{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Intro to TensorFlow Probability\n",
    "========================="
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-08-29T22:41:38.844996Z",
     "start_time": "2018-08-29T22:41:38.827646Z"
    }
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import warnings\n",
    "warnings.filterwarnings(\"ignore\")\n",
    "\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "import tensorflow as tf                            # importing Tensorflow\n",
    "import tensorflow_probability as tfp               # Tensorflow probability\n",
    "from tensorflow_probability import edward2 as ed   # Edwardlib extension\n",
    "#tf.enable_eager_execution()\n",
    "\n",
    "tfd = tfp.distributions             # Basic probability distribution toolkit\n",
    "\n",
    "plt.style.use('fivethirtyeight')        # Styling plots like FiveThirtyEight\n",
    "rc = {'xtick.labelsize': 40, 'ytick.labelsize': 40, 'axes.labelsize': 40, 'font.size': 40, 'lines.linewidth': 4.0, \n",
    "      'lines.markersize': 40, 'savefig.dpi': 200,\n",
    "      'text.usetex': False, 'legend.fontsize': 40.0, 'axes.titlesize': 40, \"figure.figsize\": [24, 16]}\n",
    "plt.rcParams.update(rc)\n",
    "\n",
    "%config InlineBackend.figure_format='retina' # improves resolution of plots\n",
    "from IPython.core.interactiveshell import InteractiveShell\n",
    "InteractiveShell.ast_node_interactivity = \"all\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## TensorFlow Probability (TFP)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Session( ) Context\n",
    "In TFP, all the variables in a model are handled within a Tensorflow session object."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-08-29T17:44:09.411306Z",
     "start_time": "2018-08-29T17:44:09.392581Z"
    }
   },
   "outputs": [],
   "source": [
    "with tf.Session() as sess1:\n",
    "    normal_rv = ed.Normal(name=\"normal\", loc=0., scale=1.)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Edward2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-08-29T17:44:12.110315Z",
     "start_time": "2018-08-29T17:44:12.079488Z"
    }
   },
   "outputs": [],
   "source": [
    "normal_rv = ed.Normal(name=\"normal_rv\", loc=0., scale=1.)\n",
    "x = normal_rv.distribution.sample(sample_shape=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-08-29T17:44:13.286111Z",
     "start_time": "2018-08-29T17:44:13.280252Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<tf.Tensor 'normal_rv/sample_1/Reshape:0' shape=(1,) dtype=float32>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-08-29T17:44:21.193470Z",
     "start_time": "2018-08-29T17:44:21.189823Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Tensor(\"normal_rv/sample_1/Reshape:0\", shape=(1,), dtype=float32)\n"
     ]
    }
   ],
   "source": [
    "print(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-08-29T17:44:23.364855Z",
     "start_time": "2018-08-29T17:44:23.355302Z"
    }
   },
   "outputs": [],
   "source": [
    "logp = normal_rv.distribution.log_prob(1.231)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-08-29T17:44:29.179584Z",
     "start_time": "2018-08-29T17:44:29.175773Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Tensor(\"normal_rv/log_prob/sub:0\", shape=(), dtype=float32)\n"
     ]
    }
   ],
   "source": [
    "print(logp)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-08-29T17:44:32.187094Z",
     "start_time": "2018-08-29T17:44:32.169194Z"
    }
   },
   "outputs": [],
   "source": [
    "dirichlet_rv = ed.Dirichlet(name=\"dirichlet_rv\", concentration=tf.zeros([2, 5]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-08-29T17:44:33.443798Z",
     "start_time": "2018-08-29T17:44:33.424754Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<tf.Tensor 'dirichlet_rv/sample_1/Reshape:0' shape=(1, 2, 5) dtype=float32>"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dir__ = dirichlet_rv.distribution.sample(sample_shape=1)\n",
    "dir__"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-08-29T17:44:35.421257Z",
     "start_time": "2018-08-29T17:44:35.417851Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Tensor(\"dirichlet_rv/sample_1/Reshape:0\", shape=(1, 2, 5), dtype=float32)\n"
     ]
    }
   ],
   "source": [
    "print(dir__)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-08-29T17:45:42.160599Z",
     "start_time": "2018-08-29T17:45:42.140185Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([[[0.2, 0.2, 0.2, 0.2, 0.2],\n",
       "         [0.2, 0.2, 0.2, 0.2, 0.2]]], dtype=float32), -1.6766189, -2.369414)"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "with tf.Session() as sess2:\n",
    "    [dir_, logp_, normal_] = sess2.run([dir__, logp, normal_rv])\n",
    "dir_, logp_, normal_    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-08-29T17:45:47.753194Z",
     "start_time": "2018-08-29T17:45:47.715228Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<tf.Tensor 'x/sample_1/Reshape:0' shape=(2, 2) dtype=float32>"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = ed.Normal(name=\"x\", loc=tf.zeros(2), scale=tf.ones(2)).distribution.sample(sample_shape=2)\n",
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-08-29T17:47:57.782435Z",
     "start_time": "2018-08-29T17:47:57.759496Z"
    }
   },
   "outputs": [],
   "source": [
    "with tf.Session() as sess3:\n",
    "    x_values = sess3.run(x)\n",
    "    \n",
    "x_values    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Random variables can interoperate with TensorFlow operations(ops): the TF ops operate on the sample"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-08-28T18:13:45.013421Z",
     "start_time": "2018-08-28T18:13:45.006051Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<tf.Tensor 'add:0' shape=(2, 2) dtype=float32>"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y = 10.\n",
    "z = x + y\n",
    "z"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-08-28T18:13:46.642144Z",
     "start_time": "2018-08-28T18:13:46.628034Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 8.123221, 10.941624],\n",
       "       [ 8.278514, 10.867475]], dtype=float32)"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "with tf.Session() as sess4:\n",
    "    z_values = sess4.run(z)\n",
    "    \n",
    "z_values    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example I"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Probabilistic models in Edward2 are expressed as Python functions. Inputs to the function are the variables conditioned on."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Prepare the data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-08-29T22:05:05.156361Z",
     "start_time": "2018-08-29T22:05:05.145329Z"
    }
   },
   "outputs": [],
   "source": [
    "num_of_variables = 10\n",
    "sample_size = 100\n",
    "input_data = tf.random_normal(shape=[sample_size, num_of_variables])\n",
    "output_data = tf.random_uniform(shape=[sample_size], minval=0, maxval=2, dtype=tf.int32)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-08-29T22:03:27.875376Z",
     "start_time": "2018-08-29T22:03:27.865306Z"
    },
    "scrolled": false
   },
   "outputs": [],
   "source": [
    "with tf.Session() as sess5:\n",
    "    data = sess5.run([output_data, input_data]) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-08-29T22:03:30.665630Z",
     "start_time": "2018-08-29T22:03:28.933138Z"
    }
   },
   "outputs": [
    {
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\n",
      "text/plain": [
       "<Figure size 1728x1152 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 990,
       "width": 1572
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(data[0]);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Build the model"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Probabilistic models in Edward2 are expressed as Python functions. Inputs to the function are the variables conditioned on."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-08-29T22:05:17.497534Z",
     "start_time": "2018-08-29T22:05:17.492833Z"
    }
   },
   "outputs": [],
   "source": [
    "def logistic_regression_model(X):\n",
    "    \n",
    "    # Priors\n",
    "    coefficients = ed.Normal(name=\"coefficients\", loc=tf.zeros(X.shape[1]), scale=1.)\n",
    "    intercept = ed.Normal(name=\"intercept\", loc=0., scale=1.)\n",
    "    \n",
    "    mean = tf.tensordot(a=X, b=coefficients, axes=[[1], [0]]) + intercept\n",
    "    \n",
    "    # likelihood\n",
    "    observations = ed.Bernoulli(name=\"observations\", logits=mean)\n",
    "    return coefficients, intercept, observations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-08-29T22:03:37.806237Z",
     "start_time": "2018-08-29T22:03:37.737764Z"
    }
   },
   "outputs": [],
   "source": [
    "# Simulate data from the model\n",
    "with tf.Session() as sess_logit_model:\n",
    "    obs_logit_ = logistic_regression_model(X=input_data)\n",
    "    obs_logit = sess_logit_model.run(obs_logit_)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-08-29T22:03:40.896989Z",
     "start_time": "2018-08-29T22:03:39.184040Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1728x1152 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 990,
       "width": 1572
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(obs_logit[2]);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Perform Inference"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-08-29T22:05:27.133571Z",
     "start_time": "2018-08-29T22:05:27.129605Z"
    }
   },
   "outputs": [],
   "source": [
    "# Define the target log-probability function\n",
    "def target_log_prob_fn(coefficients, intercept):\n",
    "    log_joint = ed.make_log_joint_fn(logistic_regression_model)\n",
    "    return log_joint(X=input_data, \n",
    "                     coefficients=coefficients, \n",
    "                     intercept=intercept, \n",
    "                     observations=output_data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-08-29T22:05:30.902562Z",
     "start_time": "2018-08-29T22:05:30.899065Z"
    }
   },
   "outputs": [],
   "source": [
    "# Pass the target log-probability function to MCMC transition kernel\n",
    "hmc_kernel = tfp.mcmc.HamiltonianMonteCarlo(\n",
    "    target_log_prob_fn=target_log_prob_fn, \n",
    "    step_size=0.1, \n",
    "    num_leapfrog_steps=5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-08-29T22:05:33.160045Z",
     "start_time": "2018-08-29T22:05:32.330777Z"
    }
   },
   "outputs": [],
   "source": [
    "posterior_, kernel_results_ = tfp.mcmc.sample_chain(\n",
    "    num_results=2000, \n",
    "    kernel=hmc_kernel, \n",
    "    current_state=[tf.random_normal([num_of_variables]), tf.random_normal([])]\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-08-29T22:05:58.861433Z",
     "start_time": "2018-08-29T22:05:56.318748Z"
    }
   },
   "outputs": [],
   "source": [
    "with tf.Session() as sess6:\n",
    "    posterior, kernel_results = sess6.run([posterior_, kernel_results_])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-08-29T18:25:03.491969Z",
     "start_time": "2018-08-29T18:25:03.484238Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[array([[ 1.23454499e+00, -5.29537320e-01,  2.56325305e-01, ...,\n",
       "         -5.61078906e-01,  6.10797286e-01, -1.50004995e+00],\n",
       "        [ 4.63765681e-01,  5.17678320e-01, -5.51589370e-01, ...,\n",
       "         -2.96718717e-01,  1.41228110e-01, -1.08574182e-01],\n",
       "        [ 7.00128555e-01, -5.37776947e-01,  1.44457191e-01, ...,\n",
       "          6.88411295e-02,  5.44470429e-01, -7.28535056e-01],\n",
       "        ...,\n",
       "        [ 2.81039625e-01, -1.36443317e-01, -1.36505626e-03, ...,\n",
       "         -1.89894766e-01, -2.54852414e-01, -1.03717774e-01],\n",
       "        [ 9.05339718e-01, -2.81044468e-02, -7.84435943e-02, ...,\n",
       "         -4.51861620e-01,  4.72477138e-01, -7.13243723e-01],\n",
       "        [-4.13052067e-02,  2.90339589e-01,  4.63036597e-02, ...,\n",
       "         -2.18547493e-01,  2.86587536e-01, -1.64738595e-01]], dtype=float32),\n",
       " array([-0.22570577, -0.49601158,  0.06852669, ..., -0.507801  ,\n",
       "         0.10641573, -0.40068737], dtype=float32)]"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "posterior"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-08-29T19:47:50.762376Z",
     "start_time": "2018-08-29T19:47:50.756860Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.4139317 ,  0.01990473, -0.05365106,  0.18452388,  0.3909374 ,\n",
       "       -0.14250118, -0.19428632, -0.2559822 ,  0.1253763 , -0.32384425],\n",
       "      dtype=float32)"
      ]
     },
     "execution_count": 74,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "posterior[0].mean(axis=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-08-29T19:48:08.330947Z",
     "start_time": "2018-08-29T19:48:08.324904Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "UncalibratedHamiltonianMonteCarloKernelResults(log_acceptance_correction=array([-35.551746  ,  -9.712345  ,   3.1811004 , ...,   0.12862158,\n",
       "         1.5010004 ,  -3.5543437 ], dtype=float32), target_log_prob=array([-102.16594,  -92.0848 ,  -95.38084, ...,  -83.56519,  -85.05496,\n",
       "        -81.36513], dtype=float32), grads_target_log_prob=[array([[ -7.6073856 ,  10.197836  , -11.527021  , ...,   4.9047294 ,\n",
       "         -7.2556667 ,  15.839924  ],\n",
       "       [  2.021736  ,  -9.721662  ,   9.841384  , ...,  -2.7480364 ,\n",
       "          2.6762094 ,  -6.533907  ],\n",
       "       [ -4.080062  ,  11.305866  ,  -8.743612  , ...,  -3.6899385 ,\n",
       "         -7.5970535 ,   7.883093  ],\n",
       "       ...,\n",
       "       [  4.6179557 ,   2.646771  ,  -2.0373013 , ...,  -0.37372175,\n",
       "          8.617219  ,  -1.397815  ],\n",
       "       [ -6.804408  ,   1.6840062 ,   1.4771062 , ...,   0.43582302,\n",
       "         -5.90917   ,   3.2831848 ],\n",
       "       [ 10.569896  ,  -5.973592  ,  -2.975623  , ...,   1.4728948 ,\n",
       "         -1.8152068 ,  -0.5249643 ]], dtype=float32), array([-2.4865043,  5.542667 , -7.162761 , ..., 11.178882 , -8.295211 ,\n",
       "        7.6152534], dtype=float32)])"
      ]
     },
     "execution_count": 76,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "kernel_results"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Diagnoze convergence"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-08-29T18:18:16.712898Z",
     "start_time": "2018-08-29T18:18:16.622088Z"
    }
   },
   "outputs": [],
   "source": [
    "import arviz as az\n",
    "# import pandas as pd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-08-29T18:48:27.654705Z",
     "start_time": "2018-08-29T18:48:27.645093Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>0</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>-0.225706</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>-0.496012</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.068527</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>-0.172776</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>-0.283585</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          0\n",
       "0 -0.225706\n",
       "1 -0.496012\n",
       "2  0.068527\n",
       "3 -0.172776\n",
       "4 -0.283585"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import pandas as pd\n",
    "posterior_df = pd.DataFrame(data=posterior[1])\n",
    "posterior_df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-08-29T18:47:24.181065Z",
     "start_time": "2018-08-29T18:47:24.178124Z"
    }
   },
   "outputs": [],
   "source": [
    "import xarray as xr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-08-29T18:48:38.012874Z",
     "start_time": "2018-08-29T18:48:38.005788Z"
    }
   },
   "outputs": [],
   "source": [
    "posterior_xr = xr.DataArray(data=posterior_df)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-08-29T18:50:07.175750Z",
     "start_time": "2018-08-29T18:50:07.165550Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<xarray.DataArray (dim_0: 2000, dim_1: 1)>\n",
       "array([[-0.225706],\n",
       "       [-0.496012],\n",
       "       [ 0.068527],\n",
       "       ...,\n",
       "       [-0.507801],\n",
       "       [ 0.106416],\n",
       "       [-0.400687]], dtype=float32)\n",
       "Coordinates:\n",
       "  * dim_0    (dim_0) int64 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 ...\n",
       "  * dim_1    (dim_1) int64 0"
      ]
     },
     "execution_count": 65,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "posterior_xr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-08-29T19:02:29.544354Z",
     "start_time": "2018-08-29T19:02:29.526206Z"
    }
   },
   "outputs": [],
   "source": [
    "az.traceplot(posterior_xr)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Critize the model"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Use the model for prediction"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example II"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Prepare the data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-08-29T22:41:43.522743Z",
     "start_time": "2018-08-29T22:41:43.517848Z"
    }
   },
   "outputs": [],
   "source": [
    "def build_toy_dataset(N, w, noise_std=0.1):\n",
    "  D = len(w)\n",
    "  x = np.random.randn(N, D)\n",
    "  y = np.dot(x, w) + np.random.normal(0, noise_std, size=N)\n",
    "  return x.astype(\"float32\"), y.astype(\"float32\")\n",
    "\n",
    "N = 40  # number of data points\n",
    "D = 10  # number of features\n",
    "\n",
    "w_true = np.random.randn(D)\n",
    "X_train, y_train = build_toy_dataset(N, w_true)\n",
    "X_test, y_test = build_toy_dataset(N, w_true)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-08-29T22:41:44.730095Z",
     "start_time": "2018-08-29T22:41:44.724572Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(40, 10)"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_train.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-08-29T22:41:47.768162Z",
     "start_time": "2018-08-29T22:41:45.993718Z"
    }
   },
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 1728x1152 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 990,
       "width": 1572
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(X_train.flatten());"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Build the model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-08-29T22:58:39.483405Z",
     "start_time": "2018-08-29T22:58:39.479175Z"
    }
   },
   "outputs": [],
   "source": [
    "def linear_regression_model(X):\n",
    "    # Priors\n",
    "    noise = ed.HalfNormal(name=\"noise\", scale=1.0)\n",
    "    coefficient = ed.Normal(name=\"coefficient\", loc=tf.zeros(shape=X.shape[1]), scale=1.0)\n",
    "    intercept = ed.Normal(name=\"intercept\", loc=0.0, scale=1.0)\n",
    "    \n",
    "    # Deterministic mean\n",
    "    mean = tf.tensordot(a=X, b=coefficient, axes=[[1], [0]]) + intercept\n",
    "    \n",
    "    # Likelihood\n",
    "    observations = ed.Normal(name=\"observations\", loc=mean, scale=noise)\n",
    "    \n",
    "    return observations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-08-29T22:58:47.042503Z",
     "start_time": "2018-08-29T22:58:46.923186Z"
    }
   },
   "outputs": [],
   "source": [
    "# Simulate data from the model\n",
    "with tf.Session() as sess_lm:\n",
    "    obs = linear_regression_model(X_train)\n",
    "    y_obs = sess_lm.run(obs)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-08-29T22:59:48.855531Z",
     "start_time": "2018-08-29T22:59:47.133099Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1728x1152 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 990,
       "width": 1572
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(y_obs);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Perform Inference"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-08-29T23:01:07.848963Z",
     "start_time": "2018-08-29T23:01:07.845149Z"
    }
   },
   "outputs": [],
   "source": [
    "# Define the target log-probability function\n",
    "log_joint = ed.make_log_joint_fn(linear_regression_model)\n",
    "\n",
    "def target_log_prob_fn_lm(coefficient, intercept, noise):\n",
    "\n",
    "    return log_joint(X=X_train, \n",
    "                     coefficient=coefficient, \n",
    "                     intercept=intercept,\n",
    "                     noise=noise,\n",
    "                     observations=y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-08-29T23:01:09.280571Z",
     "start_time": "2018-08-29T23:01:09.276998Z"
    }
   },
   "outputs": [],
   "source": [
    "# Pass the target log-probability function to MCMC transition kernel\n",
    "hmc_kernel_lm = tfp.mcmc.HamiltonianMonteCarlo(\n",
    "    target_log_prob_fn=target_log_prob_fn_lm, \n",
    "    step_size=0.1, \n",
    "    num_leapfrog_steps=5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-08-29T23:40:31.142683Z",
     "start_time": "2018-08-29T23:40:30.119840Z"
    },
    "scrolled": false
   },
   "outputs": [],
   "source": [
    "num_results = int(10e4)\n",
    "num_burnin_steps = int(1e3)\n",
    "\n",
    "# Set the chain's start state.\n",
    "initial_chain_state = [\n",
    "    tf.zeros([X_train.shape[1]], dtype=tf.float32, name=\"init_coefficient\"),\n",
    "    tf.zeros([], dtype=tf.float32, name=\"init_intercept\"),\n",
    "    tf.ones([], dtype=tf.float32, name=\"init_noise\"),\n",
    "]\n",
    "\n",
    "\n",
    "[\n",
    "posterior_coefficient, \n",
    "posterior_intercept, \n",
    "posterior_sigma\n",
    "], kernel_results_lm = tfp.mcmc.sample_chain(num_results=num_results, \n",
    "                                              num_burnin_steps=num_burnin_steps,\n",
    "                                              kernel=hmc_kernel_lm,\n",
    "                                              current_state=initial_chain_state)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-08-29T23:47:56.641800Z",
     "start_time": "2018-08-29T23:45:04.867836Z"
    }
   },
   "outputs": [],
   "source": [
    "with tf.Session() as sess_lm_model:\n",
    "    [\n",
    "        posterior_coefficient_, \n",
    "        posterior_intercept_, \n",
    "        posterior_sigma_,\n",
    "        kernel_results_lm_\n",
    "    ] = sess_lm_model.run([\n",
    "        posterior_coefficient, \n",
    "        posterior_intercept, \n",
    "        posterior_sigma,\n",
    "        kernel_results_lm        \n",
    "    ])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-08-30T00:00:53.788307Z",
     "start_time": "2018-08-30T00:00:53.784286Z"
    }
   },
   "outputs": [],
   "source": [
    "trace_coefficient = posterior_coefficient_\n",
    "trace_intercept = posterior_intercept_\n",
    "trace_sigma = posterior_sigma_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-08-30T00:00:54.384347Z",
     "start_time": "2018-08-30T00:00:54.380527Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(100000,)"
      ]
     },
     "execution_count": 81,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "trace_sigma.flatten().shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-08-30T00:01:56.886787Z",
     "start_time": "2018-08-30T00:01:55.013428Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1728x1152 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 1026,
       "width": 1673
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.title(r\"Posterior distributions of the variable $\\sigma$\")\n",
    "plt.hist(trace_intercept.flatten(), bins=35,  alpha=0.85,\n",
    "         label=r\"posterior of $\\sigma$\", color=\"#B276B2\")\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python [conda env:tfp]",
   "language": "python",
   "name": "conda-env-tfp-py"
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   "nbconvert_exporter": "python",
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   "title_cell": "Table of Contents",
   "title_sidebar": "Contents",
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   "toc_position": {
    "height": "calc(100% - 180px)",
    "left": "10px",
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