCiZuz9crzcRe\n4XhvaERlyRVdfD/X2bUprvvCwl33tTO5vYUwRqfXmNEIdst41yXk9WaR8BCwDDOfsX+IPWDJnSqU\nE9QBSxVoDPbPkdevAhwlK0EAu+8RsHvcLApJ8arFUMAiHonvrINtsWosUs5XUnsLpIGgXPWrnv/X\n0b7DP3rH8V61ZIP46lLgJ9cVWZ174/E9/9b2HHM3o4XzL+Myq+Me+z5zqeICIFWbRZqVFWcbRXU/\nNmK08l58YQ5w6mfHeV6WQBfn3OdIpw8BS5d6Cib1Z3vTyEHDGnqr4OoNEwh3H7D02jTZLbdDmDDF\nESTktki9Epa8r2Mc0CEa7K6pOh8ipYmZO0BY9VfHbvn+xhAg4SrHfrmDxcgxqnMF5Rph2O8huBsA\n3EQTGhPv6JsmunjJealL9I+HgVP5+iedPgnxuUd9u2GfAUrph3+12/vnXygG3/6mY4e7gFXvw5RB\nesxRbtuMPKZL7lVmMEC4RzXjyumT2qpD9UPcW+nn7CnvbTxyBwlfOc8arsIiIvT3j7tPdz9g75wA\nqdOCC84hPKft1KF0DtGj/juTS2xyKc0+WawwVerNy/RKWPYfKcILr0FY9haEm/8IIf0vQI/eqsy4\n+f4NBgir34ew6j0Is59zPadnH+legKaE5QkbkwbhCR+m0yKXrVEBq76+HhcuXECdt+lfSFDjVRch\nzp8GnvmOY22hxTozPujV++tpZwJL6g9ckNpq+Je7vV8jz3nXq69UBeTu39wlB6wO2jYfd5wDhTKT\ng/2BqJ453F7yBKCtbvJQPQYA/Mgh4OprPKdDpws5u2ua+/M9BUCn0h+zDxRmcQlO91AHJ3t+9Kr/\nALAuV2m35Tx37aHdf89Dmio94Vb7xLZyW5McJOSAF9nece4LrwFdrgLr+xvpXowpYy9Zn/4wzFdV\n62oClqoaUBDATBFgYWHK2DDpHOnvkQkGsD79lXM1r24wUwRYzz4ezyFNw6eA9dNPP+G5557Dn//8\nZ0yfPh2TJk3CokWLcPz48eZOH2lB4meZED/YBHH23QAgdYkuPC0d1CtlqccbJXr6D8uUFVcbS3h8\nsfTQclNx8CfOAAAgAElEQVTC0gt+woJl+qmwLwMhneTjbzX1eRFmaZVbwBGv1rvpAVilGvCsenjq\nzgp+Mk+Zdw6A1JXbOTDUuS44KD+4dRl9D1hK9VuXq6Q1nWRxjrYuLs8EESqli/1JNT5Lr9OB3Etv\n3H1g10lTFRk27YAwYgyQNADCS2/AsGkH2LUpYFPnOBY+lL9vudpP9b2wTvEwPLfWp3kQWfdrHNWX\ngipgiW4anPT+PRgcVYIkMHj9X3v8+HEsXrwYCQkJeOaZZ7By5Uo888wzSEhIwJIlSyhotRKcc/Cs\nfynjdhrNWwBwtwRDlOdedUwwKL+Q2eg0IPFa/RMTujmu6e6mtBLbCcKcxdJ7N4NSXROg+qVubq+a\nmFWOWG4eZqp8sRuGK13ghTvv197+3oelN+GOACXMXgRhutPsGToBy2NVY0gIhIxN2n3MEQzYtMeV\najwml2bamTRtRkzdOUPuANNOOpdZdLr0q8ltWAYBXNS2WTHGwFS9CIVBwx1pUE0sy4b+3mPVpifC\nmDQY1v3NvqH6t+luLBXT+Xt0HodF/M7r38QHH3yAu+++G9OmTUNSUhI6d+6MpKQkPPDAA7j77rvx\n/vuNXEKABCS+71NtI76PhIUrpaoat4MqIT3b1T27VL3bhLkveP8Q+0Bi9rtxrtVWMp2ZFNj12kZy\nFhXj6G4d0d7lfF3qgNQuwtELUb6n+mFmrxYTHp4P1u861T0YhCeXurbzAGDDfi+9CTeBTbYvfGgM\ncX1I6lWJOveoU9839gqXakH25xnKdcINwxw/IuSSSHg7sD+o5gVUV/PJpSi5dOOtzU0dgHwZNCxT\n5Un40yPSAOHLxBiTZpgH3KdF0Ok4YvCtDYu0HK9/Ez///DNGjBihe2zEiBHIz3fTIE+Ci15vOjt2\n94PaqiyTqtG+U2ewTvGucwUCmt5ocuM5G5PmKOVYOoJd0Vn/Q3upJh8uswKhoWARke7bg+wBi40c\nq0q49GK4pi+EhauA3wxWShDC+PsgvPSG811csMEjATlItjOBf73XfsD1Aae0Y4iiVK0nEzlYdIzS\nzsNuHCWl4YVXHRPxiiJYB3sX7LBw17YzvXn73JSw2M1/BJv0qEsQZ2b7/eUgLHflloNPaJgygJvd\nMl7TLqP8PSkBS3VvuQR1dS/HPiVgCY0LWM1U/cb6D5LeuBszxXQehQJVCQYarwGLMQab3tQ6ABr0\nHlIkOHWwuD3EomO1jefy2JZrU5SqHGHSLO1FMZ0gPL/OsR0bJ91r6O/BOkrvXR4e8n7odACQ06fq\nLs0G3uQ4bi/BCXc/qEo4A7v5jzBNmwPWtbsUHOSOIuEmR7WUwah92Kqwrt0hyO016i7WOj/IefF5\naeaI7teA3XwbhNfsY9Gcq8RuuUObJ0D6LuztdCy8HZhggDAvA8K8F4Hu17hUCbJ7pzuqzyKkIKNM\nG9UhSpo1395uqPT+69LVnl/7f3u5BGEvYWlmsecA69UXbLD0Y5V16ym9yp0j1MHS/nwQnsiAMMPe\n8UQOghyeS9/OmrM0c20K4G6JGXm+RjUmd8SgElag8Po30adPH+zcuVP32M6dO3HttW7aFEhw8TRa\nP7yd0htPakCXHmwGuaQEgMkPQ5m5A1iHaPmo1KA/YrR2Joir7Q/B+x4BG3ef0pVZNz3yr1x1CUvd\nIO9mclXhrqnatafkUoW6h2PvfmB6A2IB7QO0UjXYVydisd79YJi9CMzSUWqDcZ42SiZ/tjoAiiL4\nRafqxl5JYL36Su1mTj8aheGjHW17zp0Q5FnFDU7fWXunEpacjtgr7CvnumJ/mglhtWq2djnYqb8/\ne3sgM4Y4SpZKJxsOYXQa2B2TdO/vohlLM4Y5i9122GARka5LvtAiwQHHa7/ke+65BwsXLsSJEycw\naNAgREdH48KFC/jyyy/x448/YvHixd5uQYJBvYel5qNjwQQDOABh+pPgJ45rJ6C1Y6P+IHXaiOvi\nmFhVPmYwgKnGLQlLXgWipBKGYG/H4fZ7sjunAGcLNNcrE+uqx/eo21F699OZZkjniSMHCefqNLk9\n58qrpZkYrugM8fnZ0gNUDhbuVsKVP+13risHAHDt4Sh3xdbMuiCC9b8e0Omqzn77f+Db3wS7fqij\nSlKVB+bc68+pCo7FdYGgfhgzpw4jRiNYiH6bHgsJ0XaYEQQIr7wtrUclU//bsX+2Om+sZx/fu337\nOlSCtEle/3UkJCQgIyMD27dvx3vvvYeKigqYzWb069cPGRkZiIuL83YLEuDE8jLwD7TTLCH2Ckcn\njOhYsLguyi9QdnUvQG/BXHu1nGHxRp2DWrptV3L7ydXXAINGgF0/VNp/bQqYfTwOa2dyzISj+jUu\nDB8NDHfMPAFA/+GnlG6cjtk/2/Cszpx9cgBQBx519VlcAoQnX3K7MKTLjwGnYMnunAKWfD1YhBns\nZqf1uSC1y/Htb4IN/C3YlMcc7Y0GbZWgwrl0anMEMGH5O47lSux/X7rpjnQtibCJDwCJfcBCwxwT\n9gLaHpc2p7w2cp49NmSk1GEkEHhZEoW0PJ9+zsTFxeHRR32c0YAEFX48F+XLFrjsZ2PvAn9rDYSM\nTfqzG+hgY9LAUn1fHtyFXGKyNYCpFtdTVz0i3OQIpnIJ46bfudxKeGo50Cne9TMEp/aba/qBDRjs\neSol+YEslx4G3qTpeGJY7LrooRp3qhJk0TEQ/rLekSR3JTP5fDm4cvt7S6wmDy4lLOcgoWpDY6q5\n9VhIiO7Kx8LSN4D20a77R/3Bca06yKnbsp1Lro0NWCGhjnFhfsbCTW5Xhib+cUnl71OnTuH777/H\nlVdeiZQUN3X/JCjw44c12+yOSUDBL2ARkeBAo37tsvB2wFWJl5wW5SHoaQHEdibpoZjQDax3slTa\n0pm2iNnbx/Q+Q1j9vtTeAsBg71bPiwr15zBlkNapApTAJTw4z3tm5Mv/9AjkDgua/c6LQfqANzRo\nKjnl78v4m0GoV8/aoa4SDA1z9HL0EWvM2CejUfPDgMVfCeGlzY36PEJ85TVgnTp1CuvWrcPp06fR\ns2dPTJgwAcuXL0dcXBxOnz6NiRMnYvTo0d5uQwKQ7YHblC7WAMBuGAbh91IPNu7chtSSPJV2YjqB\n9egNYcpsx77G/oo3uc6lxzrG6f+aDm8HZukIYeNHEJ+Y0qjPAQBh6O8bfY1bbgY7G5MGwJCq6jGp\nqs4zuJuJowkYNu2QlnVxruJUrxNG1WqkCXkNWG+++SZSU1Mxa9Ys7Nu3D8uXL8eTTz6J3r174/jx\n41i/fj0FrCDGs/eh3fQnUP3xX7W97uITILz+j8v/gAiz/kKHbggbP1RKP3pYlAVMHawAj+dfDnUA\nY0aj/srJLcnd56sCtrBsi+uSGs2IeZiVXXjxdccQBkKagNeAdfLkSSxatAiMMdx5553YuXMneveW\nZkXu1asXSkvdDzglgYn/8pNjstG6OoQkDUDtb250aXx324mgEYQXXm1UV+XGBh9h4SrtMhHNqTHj\niZqDc4cGALi6F4QoC1BnH8PlZaqrlkTBijQ1rwFLFEVHXbnRiFBflromAU1csVDbRdsUCeZuUtDL\n5MtEpZd1/67dm/X+asKCV3yfg7AZsM6ugdnw1CvSIOE6D8MSCGklvAashoYGZGVlKd1YGxoasGvX\nLuW4u1kwSAAzRWoCFmvXDrjoeYwRkapJ/YV6qxHiQ8Dq2bMn9u51DFZMTEzEvn37NMdJ8OAlRS5L\nsjOaK40QEgS8BqznnnvO43GxMRNbEr/j3+z3dxIIIeSSXNasjvX19bj77rubKi2kJVzqCr2EEOJn\nNA1xW1NXC/bHe/2dCkIIaTSaabKN4BcrwL89ANTWSEvOA9LyFj3crM5LCCEBhkpYbQTP+if4O+uk\ndZXC5MUOx8DwsOs8goQQEoi8lrCeffZZtwNIqcNFELEv7c73fQbWKwnCw/OBa1zn4COEkEDlNWCN\nHDnS4/FRo0Z5PE78z7byWaCyQtlmoeFgvxnsxxQRQkjjeQ1Y+fn5uP/++5XtXbt2aYLYK6+8guHD\nhzdL4sjlE/d+ChzJ0e4MD/dPYggh5DJ4bcPas2ePZvvdd9/VbB8+rF2eggSY/GOu+9q5zlZOCCGB\nzmsJi3tZusHbceI/tqenA+fPuB5o536GbUIICVReS1jeZuxuihm9STNxClZsiL29kUpYhJAg5LWE\nZbPZ8MMPPyjboii6bJPgwP48E/yLz6mERQgJSl4DVocOHbBx40ZlOzIyUrPdvn375kkZaTJs6C3g\nez8FMxggpD8PRqvAEkKCkNeAtX79+mZPxJdffont27ejoKAAGRkZ6N7dscZRZmYmsrKyYDAYMHny\nZKSkpACQei9u2LAB9fX1GDBgACZPngxAWv5k3bp1yM/Ph9lsRnp6OmJjYwEAu3fvRmZmJgDg9ttv\nx7Bhw5o9b4GA3Tsd7LZ7pPd9Bvg5NYQQcmkCYqaLrl27Yu7cuejTp49mf0FBAQ4cOICVK1diwYIF\n2Lx5s9LJY/PmzZg+fTpWr16Ns2fPIidH6rq9a9cuREZGYs2aNRgzZgy2bt0KAKisrMSHH36IjIwM\nvPjii/j73/+OqqrWtwaUmPVP8IuVmn1MMIB1iPZTigghpGkERMDq3Lkz4uPjXfYfPHgQQ4YMgcFg\nQKdOnRAfH4+8vDyUlpaiuroaiYmJAIChQ4ciOzsbAJCdna2UnAYNGqS0tx06dAjJyckwmUyIiIhA\ncnKyEuRaE/7ea+A5X8K2McPfSSGEkCYVEAHLHavVqlTnAYDFYoHVaoXVakVMTIyyPyYmBlarVblG\nPiYIAkwmEyorK12uke/VKnEOfHvA36kghJAm1WKztS9evBhlZWXKNuccjDFMnDgRqampzfa5rXmc\nGC+1gv94GMINUomSN9RLr2+v9WeyCCGkWbRYwFq4cGGjr7FYLCguLla2S0pKYLFYYLFYUFJS4rJf\nvkbeFkUR1dXViIyMhMViQW5uruaavn376n5ubm6u5ty0tDSYzeZGp7+5VW1/E3WffQzzzWMBAKX3\nj9U9z1vaQ0NDAzJ/TYXyF9xac/5ac95k27ZtU94nJSUhKSnpku8V0OthpaamYs2aNRg7diysVisK\nCwuRmJgIxhhMJhPy8vLQo0cP7N27F7feeqtyzZ49e9CzZ08cOHBACUopKSn44IMPUFVVBVEUcfjw\nYdx7r/5ChnpfakVFhe65/iSWXgCgSpt9RnZF8kDg+2yvaTebzQGZv6ZC+QturTl/rTlvgJS/tLS0\nJrtfQASsr7/+Glu2bEF5eTleeukldOvWDU899RQSEhIwePBgpKenw2g0Ytq0acrMGlOnTsX69euV\nbu39+/cHIM0uv3btWsyaNQtmsxmzZ88GII0fu+OOOzB//nwwxjBhwgRERATvjA+8thb8a+08j4i/\nEjj7KwBpkDAzd4D4fbYfUkcIIU2P8dbcyNOEzpzRmZPPj3j+jxAz5gEADJt2ANDOHSgs2wIWFQNe\nWQ4W6Xlwd1v4lUf5C16tOX+tOW+A1AO8KQV0L0HiIP77Q/Aa/XFj/Ogh8KqLQGkxYLQXmttFAoDX\nYEUIIcEiIKoEiXf8w7fB4q8EUq6XdqiCF/9qN/gKqVOLsOo9QBDAwmj6JUJI60IBK6hI7Xf82wPg\nB/+n7OX7P3ecERHZ4qkihJCWQAEriIiffgh26Cvw//0X4CJwbQpw9JC/k0UIIS2C2rCCyU9HwPd9\nJgUrACyJJrIlhLQdFLCCgPjlbv0D0bH6+wkhpBWigBXgeH09+BsrpI0uV2mOsfZRfkgRIYT4BwWs\nQFfqmIIK9XXaY2YKWISQtoMCVoDi1iLpTdkFx87aGu1J0ZaWSxAhhPgZBawAxKurID45VdqoVg0W\nVgUvNmQUEN5Oc52Q/nxLJI8QQvyCurUHEF5UCPHDt8D6Scut8IYGoK4GiOkElJyXTmIM4BwsORVM\nMDguvroXWB/qNUgIab0oYLUw8V/bgdAwCDff5nKM7/l/wDdfgH/zhbSjogziq0vBBo0AtxZL3dkN\nBqChAbAHK+G1j4HTJ4GI1r1EASGEUJVgC+OZ74JnvuO6n3PwX/K0O38+Kr2GhUHI2AQAYGPuks5v\naJC2BQHsyqvBLNTFnRDSulHA8gdRZ4L8X08APx7Wnvbay9KbkDCwmI7Se8H+V1Zf24wJJISQwEMB\nqwXxc/YlSjgHF22wPXAbeG0N+KGvgeqLnq50vBVt0mt9fbOlkxBCAhG1YbUg8Znp0htbA8RlT0v7\nZtpX4/zNYNcL2kcB5aVSu5XMZp+WKT6hOZNKCCEBh0pY/pJ3RLtdUQYAYOPuU3YJDz4hvVGvaSXa\nYNi0A6xX3+ZOISGEBBQKWC1AfHsteFWl55OsxdJruEnZxa7pC6RcD9Z/kLT955lgw0c3VzIJISSg\nUcBqZpxz8K/3AmWl0hgqd+RxVkZtLa1h5jNgcV0AAMJNvwOLjmmupBJCSECjgNXcaqqBulppHsB2\nEd7Pt7dXsWG/b+aEEUJIcKGA1QxsGfPAT/0sbZRZpdf6OqCdyf1FMoNUwmLXD2um1BFCSHCigNUc\n8n8EP2YfU1UqBSxedFY7ka0bLHkghOfWAj37NGcKCSEk6FC39uYiCODHvgfP+QoAwN9Y6fn8dhGA\nIIBFRAIRkS2QQEIICS4UsJqLIEBc/ozvp/9lHVBe1owJIoSQ4EZVgk2EH8mBbdkCx46a6kZdz6Ji\nwLp2b+JUEUJI60EBq4nw3G+B47ng9qmTeOa73i8KCwcACDMXNmfSCCGkVaCA1VRCQgEAfN9/9I93\n6+m6T+7CnjKwuVJFCCGtBrVhNZXQMAAA37pBu7+dCcLz66XSVPE5sK7dYVv8GHAqX+nCTgghxDt6\nYjaV0FDHe4MRsEnrVYExx+wU9jYqNuoPwC8/gY38A1Bb08IJJYSQ4EQBq6kYQxzvu3YHThyX3guu\nta7CkFHAkFEtlDBCCGkdqA2rqdiX/QCkwb8Kc5QfEkMIIa0PBawmwEuKlOXs2R/uhjBWWsYeVyVC\nmPuCH1NGCCGtB1UJXiZx59/A934KXLAvDyK3XQFg/a4Da08lLEIIaQoUsC4T/8dftTvsXdWFDR9q\nVwomhBByWShgXQZ+6Gvtjt7JYLfcAQBgISE6VxBCCLlU1IZ1GcR1S7Q7jEawsDD/JIYQQlq5gChh\nffnll9i+fTsKCgqQkZGB7t2l8UpFRUVIT09Hly7Sirs9e/bEtGnTAAD5+fnYsGED6uvrMWDAAEye\nPBkA0NDQgHXr1iE/Px9msxnp6emIjY0FAOzevRuZmZkAgNtvvx3Dhl36mlO8sMBlH7sq8ZLvRwgh\nxLOACFhdu3bF3Llz8frrr7sci4uLw9KlS132b968GdOnT0diYiIyMjKQk5OD/v37Y9euXYiMjMSa\nNWvwxRdfYOvWrXjsscdQWVmJDz/8EEuXLgXnHPPnz8fAgQNhMvmwqKIOceEjmm0h/XmwPgMu6V6E\nEEK8C4gqwc6dOyM+Pl73GOfcZV9paSmqq6uRmCiVaIYOHYrs7GwAQHZ2tlJyGjRoEH744QcAwKFD\nh5CcnAyTyYSIiAgkJycjJyfnktJre+A2153tIi7pXoQQQnwTECUsT4qKivDkk0/CZDLhrrvuQu/e\nvWG1WhETE6OcExMTA6tVWtlXfUwQBJhMJlRWVrpcY7FYlGsaQ8z+n/6BdpdWUiOEEOKbFgtYixcv\nRlmZY4FCzjkYY5g4cSJSU1N1r4mOjsaGDRsQGRmJ/Px8LFu2DCtXelm514leCc2b3Nxc5ObmKttp\naWkwm83gog1lr7+s7I+Y9wIuLnsaABDZ8QoIZnOjPysQhIaGwhykafcF5S+4teb8tea8ybZt26a8\nT0pKQlJS0iXfq8UC1sKFjV/zyWg0IjJSWi6+e/fuiIuLw5kzZ2CxWFBSUqKcV1JSAovFAgDKMYvF\nAlEUUV1djcjISFgsFk0QKikpQd++fXU/V+9LraioAK+u0uyrjr9KeV8pAqyiotF5DARmsxkVQZp2\nX1D+gltrzl9rzhsg5S8tLa3J7hcQbVjulJeXQxSlOfrOnTuHwsJCXHHFFYiKioLJZEJeXh4459i7\ndy8GDpTm70tNTcWePXsAAAcOHFCCUkpKCg4fPoyqqipUVlbi8OHDSElJaVyCap1WEY40A916Qnjh\nVRp3RQghzSwg2rC+/vprbNmyBeXl5XjppZfQrVs3PPXUUzh69Ci2bdsGo9EIxhgeeOABRERInRum\nTp2K9evXK93a+/fvDwAYOXIk1q5di1mzZsFsNmP27NkAgMjISNxxxx2YP38+GGOYMGGCci+fOS17\nzxiD4enll/8FEEII8YrxS2nkaYPOnDkDfjIP4pI50o4oCwzL3vJrmppKW6iWoPwFr9acv9acN0Dq\nAd6UArpKMODUqBZbNFIVICGEtCQKWI2hbsMKC/dfOgghpA0KiDasYMHlNqyu3SE88pR/E0MIIW0M\nlbAao1aqEmRXJYLFdPJzYgghpG2hgNUYcpVgKM3ITgghLY0Clo/4qZ/Bd/0T6JcKNu5efyeHEELa\nHApYPhI/+RtQVAh2TV+wcJo3kBBCWhoFLB+xK6TZ5NkNw/2bEEIIaaMoYPmqXQTYLbeDRVn8nRJC\nCGmTKGD5qr6Oxl4RQogfUcDyEf/nNiA01N/JIISQNosCVmNQd3ZCCPEbCliN4TRbOyGEkJZDAasx\nwtv5OwWEENJmUcDyEbvuRggjxvg7GYQQ0mZRwPIVtV8RQohfUcDyEa+p8ncSCCGkTaOA5auCX/yd\nAkIIadMoYPmqtsb7OYQQQpoNBSwfCfNf9ncSCCGkTaOA5SPWMc7fSSCEkDaNAhYhhJCgQAGLEEJI\nUKCARQghJChQwCKEEBIUKGARQggJChSwCCGEBAUKWIQQQoICBSxCCCFBgQIWIYSQoEABixBCSFCg\ngEUIISQoUMAihBASFChgEUIICQoUsAghhAQFo78TAABbt27FN998A6PRiCuuuAKPPPIITCYTACAz\nMxNZWVkwGAyYPHkyUlJSAAD5+fnYsGED6uvrMWDAAEyePBkA0NDQgHXr1iE/Px9msxnp6emIjY0F\nAOzevRuZmZkAgNtvvx3Dhg1r+cwSQgi5JAFRwkpOTsby5cuxbNkyxMfH4+OPPwYAFBQU4MCBA1i5\nciUWLFiAzZs3g3MOANi8eTOmT5+O1atX4+zZs8jJyQEA7Nq1C5GRkVizZg3GjBmDrVu3AgAqKyvx\n4YcfIiMjAy+++CL+/ve/o6qqyj8ZJoQQ0mgBE7AEQUpKz549UVJSAgA4ePAghgwZAoPBgE6dOiE+\nPh55eXkoLS1FdXU1EhMTAQBDhw5FdnY2ACA7O1spOQ0aNAg//PADAODQoUNITk6GyWRCREQEkpOT\nlSBHCCEk8AVEwFLLysrCgAEDAABWq1WpzgMAi8UCq9UKq9WKmJgYZX9MTAysVqtyjXxMEASYTCZU\nVla6XCPfixBCSHBosTasxYsXo6ysTNnmnIMxhokTJyI1NRUA8NFHH8FgMOC3v/1tk32uXIVICCEk\nuLVYwFq4cKHH47t378Z3332HZ599VtlnsVhQXFysbJeUlMBiscBisSjVhur98jXytiiKqK6uRmRk\nJCwWC3JzczXX9O3bVzctubm5mnPT0tLQuXPnxmU4yJjNZn8noVlR/oJba85fa84bAGzbtk15n5SU\nhKSkpEu+V0BUCebk5GDHjh144oknEBISouxPTU3FF198gYaGBpw/fx6FhYVITExEVFQUTCYT8vLy\nwDnH3r17MXDgQOWaPXv2AAAOHDigBKWUlBQcPnwYVVVVqKysxOHDh5Ueh86SkpKQlpam/FF/4a0R\n5S+4Uf6CV2vOGyDlT/0svZxgBQRIt/Y333wTDQ0NWLJkCQCp48W0adOQkJCAwYMHIz09HUajEdOm\nTQNjDAAwdepUrF+/XunW3r9/fwDAyJEjsXbtWsyaNQtmsxmzZ88GAERGRuKOO+7A/PnzwRjDhAkT\nEBER4Z8ME0IIabSACFhr1qxxe2z8+PEYP368y/7u3btj+fLlLvtDQkIwZ84c3XsNHz4cw4cPv+R0\nEkII8Z+AqBIMdJdbjA10lL/gRvkLXq05b0DT549x6kZHCCEkCFAJixBCSFCggEUIISQoBESni0CW\nk5ODt956C5xzjBgxAuPGjfN3khqlpKQE69atQ1lZGRhjGDVqFEaPHo3KykqsWrUKRUVF6NSpE9LT\n071OOBzIRFHEggULYLFY8OSTT7aq/FVVVeHVV1/Fr7/+CsYYHn74YcTHx7ea/O3cuRNZWVlgjKFr\n16545JFHUFNTE7T527hxI7799lt06NABr7zyCgBc0r9HdxN8+5te/ppyAnOPOHHLZrPxmTNn8vPn\nz/P6+no+d+5cXlBQ4O9kNcqFCxf4iRMnOOecV1dX81mzZvGCggL+7rvv8o8//phzznlmZibfunUr\n55zzX3/9lc+bN483NDTwc+fO8ZkzZ3JRFP2VfJ998sknfPXq1fyll17inPNWlb9169bxXbt2cc45\nb2ho4BcvXmw1+SspKeEzZszg9fX1nHPOV6xYwbOysoI6f0ePHuUnTpzgjz/+uLLvUvKzYMEC/tNP\nP3HOOX/xxRf5d99918I50aeXv0OHDnGbzcY553zr1q38r3/9K+e86fNHVYIe5OXlIT4+Hh07doTR\naMSNN96oTLIbLKKiotCtWzcAQHh4OLp06YKSkhIcPHhQmSR4+PDhSr7cTTgcyEpKSvDdd99h1KhR\nyr7Wkr+qqiocO3YMI0aMAAAYDAaYTKZWkz9AKh3X1NTAZrOhrq4OFoslqPPXu3dvlzGejc2Ppwm+\n/U0vf005gbknVCXogd6EuYH2n6Mxzp8/j5MnT6JXr14oKytDVFQUACmoyfM8Wq1W9OrVS7kmGCYJ\nfvvtt/GnP/1Js1xMa8nf+fPnYTabsWHDBpw8eRLdu3fH5MmTW03+LBYLxo4di0ceeQRhYWFITk5G\ncnDaGmwAAAYzSURBVHJyq8mfrLH5MRgMbif4DnRZWVm48cYbATR9/qiE1UbU1NRgxYoVmDx5MsLD\nw12OyzOIBBu5Lr1bt24eJzoO1vyJoogTJ07glltuwdKlSxEWFqasF6cWrPm7ePEiDh48iA0bNuC1\n115DbW0t9u3b53JesObPndaWH1lzTGCuRiUsD5wn37Varcoku8HEZrNh+fLlGDp0qDLnYlRUFEpL\nS5XXDh06AHA/4XCgOnbsGA4ePIjvvvsOdXV1qK6uxtq1a1tN/iwWC2JiYtCjRw8A0hpvH3/8cavJ\n3+HDh9GpUydERkYCAK6//nr8+OOPrSZ/ssbmx9ME34GqqSYw94RKWB4kJiaisLAQRUVFaGhowP79\n+5WlUILJxo0bkZCQgNGjRyv7rrvuOuzevRuA9A9Nzpe7CYcD1T333IONGzdi3bp1eOyxx9C3b188\n+uijrSZ/UVFRiImJwZkzZwBID/iEhIRWk7/Y2Fj89NNPqKurA+e81eSPc64p8Tc2P54m+A4Ezvlr\nygnMPaGZLrzIycnBli1bwDnHyJEjg65b+7Fjx7Bo0SJ07doVjDEwxnD33XcjMTERK1euRHFxMTp2\n7Ij09HSlITUzMxO7du2C0WgMyG7D7hw5cgSffPKJ0q29teTvl19+wWuvvYaGhgaly7Aoiq0mf9u3\nb8cXX3wBg8GAbt26Yfr06aipqQna/K1evRpHjhxBRUUFOnTogLS0NAwcOLDR+cnPz9dM8D1lyhR/\nZkuhl7/MzEw0NDQoS6XIE5gDTZs/CliEEEKCAlUJEkIICQoUsAghhAQFCliEEEKCAgUsQgghQYEC\nFiGEkKBAAYsQQkhQoIBFSDN6/PHHceTIEb98dnFxMSZNmuRxyipCggmNwyKkBWzfvh3nzp3DzJkz\nm+0zZsyYgYcffhh9+/Ztts8gxJ+ohEVIEBBF0d9JIMTvqIRFSDOaMWMGpk6dqqzMajQaERcXh5df\nfhlVVVV455138N1330EQBAwbNgx33XUXGGPYvXs3Pv/8cyQmJmLv3r343e9+h+HDh+O1117DyZMn\nwRhDcnIypk2bBpPJhHXr1mHfvn0IDQ2FIAi44447MHjwYMycORPvv/8+BEHAhQsXsGnTJhw7dgxm\nsxm33XabsobY9u3bUVBQgJCQEGRnZyM2NhYzZsxA9+7d/fn1EaJBs7UT0owYYwgNDcX48eNdqgTX\nr1+P6OhorF27FjU1NVi6dCliY2Nx8803A5AWEP3tb3+LTZs2wWazoaSkBOPHj0efPn1QVVWF5cuX\nY/v27Zg0aRJmzpyJo0ePaqoEi4qKNGlZtWoVrrrqKrz++usoKCjAkiVLEBcXh6SkJADAN998g7lz\n52LGjBl4//338cYbb+CFF15ooW+KEO+oSpCQZuSuAqOsrAw5OTmYNGkSQkND0b59e4wePRr79+9X\nzrFYLLjlllsgCAJCQkIQFxeHfv36wWAwwGw2Y8yYMT536CguLsbx48dx7733wmg0olu3bhg5ciT2\n7NmjnNO7d2/0798fjDEMHToUp06durzME9LEqIRFiB/IS9Y8+OCDyj7OOWJjY5Vt9YqsgBTktmzZ\ngmPHjqGmpgaiKCrrSHlTWlqKyMhIhIWFKfs6duyIEydOKNvyirgAEBYWhrq6OoiiqCx9Toi/UcAi\npAU4rzAbGxuL0NBQvPnmm25Xn3XeL7dFrVixAiaTCdnZ2XjzzTfdnq8WHR2NyspK1NTUKCtOFxcX\nIzo6+lKzREiLo59OhLSADh06oKioSKkijIqKQnJyMt5++21UV1eDc45z5855rOKrrq5GeHg4wsPD\nYbVasWPHDs3xqKgonDt3TvfamJgY9OrVC++99x7q6+tx8uRJ7Nq1C0OHDm26TBLSzChgEdKM5FLP\n4MGDwTnH/fffj/nz5wOQehA2NDRgzpw5uP/++7FixQqUlpa6vdedd96J/Px8TJkyBUuXLsUNN9yg\nOT5u3Dh8+OGHmDJlCnbu3Oly/ezZs3H+/Hk89NBDWL58Oe666y4as0WCCnVrJ4QQEhSohEUIISQo\nUMAihBASFChgEUIICQoUsAghhAQFCliEEEKCAgUsQgghQYECFiGEkKBAAYsQQkhQoIBFCCEkKPx/\ncGLm/m5gd68AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x111a7d410>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(-np.array(logf))\n",
    "plt.xlabel('iteration')\n",
    "plt.ylabel('ELBO')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x115e5edd0>"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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NLfkuQ0g8yITzm1cM9Xp3ri/dctQ6xtelYW8xWydqQ43VlHZq6f7PUwPuPKGK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rNyQy7skDMpdPaiUutKdFW7baSSrw+XayA7A+m2VXbfA+Gl67We5pwMrZ5926Oh3+Z3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\n2AsEAoEdIIK9QCAQ2AEi2AsEAoEd8P9Xos/snpFsMQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1158da110>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot()\n",
    "plt.title(\"Predictions after training\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.12"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}
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