{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Populating the interactive namespace from numpy and matplotlib\n"
     ]
    }
   ],
   "source": [
    "%pylab inline\n",
    "import pandas as pd\n",
    "import theano\n",
    "theano.config.floatX = 'float64'\n",
    "import pymc3 as pm\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import theano.tensor as tt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import time"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/vale/anaconda/lib/python3.6/site-packages/ipykernel/__main__.py:10: VisibleDeprecationWarning: using a non-integer number instead of an integer will result in an error in the future\n",
      "Average ELBO = -30.05: 100%|██████████| 20000/20000 [00:01<00:00, 15668.21it/s] \n",
      "Finished [100%]: Average ELBO = -29.765\n",
      "Average ELBO = -16,711: 100%|██████████| 20000/20000 [00:05<00:00, 3405.25it/s]   \n",
      "Finished [100%]: Average ELBO = -16,384\n",
      "Average ELBO = -33,637: 100%|██████████| 20000/20000 [00:10<00:00, 1908.36it/s]   \n",
      "Finished [100%]: Average ELBO = -32,888\n",
      "Average ELBO = -50,193: 100%|██████████| 20000/20000 [00:15<00:00, 1282.30it/s]   \n",
      "Finished [100%]: Average ELBO = -49,196\n",
      "Average ELBO = -67,139: 100%|██████████| 20000/20000 [00:20<00:00, 976.42it/s]   \n",
      "Finished [100%]: Average ELBO = -65,887\n",
      "Average ELBO = -83,476: 100%|██████████| 20000/20000 [00:26<00:00, 755.49it/s]    \n",
      "Finished [100%]: Average ELBO = -81,943\n",
      "Average ELBO = -1.0016e+05: 100%|██████████| 20000/20000 [00:32<00:00, 623.77it/s]\n",
      "Finished [100%]: Average ELBO = -97,998\n",
      "Average ELBO = -1.1732e+05: 100%|██████████| 20000/20000 [00:38<00:00, 520.41it/s]\n",
      "Finished [100%]: Average ELBO = -1.1496e+05\n",
      "Average ELBO = -1.3449e+05: 100%|██████████| 20000/20000 [00:45<00:00, 443.79it/s]\n",
      "Finished [100%]: Average ELBO = -1.3183e+05\n",
      "Average ELBO = -1.511e+05: 100%|██████████| 20000/20000 [00:49<00:00, 405.42it/s] \n",
      "Finished [100%]: Average ELBO = -1.4807e+05\n"
     ]
    }
   ],
   "source": [
    "advi_times = []\n",
    "sizes = np.linspace(20, 200000, 10)\n",
    "for size in sizes:\n",
    "    true_intercept = 1\n",
    "    true_slope = 2\n",
    "\n",
    "    x = np.linspace(0, 1, size)\n",
    "\n",
    "    true_regression_line = true_intercept + true_slope * x\n",
    "    y = true_regression_line + np.random.normal(scale=.5, size=size)\n",
    "\n",
    "    data = dict(x=x, y=y)\n",
    "    \n",
    "    with pm.Model() as model:\n",
    "        # Define priors\n",
    "        sigma = pm.HalfCauchy('sigma', beta=10, testval=1.)\n",
    "        intercept = pm.Normal('Intercept', 0, sd=20)\n",
    "        x_coeff = pm.Normal('x', 0, sd=20)\n",
    "\n",
    "        mu = intercept + x_coeff * x\n",
    "        likelihood = pm.Normal('y', mu=mu, sd=sigma, observed=y)\n",
    "\n",
    "    t0 = time.time()\n",
    "    with model:\n",
    "        means, sds, elbos = pm.variational.advi(n=20000)\n",
    "        \n",
    "    advi_times.append(time.time() - t0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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Jw3vQrEEdp2NJANNudREP+G7HYcbPTOZwXgFPXNOFO/vHaWy5eJwKXaQGFZeU8uryNF5b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\nAwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1214b7eb8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(sizes, advi_times);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "x_t = tt.vector()\n",
    "x_t.tag.test_value = np.zeros(1)\n",
    "\n",
    "y_t = tt.vector()\n",
    "y_t.tag.test_value = np.zeros(1)\n",
    "\n",
    "minibatch_tensors = [x_t, y_t]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "with pm.Model() as model:\n",
    "    # Define priors\n",
    "    sigma = pm.HalfCauchy('sigma', beta=10, testval=1.)\n",
    "    intercept = pm.Normal('Intercept', 0, sd=20)\n",
    "    x_coeff = pm.Normal('x', 0, sd=20)\n",
    "    \n",
    "    mu = intercept + x_coeff * x_t\n",
    "    likelihood = pm.Normal('y', mu=mu, sd=sigma, observed=y_t)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "minibatch_RVs = [likelihood]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def minibatch_gen(data):\n",
    "    rng = np.random.RandomState(9)\n",
    "    \n",
    "    while True:\n",
    "        ixs = rng.randint(len(data['x']), size=100)\n",
    "        yield data['x'][ixs], data['y'][ixs]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/vale/anaconda/lib/python3.6/site-packages/ipykernel/__main__.py:9: VisibleDeprecationWarning: using a non-integer number instead of an integer will result in an error in the future\n",
      "Average ELBO = -32.85: 100%|██████████| 20000/20000 [00:04<00:00, 4615.38it/s]\n",
      "Finished minibatch ADVI: ELBO = -29.05\n",
      "/Users/vale/anaconda/lib/python3.6/site-packages/ipykernel/__main__.py:9: VisibleDeprecationWarning: using a non-integer number instead of an integer will result in an error in the future\n",
      "Average ELBO = -16,683.61: 100%|██████████| 20000/20000 [00:04<00:00, 4612.16it/s]\n",
      "Finished minibatch ADVI: ELBO = -16,185.61\n",
      "Average ELBO = -33,776.46: 100%|██████████| 20000/20000 [00:04<00:00, 4604.23it/s]\n",
      "Finished minibatch ADVI: ELBO = -34,384.99\n",
      "Average ELBO = -49,932.86: 100%|██████████| 20000/20000 [00:04<00:00, 4587.49it/s]\n",
      "Finished minibatch ADVI: ELBO = -50,458.88\n",
      "Average ELBO = -67,123.26: 100%|██████████| 20000/20000 [00:04<00:00, 4404.64it/s]\n",
      "Finished minibatch ADVI: ELBO = -69,393.39\n",
      "Average ELBO = -83,768.66: 100%|██████████| 20000/20000 [00:04<00:00, 4509.50it/s]  \n",
      "Finished minibatch ADVI: ELBO = -82,517.77\n",
      "Average ELBO = -100,630.14: 100%|██████████| 20000/20000 [00:04<00:00, 4508.07it/s] \n",
      "Finished minibatch ADVI: ELBO = -104,210.03\n",
      "Average ELBO = -117,037.14: 100%|██████████| 20000/20000 [00:04<00:00, 4518.11it/s] \n",
      "Finished minibatch ADVI: ELBO = -111,294.43\n",
      "Average ELBO = -135,231.70: 100%|██████████| 20000/20000 [00:04<00:00, 4457.70it/s] \n",
      "Finished minibatch ADVI: ELBO = -139,700.64\n",
      "Average ELBO = -150,743.20: 100%|██████████| 20000/20000 [00:04<00:00, 4416.26it/s] \n",
      "Finished minibatch ADVI: ELBO = -151,995.85\n"
     ]
    }
   ],
   "source": [
    "mb_advi_times = []\n",
    "for size in sizes:\n",
    "    true_intercept = 1\n",
    "    true_slope = 2\n",
    "\n",
    "    x = np.linspace(0, 1, size)\n",
    "\n",
    "    true_regression_line = true_intercept + true_slope * x\n",
    "    y = true_regression_line + np.random.normal(scale=.5, size=size)\n",
    "\n",
    "    data = dict(x=x, y=y)\n",
    "    \n",
    "    minibatches = minibatch_gen(data)\n",
    "    \n",
    "    t0 = time.time()\n",
    "    means, sds, elbos = pm.variational.advi_minibatch(\n",
    "        model=model, n=20000, minibatch_tensors=minibatch_tensors,\n",
    "        minibatch_RVs=minibatch_RVs, minibatches=minibatches,\n",
    "        total_size=len(data['x'])\n",
    "    )\n",
    "    \n",
    "    mb_advi_times.append(time.time() - t0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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Vnrl4WQ5ZqYlWl6NU3NKA91Pu9i5ZYIxeaJ2LTc2HaTk8rJOblLKYBryfioJM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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11e654320>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(sizes, mb_advi_times);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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ubMeoi1rbHcImi68ni5tmJgHXXsCaljAmyKVnKG8t3sy/F8TRsEYEn486nx7N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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1206b2358>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(sizes, advi_times, label='ADVI');\n",
    "plt.plot(sizes, mb_advi_times, label='Mini-batch ADVI');\n",
    "plt.title('Linear Regression Model (20,000 iterations)');\n",
    "plt.legend();\n",
    "plt.xlabel('Data size (# observations)')\n",
    "plt.ylabel('Time (seconds)');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 105,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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tvX8enU4gzzozqwzUBbb69LOj8kzzx+qZWWXfygmWJZI0o/omNk35vJOa0bpB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\nAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x12418cb70>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(elbos)\n",
    "plt.ylim(-1e6, 0);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 107,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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5/XDc3SMaD/SNdfu1iSN2ovLRsj339Iy2e06nqLqYPb4zYisVvmpg3kS5pcpW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\ngg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1217089b0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x, y);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 108,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'Intercept': array(1.0375121604515822),\n",
       " 'sigma_log_': array(-0.692413011804754),\n",
       " 'x': array(1.9445221003700959)}"
      ]
     },
     "execution_count": 108,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "means"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
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