2 - Simple linear regression in Keras with uncertainty.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 2 - Simple regression model in TensorFlow 2.0... probabilistically."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's get some data from the `cars` data set!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.0.0\n"
     ]
    }
   ],
   "source": [
    "import pathlib\n",
    "from typing import Any, Optional\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import seaborn as sns\n",
    "import tensorflow as tf\n",
    "from tensorflow import keras\n",
    "from tensorflow.keras import layers\n",
    "import tensorflow_probability as tfp\n",
    "from tensorflow_probability import distributions as tfd\n",
    "\n",
    "print(tf.__version__)\n",
    "tf.get_logger().setLevel('ERROR')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'/Users/zach_anglin/.keras/datasets/auto-mpg.data'"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dataset_path = keras.utils.get_file(\"auto-mpg.data\", \"http://archive.ics.uci.edu/ml/machine-learning-databases/auto-mpg/auto-mpg.data\")\n",
    "dataset_path"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>MPG</th>\n",
       "      <th>Cylinders</th>\n",
       "      <th>Displacement</th>\n",
       "      <th>Horsepower</th>\n",
       "      <th>Weight</th>\n",
       "      <th>Acceleration</th>\n",
       "      <th>Model Year</th>\n",
       "      <th>Origin</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>393</td>\n",
       "      <td>27.0</td>\n",
       "      <td>4</td>\n",
       "      <td>140.0</td>\n",
       "      <td>86.0</td>\n",
       "      <td>2790.0</td>\n",
       "      <td>15.6</td>\n",
       "      <td>82</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>394</td>\n",
       "      <td>44.0</td>\n",
       "      <td>4</td>\n",
       "      <td>97.0</td>\n",
       "      <td>52.0</td>\n",
       "      <td>2130.0</td>\n",
       "      <td>24.6</td>\n",
       "      <td>82</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>395</td>\n",
       "      <td>32.0</td>\n",
       "      <td>4</td>\n",
       "      <td>135.0</td>\n",
       "      <td>84.0</td>\n",
       "      <td>2295.0</td>\n",
       "      <td>11.6</td>\n",
       "      <td>82</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>396</td>\n",
       "      <td>28.0</td>\n",
       "      <td>4</td>\n",
       "      <td>120.0</td>\n",
       "      <td>79.0</td>\n",
       "      <td>2625.0</td>\n",
       "      <td>18.6</td>\n",
       "      <td>82</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>397</td>\n",
       "      <td>31.0</td>\n",
       "      <td>4</td>\n",
       "      <td>119.0</td>\n",
       "      <td>82.0</td>\n",
       "      <td>2720.0</td>\n",
       "      <td>19.4</td>\n",
       "      <td>82</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      MPG  Cylinders  Displacement  Horsepower  Weight  Acceleration  \\\n",
       "393  27.0          4         140.0        86.0  2790.0          15.6   \n",
       "394  44.0          4          97.0        52.0  2130.0          24.6   \n",
       "395  32.0          4         135.0        84.0  2295.0          11.6   \n",
       "396  28.0          4         120.0        79.0  2625.0          18.6   \n",
       "397  31.0          4         119.0        82.0  2720.0          19.4   \n",
       "\n",
       "     Model Year  Origin  \n",
       "393          82       1  \n",
       "394          82       2  \n",
       "395          82       1  \n",
       "396          82       1  \n",
       "397          82       1  "
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "column_names = ['MPG','Cylinders','Displacement','Horsepower','Weight',\n",
    "                'Acceleration', 'Model Year', 'Origin']\n",
    "\n",
    "raw_dataset = pd.read_csv(dataset_path, names=column_names,\n",
    "                      na_values = \"?\", comment='\\t',\n",
    "                      sep=\" \", skipinitialspace=True)\n",
    "\n",
    "dataset = raw_dataset.copy()\n",
    "dataset.tail()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Now that we have some data, we need to go about cleaning it."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Drop NA values\n",
    "dataset = dataset.dropna()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "# We need to turn origin into a one-hot encoded vector.\n",
    "\n",
    "origin = dataset.pop('Origin')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>MPG</th>\n",
       "      <th>Cylinders</th>\n",
       "      <th>Displacement</th>\n",
       "      <th>Horsepower</th>\n",
       "      <th>Weight</th>\n",
       "      <th>Acceleration</th>\n",
       "      <th>Model Year</th>\n",
       "      <th>USA</th>\n",
       "      <th>Europe</th>\n",
       "      <th>Japan</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>393</td>\n",
       "      <td>27.0</td>\n",
       "      <td>4</td>\n",
       "      <td>140.0</td>\n",
       "      <td>86.0</td>\n",
       "      <td>2790.0</td>\n",
       "      <td>15.6</td>\n",
       "      <td>82</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
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       "    <tr>\n",
       "      <td>394</td>\n",
       "      <td>44.0</td>\n",
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       "      <td>97.0</td>\n",
       "      <td>52.0</td>\n",
       "      <td>2130.0</td>\n",
       "      <td>24.6</td>\n",
       "      <td>82</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>395</td>\n",
       "      <td>32.0</td>\n",
       "      <td>4</td>\n",
       "      <td>135.0</td>\n",
       "      <td>84.0</td>\n",
       "      <td>2295.0</td>\n",
       "      <td>11.6</td>\n",
       "      <td>82</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>396</td>\n",
       "      <td>28.0</td>\n",
       "      <td>4</td>\n",
       "      <td>120.0</td>\n",
       "      <td>79.0</td>\n",
       "      <td>2625.0</td>\n",
       "      <td>18.6</td>\n",
       "      <td>82</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>397</td>\n",
       "      <td>31.0</td>\n",
       "      <td>4</td>\n",
       "      <td>119.0</td>\n",
       "      <td>82.0</td>\n",
       "      <td>2720.0</td>\n",
       "      <td>19.4</td>\n",
       "      <td>82</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      MPG  Cylinders  Displacement  Horsepower  Weight  Acceleration  \\\n",
       "393  27.0          4         140.0        86.0  2790.0          15.6   \n",
       "394  44.0          4          97.0        52.0  2130.0          24.6   \n",
       "395  32.0          4         135.0        84.0  2295.0          11.6   \n",
       "396  28.0          4         120.0        79.0  2625.0          18.6   \n",
       "397  31.0          4         119.0        82.0  2720.0          19.4   \n",
       "\n",
       "     Model Year  USA  Europe  Japan  \n",
       "393          82  1.0     0.0    0.0  \n",
       "394          82  0.0     1.0    0.0  \n",
       "395          82  1.0     0.0    0.0  \n",
       "396          82  1.0     0.0    0.0  \n",
       "397          82  1.0     0.0    0.0  "
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dataset['USA'] = (origin == 1) * 1.0  # Cast Series to float\n",
    "dataset['Europe'] = (origin == 2) * 1.0\n",
    "dataset['Japan'] = (origin == 3) * 1.0\n",
    "dataset.tail()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "train_dataset = dataset.sample(frac=0.8,random_state=0)\n",
    "test_dataset = dataset.drop(train_dataset.index)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>count</th>\n",
       "      <th>mean</th>\n",
       "      <th>std</th>\n",
       "      <th>min</th>\n",
       "      <th>25%</th>\n",
       "      <th>50%</th>\n",
       "      <th>75%</th>\n",
       "      <th>max</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>Cylinders</td>\n",
       "      <td>314.0</td>\n",
       "      <td>5.477707</td>\n",
       "      <td>1.699788</td>\n",
       "      <td>3.0</td>\n",
       "      <td>4.00</td>\n",
       "      <td>4.0</td>\n",
       "      <td>8.00</td>\n",
       "      <td>8.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>Displacement</td>\n",
       "      <td>314.0</td>\n",
       "      <td>195.318471</td>\n",
       "      <td>104.331589</td>\n",
       "      <td>68.0</td>\n",
       "      <td>105.50</td>\n",
       "      <td>151.0</td>\n",
       "      <td>265.75</td>\n",
       "      <td>455.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>Horsepower</td>\n",
       "      <td>314.0</td>\n",
       "      <td>104.869427</td>\n",
       "      <td>38.096214</td>\n",
       "      <td>46.0</td>\n",
       "      <td>76.25</td>\n",
       "      <td>94.5</td>\n",
       "      <td>128.00</td>\n",
       "      <td>225.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>Weight</td>\n",
       "      <td>314.0</td>\n",
       "      <td>2990.251592</td>\n",
       "      <td>843.898596</td>\n",
       "      <td>1649.0</td>\n",
       "      <td>2256.50</td>\n",
       "      <td>2822.5</td>\n",
       "      <td>3608.00</td>\n",
       "      <td>5140.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>Acceleration</td>\n",
       "      <td>314.0</td>\n",
       "      <td>15.559236</td>\n",
       "      <td>2.789230</td>\n",
       "      <td>8.0</td>\n",
       "      <td>13.80</td>\n",
       "      <td>15.5</td>\n",
       "      <td>17.20</td>\n",
       "      <td>24.8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>Model Year</td>\n",
       "      <td>314.0</td>\n",
       "      <td>75.898089</td>\n",
       "      <td>3.675642</td>\n",
       "      <td>70.0</td>\n",
       "      <td>73.00</td>\n",
       "      <td>76.0</td>\n",
       "      <td>79.00</td>\n",
       "      <td>82.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>USA</td>\n",
       "      <td>314.0</td>\n",
       "      <td>0.624204</td>\n",
       "      <td>0.485101</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.00</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.00</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>Europe</td>\n",
       "      <td>314.0</td>\n",
       "      <td>0.178344</td>\n",
       "      <td>0.383413</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.00</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>Japan</td>\n",
       "      <td>314.0</td>\n",
       "      <td>0.197452</td>\n",
       "      <td>0.398712</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.00</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "              count         mean         std     min      25%     50%  \\\n",
       "Cylinders     314.0     5.477707    1.699788     3.0     4.00     4.0   \n",
       "Displacement  314.0   195.318471  104.331589    68.0   105.50   151.0   \n",
       "Horsepower    314.0   104.869427   38.096214    46.0    76.25    94.5   \n",
       "Weight        314.0  2990.251592  843.898596  1649.0  2256.50  2822.5   \n",
       "Acceleration  314.0    15.559236    2.789230     8.0    13.80    15.5   \n",
       "Model Year    314.0    75.898089    3.675642    70.0    73.00    76.0   \n",
       "USA           314.0     0.624204    0.485101     0.0     0.00     1.0   \n",
       "Europe        314.0     0.178344    0.383413     0.0     0.00     0.0   \n",
       "Japan         314.0     0.197452    0.398712     0.0     0.00     0.0   \n",
       "\n",
       "                  75%     max  \n",
       "Cylinders        8.00     8.0  \n",
       "Displacement   265.75   455.0  \n",
       "Horsepower     128.00   225.0  \n",
       "Weight        3608.00  5140.0  \n",
       "Acceleration    17.20    24.8  \n",
       "Model Year      79.00    82.0  \n",
       "USA              1.00     1.0  \n",
       "Europe           0.00     1.0  \n",
       "Japan            0.00     1.0  "
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "train_stats = train_dataset.describe()\n",
    "train_stats.pop(\"MPG\") \n",
    "train_stats = train_stats.transpose()\n",
    "train_stats"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Split the data set into an 80/20 train/test division."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "train_labels = train_dataset.pop('MPG')\n",
    "test_labels = test_dataset.pop('MPG')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Normal-transform data set for use in a regression network."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "def norm(x: pd.DataFrame) -> pd.DataFrame:\n",
    "    \"\"\"Norm all columns to zero mean and unit standard deviation.\"\"\"\n",
    "    return (x - train_stats['mean']) / train_stats['std']\n",
    "\n",
    "normed_train_data = norm(train_dataset)\n",
    "normed_test_data = norm(test_dataset)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Do it probabilistically!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Going to replace the first `Dense` layer with one that's probabilistic."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "def build_model():\n",
    "    model = keras.Sequential([\n",
    "        tfp.layers.DenseVariational(64, activation='relu', input_shape=[len(train_dataset.keys())]),\n",
    "        layers.Dense(64, activation='relu'),\n",
    "        layers.Dense(1),\n",
    "    ])\n",
    "\n",
    "    optimizer = tf.keras.optimizers.RMSprop(0.001)\n",
    "\n",
    "    model.compile(loss='mse',\n",
    "                optimizer=optimizer,\n",
    "                metrics=['mae', 'mse'])\n",
    "    return model"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`DenseVariational`? This is a vanilla densely-connected neural network layer that, rather than fitting point estimates, fits distributions over its weights using _variational inference_. Variational inference as a topic is beyond the scope of this talk, but for now let's consider it a way to update prior Bayesian beliefs about a distribution in response to observed data that's more computationally efficient than Markov Chain Monte Carlo sampling.\n",
    "\n",
    "For further research, I recommend starting with this overview by Volodymyr Kuleshov and Stefano Ermon with the Stanford Probabilistic Graphical Modeling course."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<iframe src=\"https://ermongroup.github.io/cs228-notes/inference/variational/\" width=\"900\" height=\"500\"></iframe>\n",
       "\n"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%%HTML\n",
    "<iframe src=\"https://ermongroup.github.io/cs228-notes/inference/variational/\" width=\"900\" height=\"500\"></iframe>\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And it's just that easy."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "ename": "TypeError",
     "evalue": "__init__() missing 2 required positional arguments: 'make_posterior_fn' and 'make_prior_fn'",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mTypeError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-12-671884cecb64>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mmodel\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mbuild_model\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;32m<ipython-input-11-e2f5a6dc23ba>\u001b[0m in \u001b[0;36mbuild_model\u001b[0;34m()\u001b[0m\n\u001b[1;32m      1\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0mbuild_model\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      2\u001b[0m     model = keras.Sequential([\n\u001b[0;32m----> 3\u001b[0;31m         \u001b[0mtfp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mlayers\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mDenseVariational\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m64\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mactivation\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m'relu'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0minput_shape\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mtrain_dataset\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mkeys\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      4\u001b[0m         \u001b[0mlayers\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mDense\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m64\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mactivation\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m'relu'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      5\u001b[0m         \u001b[0mlayers\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mDense\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mTypeError\u001b[0m: __init__() missing 2 required positional arguments: 'make_posterior_fn' and 'make_prior_fn'"
     ]
    }
   ],
   "source": [
    "model = build_model()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Well, maybe not quite that easy."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Specify trainable priors and posterior functions."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In order to work with the `DenseVariational` layer, we need to provide it with a function to make its posterior (learned) distribution of weights and a prior distribution to apply to the weights in the absence of any observed data.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Our `make_posterior_fn` must take a kernel_size, bias_size, and data type, return a callable that creates\n",
    "a tfd.Distribution instance. In our case, it's going to execute the mean field approximation for variational inference -- again, this topic is beyond the scope of today's talk, but you are encouraged to research more, perhaps starting [here](https://www.cs.cmu.edu/~epxing/Class/10708-17/notes-17/10708-scribe-lecture13.pdf)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "def posterior_mean_field(kernel_size: int, bias_size: int, dtype: Any) -> tf.keras.Model:\n",
    "    \"\"\"Specify the surrogate posterior over `keras.layers.Dense` `kernel` and `bias`.\"\"\"\n",
    "    n = kernel_size + bias_size\n",
    "    c = np.log(np.expm1(1.))\n",
    "    \n",
    "    return tf.keras.Sequential([\n",
    "      tfp.layers.VariableLayer(2 * n, dtype=dtype),\n",
    "      tfp.layers.DistributionLambda(lambda t: tfd.Independent(\n",
    "          tfd.Normal(loc=t[..., :n],\n",
    "                     scale=1e-5 + tf.nn.softplus(c + t[..., n:])),\n",
    "          reinterpreted_batch_ndims=1)),\n",
    "  ])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For our `make_prior_fn`, we'll define a normal distribution with a _trainable_ mean -- that is, we won't place any expectations on the mean of our prior for the weights in our `DenseVariational` layer, and we'll allow that parameter to be learned from the data. Our prior on the standard deviation of the layer weights is 1."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "def prior_trainable(kernel_size: int, bias_size: int, dtype: Any) -> tf.keras.Model:\n",
    "    \"\"\"Specify the prior over `keras.layers.Dense` `kernel` and `bias`.\"\"\"\n",
    "    n = kernel_size + bias_size\n",
    "    \n",
    "    return tf.keras.Sequential([\n",
    "      tfp.layers.VariableLayer(n, dtype=dtype),  # Returns a trainable variable of shape n, regardless of input\n",
    "      tfp.layers.DistributionLambda(lambda t: tfd.Independent(\n",
    "          tfd.Normal(loc=t, scale=1),\n",
    "          reinterpreted_batch_ndims=1)),\n",
    "    ])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now that we've defined our make_posterior_fn and make_prior_fn, we can pass them in as named arguments to the `DenseVariational` layer as a drop-in replacement for the previous `Dense` layer."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "def build_model():\n",
    "    model = keras.Sequential([\n",
    "        tfp.layers.DenseVariational(64, activation='relu', \n",
    "                                input_shape=[len(train_dataset.keys())], \n",
    "                                make_posterior_fn=posterior_mean_field, \n",
    "                                make_prior_fn=prior_trainable),\n",
    "        layers.Dense(64, activation='relu'),\n",
    "        layers.Dense(1),\n",
    "    ])\n",
    "\n",
    "    optimizer = tf.keras.optimizers.RMSprop(0.001)\n",
    "\n",
    "    model.compile(loss='mse',\n",
    "                optimizer=optimizer,\n",
    "                metrics=['mae', 'mse'])\n",
    "    return model\n",
    "\n",
    "model = build_model()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Model: \"sequential\"\n",
      "_________________________________________________________________\n",
      "Layer (type)                 Output Shape              Param #   \n",
      "=================================================================\n",
      "dense_variational (DenseVari (None, 64)                1920      \n",
      "_________________________________________________________________\n",
      "dense (Dense)                (None, 64)                4160      \n",
      "_________________________________________________________________\n",
      "dense_1 (Dense)              (None, 1)                 65        \n",
      "=================================================================\n",
      "Total params: 6,145\n",
      "Trainable params: 6,145\n",
      "Non-trainable params: 0\n",
      "_________________________________________________________________\n"
     ]
    }
   ],
   "source": [
    "model.summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note the increased number of parameters in the first layer vs our previous try. The non-variational version of this model had 640 parameters, so we're training triple the number with this variational layer."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's try our previous exercise of predicting an example batch of training data through the untrained model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.32688773],\n",
       "       [1.1666714 ],\n",
       "       [4.4246945 ],\n",
       "       [1.3378894 ],\n",
       "       [0.38400805],\n",
       "       [2.2721694 ],\n",
       "       [0.8252253 ],\n",
       "       [1.3737593 ],\n",
       "       [2.2538216 ],\n",
       "       [1.5290165 ]], dtype=float32)"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "example_batch = normed_train_data[:10]\n",
    "example_result = model.predict(example_batch)\n",
    "example_result"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And if we do it again, we should get the same results."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.2614611],\n",
       "       [-0.8945936],\n",
       "       [ 2.2889018],\n",
       "       [ 0.5174635],\n",
       "       [ 3.258319 ],\n",
       "       [ 0.4016528],\n",
       "       [ 2.9797814],\n",
       "       [ 2.69539  ],\n",
       "       [ 1.4225549],\n",
       "       [ 2.5393457]], dtype=float32)"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "example_batch = normed_train_data[:10]\n",
    "example_result = model.predict(example_batch)\n",
    "example_result"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "They're different! The predictions through the untrained model aren't the same, even though they're going through the same network. Let's take a look at those network layers."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<tensorflow_probability.python.layers.dense_variational_v2.DenseVariational at 0x10f737080>"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.layers[0]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ok, the first layer is this `DenseVariational` layer from `tensorflow_probability`. What's happening here is that the model isn't learning weights for that layer (and hasn't initialized them). Rather, it's trying to learn _distributions_ over the weights. We've initialized these to be normal distributions with mean 0 and standard deviation 1, and each time we pass a prediction through the network, the actual weights used for that prediction are each _random draws_ from the distributions that describe them."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Again, this network is completely untrained right now, so let's let it learn something."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "....................................................................................................\n",
      "....................................................................................................\n",
      "....................................................................................................\n",
      "....................................................................................................\n",
      "....................................................................................................\n",
      "....................................................................................................\n",
      "....................................................................................................\n",
      "....................................................................................................\n",
      "....................................................................................................\n",
      "...................................................................................................."
     ]
    }
   ],
   "source": [
    "class PrintDot(keras.callbacks.Callback):\n",
    "    \"\"\"\n",
    "    Display training progress by printing a single dot for \n",
    "    each completed epoch.\n",
    "    \"\"\"\n",
    "    def on_epoch_end(self, epoch, logs) -> None:\n",
    "        \"\"\"\n",
    "        `on_epoc_end` hook to take the epoch number and logs.\n",
    "        This will run whenever the training loop finishes an epoch.\n",
    "        \"\"\"\n",
    "        if epoch % 100 == 0: \n",
    "            print('')\n",
    "        print('.', end='')\n",
    "\n",
    "        \n",
    "EPOCHS = 1_000\n",
    "\n",
    "history = model.fit(\n",
    "  normed_train_data, train_labels,\n",
    "  epochs=EPOCHS, validation_split = 0.2, verbose=0,\n",
    "  callbacks=[PrintDot()])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>loss</th>\n",
       "      <th>mae</th>\n",
       "      <th>mse</th>\n",
       "      <th>val_loss</th>\n",
       "      <th>val_mae</th>\n",
       "      <th>val_mse</th>\n",
       "      <th>epoch</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>995</td>\n",
       "      <td>14.385945</td>\n",
       "      <td>2.578062</td>\n",
       "      <td>12.164734</td>\n",
       "      <td>17.210832</td>\n",
       "      <td>2.847568</td>\n",
       "      <td>13.066010</td>\n",
       "      <td>995</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>996</td>\n",
       "      <td>19.824579</td>\n",
       "      <td>3.173980</td>\n",
       "      <td>16.494396</td>\n",
       "      <td>11.495757</td>\n",
       "      <td>2.490174</td>\n",
       "      <td>11.315204</td>\n",
       "      <td>996</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>997</td>\n",
       "      <td>16.308277</td>\n",
       "      <td>2.725559</td>\n",
       "      <td>13.512956</td>\n",
       "      <td>23.103594</td>\n",
       "      <td>3.169920</td>\n",
       "      <td>17.353140</td>\n",
       "      <td>997</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>998</td>\n",
       "      <td>18.065331</td>\n",
       "      <td>2.993322</td>\n",
       "      <td>15.840591</td>\n",
       "      <td>21.253056</td>\n",
       "      <td>3.133522</td>\n",
       "      <td>15.220228</td>\n",
       "      <td>998</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>999</td>\n",
       "      <td>20.036528</td>\n",
       "      <td>3.038479</td>\n",
       "      <td>15.040870</td>\n",
       "      <td>13.434915</td>\n",
       "      <td>2.618584</td>\n",
       "      <td>10.557711</td>\n",
       "      <td>999</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          loss       mae        mse   val_loss   val_mae    val_mse  epoch\n",
       "995  14.385945  2.578062  12.164734  17.210832  2.847568  13.066010    995\n",
       "996  19.824579  3.173980  16.494396  11.495757  2.490174  11.315204    996\n",
       "997  16.308277  2.725559  13.512956  23.103594  3.169920  17.353140    997\n",
       "998  18.065331  2.993322  15.840591  21.253056  3.133522  15.220228    998\n",
       "999  20.036528  3.038479  15.040870  13.434915  2.618584  10.557711    999"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "hist = pd.DataFrame(history.history)\n",
    "hist['epoch'] = history.epoch\n",
    "hist.tail()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Our errors are a bit higher than they were with the previous network, but note the difference between the training and validation losses. They're very close to one another, whereas before we were hopelessly overfit."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def plot_history(hist: pd.DataFrame) -> None:\n",
    "    \"\"\"\n",
    "    Plot training vs validation MAE and MSE over epoch.\n",
    "    \"\"\"\n",
    "    plt.figure()\n",
    "    plt.xlabel('Epoch')\n",
    "    plt.ylabel('Mean Abs Error [MPG]')\n",
    "    plt.plot(hist['epoch'], hist['mae'],\n",
    "           label='Train Error')\n",
    "    plt.plot(hist['epoch'], hist['val_mae'],\n",
    "           label = 'Val Error')\n",
    "    plt.ylim([0,5])\n",
    "    plt.legend()\n",
    "\n",
    "    plt.figure()\n",
    "    plt.xlabel('Epoch')\n",
    "    plt.ylabel('Mean Square Error [$MPG^2$]')\n",
    "    plt.plot(hist['epoch'], hist['mse'],\n",
    "           label='Train Error')\n",
    "    plt.plot(hist['epoch'], hist['val_mse'],\n",
    "           label = 'Val Error')\n",
    "    plt.ylim([0,20])\n",
    "    plt.legend()\n",
    "    plt.show()\n",
    "\n",
    "\n",
    "plot_history(hist)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "That's actually not very helpful anymore, because our training and validation errors are right on top of one another. Let's increase the y-axis scale to zoom out a bit and decrease the transparency so we can actually see what's going on."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def plot_history(hist: pd.DataFrame) -> None:\n",
    "    \"\"\"\n",
    "    Plot training vs validation MAE and MSE over epoch.\n",
    "    \"\"\"\n",
    "\n",
    "    plt.figure()\n",
    "    plt.xlabel('Epoch')\n",
    "    plt.ylabel('Mean Abs Error [MPG]')\n",
    "    plt.plot(hist['epoch'], hist['mae'],\n",
    "           label='Train Error')\n",
    "    plt.plot(hist['epoch'], hist['val_mae'], alpha=0.5,\n",
    "           label = 'Val Error')\n",
    "    plt.ylim([0,10])\n",
    "    plt.legend()\n",
    "\n",
    "    plt.figure()\n",
    "    plt.xlabel('Epoch')\n",
    "    plt.ylabel('Mean Square Error [$MPG^2$]')\n",
    "    plt.plot(hist['epoch'], hist['mse'],\n",
    "           label='Train Error')\n",
    "    plt.plot(hist['epoch'], hist['val_mse'], alpha=0.5,\n",
    "           label = 'Val Error')\n",
    "    plt.ylim([0,50])\n",
    "    plt.legend()\n",
    "    plt.show()\n",
    "\n",
    "\n",
    "plot_history(hist)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "How fascinating! Even after 1,000 epochs, we're not yet overfit. Our training and validation errors are tracking together almost exactly."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's check out our model predictions vs true values of MPG."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "test_predictions = model.predict(normed_test_data).flatten()\n",
    "\n",
    "a = plt.axes(aspect='equal')\n",
    "plt.scatter(test_labels, test_predictions)\n",
    "plt.xlabel('True Values [MPG]')\n",
    "plt.ylabel('Predictions [MPG]')\n",
    "lims = [0, 50]\n",
    "plt.xlim(lims)\n",
    "plt.ylim(lims)\n",
    "_ = plt.plot(lims, lims)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And what if we do it again?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "test_predictions = model.predict(normed_test_data).flatten()\n",
    "\n",
    "a = plt.axes(aspect='equal')\n",
    "plt.scatter(test_labels, test_predictions)\n",
    "plt.xlabel('True Values [MPG]')\n",
    "plt.ylabel('Predictions [MPG]')\n",
    "lims = [0, 50]\n",
    "plt.xlim(lims)\n",
    "plt.ylim(lims)\n",
    "_ = plt.plot(lims, lims)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The dots moved! TensorFlow Probability is transparently drawing new samples from the distributions we've trained over our network's weights, and it's interacting completely seamlessly with the `tf.keras.Model` predict method."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can even ask the model to give us a sample of predictions from each incoming x and use that to give us quantified estimates of its uncertainty."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Use a list comprehension to predict over each test instance 100 times.\n",
    "yhats = [model.predict(normed_test_data).flatten() for _ in range(100)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "df = pd.DataFrame(yhats).T\n",
    "df['y'] = test_labels.values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "      <td>12.887467</td>\n",
       "      <td>15.923960</td>\n",
       "      <td>15.505637</td>\n",
       "      <td>12.546011</td>\n",
       "      <td>13.689652</td>\n",
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       "      <td>19.066832</td>\n",
       "      <td>18.606964</td>\n",
       "      <td>19.505543</td>\n",
       "      <td>22.086630</td>\n",
       "      <td>18.432629</td>\n",
       "      <td>16.893812</td>\n",
       "      <td>17.977459</td>\n",
       "      <td>17.041204</td>\n",
       "      <td>19.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5 rows × 101 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "           0          1          2          3          4          5  \\\n",
       "0  13.363284  15.835321  15.865869  20.544353  17.625397  15.531554   \n",
       "1  12.301462  12.610791  12.342657  16.020754  17.988195  14.976175   \n",
       "2  14.058670  12.207358  13.075133  15.029735  19.157524  16.387600   \n",
       "3  23.141998  22.198931  25.900690  23.726131  24.094572  24.262974   \n",
       "4  18.783911  18.439713  18.373770  18.552011  19.527012  18.235975   \n",
       "\n",
       "           6          7          8          9  ...         91         92  \\\n",
       "0  15.764424  17.965830  14.055731  19.149620  ...  17.677158  18.755899   \n",
       "1  14.100382  18.363697  12.930146  15.498043  ...  17.002396  15.585348   \n",
       "2  13.859962  17.924404  13.523514  14.212229  ...  17.095249  14.136136   \n",
       "3  28.549530  23.285227  29.220200  24.426865  ...  23.213930  24.171682   \n",
       "4  18.082481  19.182163  18.156639  19.144215  ...  17.407974  19.066832   \n",
       "\n",
       "          93         94         95         96         97         98  \\\n",
       "0  14.618988  16.962294  14.754986  14.091138  16.275694  14.836803   \n",
       "1  13.492046  15.567333  13.904748  12.797685  14.102706  13.642060   \n",
       "2  12.887467  15.923960  15.505637  12.546011  13.689652  14.001096   \n",
       "3  23.871946  25.018211  25.245325  25.353977  26.898003  23.495211   \n",
       "4  18.606964  19.505543  22.086630  18.432629  16.893812  17.977459   \n",
       "\n",
       "          99     y  \n",
       "0  16.325336  15.0  \n",
       "1  13.878819  10.0  \n",
       "2  13.068793   9.0  \n",
       "3  24.002716  25.0  \n",
       "4  17.041204  19.0  \n",
       "\n",
       "[5 rows x 101 columns]"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Great! Now, what we want in order to examine this is every predicted y-hat along with its true y-value in a tuple. Here's a somewhat hacky way to accomplish that using `itertools.chain.from_iterable`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [],
   "source": [
    "import itertools\n",
    "\n",
    "sample_preds = list(itertools.chain.from_iterable([[(j, x[-1]) for j in x if j != x[-1]] for x in df.values]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[(13.36328411102295, 15.0),\n",
       " (15.835321426391602, 15.0),\n",
       " (15.86586856842041, 15.0),\n",
       " (20.544353485107422, 15.0),\n",
       " (17.625396728515625, 15.0),\n",
       " (15.531554222106934, 15.0),\n",
       " (15.764424324035645, 15.0),\n",
       " (17.965829849243164, 15.0),\n",
       " (14.055730819702148, 15.0),\n",
       " (19.149620056152344, 15.0),\n",
       " (13.139802932739258, 15.0),\n",
       " (15.716266632080078, 15.0),\n",
       " (15.275647163391113, 15.0),\n",
       " (12.19444465637207, 15.0),\n",
       " (14.676457405090332, 15.0)]"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sample_preds[:15]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Alright! Now let's plot these as we just did for the single-batch predictions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "a = plt.axes(aspect='equal')\n",
    "plt.scatter([x[1] for x in sample_preds], [x[0] for x in sample_preds])\n",
    "plt.xlabel('True Values [MPG]')\n",
    "plt.ylabel('Predictions [MPG]')\n",
    "lims = [0, 50]\n",
    "plt.xlim(lims)\n",
    "plt.ylim(lims)\n",
    "_ = plt.plot(lims, lims)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Overlapping plot points in `matplotlib` are hurting us. Let's add some transparency, so we can see the relative frequency of each point."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "a = plt.axes(aspect='equal')\n",
    "plt.scatter([x[1] for x in sample_preds], [x[0] for x in sample_preds], alpha=0.1)\n",
    "plt.xlabel('True Values [MPG]')\n",
    "plt.ylabel('Predictions [MPG]')\n",
    "lims = [0, 50]\n",
    "plt.xlim(lims)\n",
    "plt.ylim(lims)\n",
    "_ = plt.plot(lims, lims)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here, our model is actually _telling us_ where it's not sure, indicated by the range of predictions that it's outputting for each of the input __x__'s. We can confirm visually that the model is less confidednt as we move up in the predicted MPG and in fact consistently underpredicts the true value as we get to the higher ranges."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can also run our same error analysis from earlier, just using a single random draw from the weight distributions to make a model prediction."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "test_predictions = model.predict(normed_test_data).flatten()\n",
    "error = test_predictions - test_labels\n",
    "plt.hist(error, bins = 25)\n",
    "plt.xlabel(\"Prediction Error [MPG]\")\n",
    "_ = plt.ylabel(\"Count\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "What's more, every time we run this, we'll get a different set of predictions (and therefore a different set of errors)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "test_predictions = model.predict(normed_test_data).flatten()\n",
    "error = test_predictions - test_labels\n",
    "plt.hist(error, bins = 25)\n",
    "plt.xlabel(\"Prediction Error [MPG]\")\n",
    "_ = plt.ylabel(\"Count\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Instead of calling that predict routine, why don't we use our sample of 100 predictions from earlier."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "error = [x[0] - x[1] for x in sample_preds]\n",
    "plt.hist(error, bins = 25)\n",
    "plt.xlabel(\"Prediction Error [MPG]\")\n",
    "_ = plt.ylabel(\"Count\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we're starting to see that normal distribution manifest itself. This is because we're now conducting a true Monte Carlo sample from the distributions that describe each of the model weights every time we make a prediction, and therefore we have transparent understanding of the root uncertainty the model contains."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Moreover, because our model hasn't shown the tendency to overfit, we can keep training it!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "....................................................................................................\n",
      "....................................................................................................\n",
      "....................................................................................................\n",
      "....................................................................................................\n",
      "....................................................................................................\n",
      "....................................................................................................\n",
      "....................................................................................................\n",
      "....................................................................................................\n",
      ".........................."
     ]
    },
    {
     "ename": "KeyboardInterrupt",
     "evalue": "",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mKeyboardInterrupt\u001b[0m                         Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-37-50fbb8541ce3>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m      5\u001b[0m     \u001b[0mvalidation_split\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;36m0.2\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      6\u001b[0m     \u001b[0mverbose\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 7\u001b[0;31m     \u001b[0mcallbacks\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mPrintDot\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      8\u001b[0m )\n",
      "\u001b[0;32m~/.pyenv/versions/3.7.3/lib/python3.7/site-packages/tensorflow_core/python/keras/engine/training.py\u001b[0m in \u001b[0;36mfit\u001b[0;34m(self, x, y, batch_size, epochs, verbose, callbacks, validation_split, validation_data, shuffle, class_weight, sample_weight, initial_epoch, steps_per_epoch, validation_steps, validation_freq, max_queue_size, workers, use_multiprocessing, **kwargs)\u001b[0m\n\u001b[1;32m    726\u001b[0m         \u001b[0mmax_queue_size\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mmax_queue_size\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    727\u001b[0m         \u001b[0mworkers\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mworkers\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 728\u001b[0;31m         use_multiprocessing=use_multiprocessing)\n\u001b[0m\u001b[1;32m    729\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    730\u001b[0m   def evaluate(self,\n",
      "\u001b[0;32m~/.pyenv/versions/3.7.3/lib/python3.7/site-packages/tensorflow_core/python/keras/engine/training_arrays.py\u001b[0m in \u001b[0;36mfit\u001b[0;34m(self, model, x, y, batch_size, epochs, verbose, callbacks, validation_split, validation_data, shuffle, class_weight, sample_weight, initial_epoch, steps_per_epoch, validation_steps, validation_freq, **kwargs)\u001b[0m\n\u001b[1;32m    672\u001b[0m         \u001b[0mvalidation_steps\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mvalidation_steps\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    673\u001b[0m         \u001b[0mvalidation_freq\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mvalidation_freq\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 674\u001b[0;31m         steps_name='steps_per_epoch')\n\u001b[0m\u001b[1;32m    675\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    676\u001b[0m   def evaluate(self,\n",
      "\u001b[0;32m~/.pyenv/versions/3.7.3/lib/python3.7/site-packages/tensorflow_core/python/keras/engine/training_arrays.py\u001b[0m in \u001b[0;36mmodel_iteration\u001b[0;34m(model, inputs, targets, sample_weights, batch_size, epochs, verbose, callbacks, val_inputs, val_targets, val_sample_weights, shuffle, initial_epoch, steps_per_epoch, validation_steps, validation_freq, mode, validation_in_fit, prepared_feed_values_from_dataset, steps_name, **kwargs)\u001b[0m\n\u001b[1;32m    437\u001b[0m           \u001b[0mvalidation_in_fit\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mTrue\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    438\u001b[0m           \u001b[0mprepared_feed_values_from_dataset\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mval_iterator\u001b[0m \u001b[0;32mis\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0;32mNone\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 439\u001b[0;31m           steps_name='validation_steps')\n\u001b[0m\u001b[1;32m    440\u001b[0m       \u001b[0;32mif\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0misinstance\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mval_results\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mlist\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    441\u001b[0m         \u001b[0mval_results\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0mval_results\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/.pyenv/versions/3.7.3/lib/python3.7/site-packages/tensorflow_core/python/keras/engine/training_arrays.py\u001b[0m in \u001b[0;36mmodel_iteration\u001b[0;34m(model, inputs, targets, sample_weights, batch_size, epochs, verbose, callbacks, val_inputs, val_targets, val_sample_weights, shuffle, initial_epoch, steps_per_epoch, validation_steps, validation_freq, mode, validation_in_fit, prepared_feed_values_from_dataset, steps_name, **kwargs)\u001b[0m\n\u001b[1;32m    391\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    392\u001b[0m         \u001b[0;31m# Get outputs.\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 393\u001b[0;31m         \u001b[0mbatch_outs\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mf\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mins_batch\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    394\u001b[0m         \u001b[0;32mif\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0misinstance\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mbatch_outs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mlist\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    395\u001b[0m           \u001b[0mbatch_outs\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0mbatch_outs\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/.pyenv/versions/3.7.3/lib/python3.7/site-packages/tensorflow_core/python/keras/backend.py\u001b[0m in \u001b[0;36m__call__\u001b[0;34m(self, inputs)\u001b[0m\n\u001b[1;32m   3738\u001b[0m         \u001b[0mvalue\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mmath_ops\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcast\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mvalue\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mtensor\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdtype\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   3739\u001b[0m       \u001b[0mconverted_inputs\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mappend\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mvalue\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 3740\u001b[0;31m     \u001b[0moutputs\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_graph_fn\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mconverted_inputs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   3741\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   3742\u001b[0m     \u001b[0;31m# EagerTensor.numpy() will often make a copy to ensure memory safety.\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/.pyenv/versions/3.7.3/lib/python3.7/site-packages/tensorflow_core/python/eager/function.py\u001b[0m in \u001b[0;36m__call__\u001b[0;34m(self, *args, **kwargs)\u001b[0m\n\u001b[1;32m   1079\u001b[0m       \u001b[0mTypeError\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0mFor\u001b[0m \u001b[0minvalid\u001b[0m \u001b[0mpositional\u001b[0m\u001b[0;34m/\u001b[0m\u001b[0mkeyword\u001b[0m \u001b[0margument\u001b[0m \u001b[0mcombinations\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1080\u001b[0m     \"\"\"\n\u001b[0;32m-> 1081\u001b[0;31m     \u001b[0;32mreturn\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_call_impl\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   1082\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1083\u001b[0m   \u001b[0;32mdef\u001b[0m \u001b[0m_call_impl\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mkwargs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mcancellation_manager\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mNone\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/.pyenv/versions/3.7.3/lib/python3.7/site-packages/tensorflow_core/python/eager/function.py\u001b[0m in \u001b[0;36m_call_impl\u001b[0;34m(self, args, kwargs, cancellation_manager)\u001b[0m\n\u001b[1;32m   1119\u001b[0m       raise TypeError(\"Keyword arguments {} unknown. Expected {}.\".format(\n\u001b[1;32m   1120\u001b[0m           list(kwargs.keys()), list(self._arg_keywords)))\n\u001b[0;32m-> 1121\u001b[0;31m     \u001b[0;32mreturn\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_call_flat\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcaptured_inputs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mcancellation_manager\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   1122\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1123\u001b[0m   \u001b[0;32mdef\u001b[0m \u001b[0m_filtered_call\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/.pyenv/versions/3.7.3/lib/python3.7/site-packages/tensorflow_core/python/eager/function.py\u001b[0m in \u001b[0;36m_call_flat\u001b[0;34m(self, args, captured_inputs, cancellation_manager)\u001b[0m\n\u001b[1;32m   1222\u001b[0m     \u001b[0;32mif\u001b[0m \u001b[0mexecuting_eagerly\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1223\u001b[0m       flat_outputs = forward_function.call(\n\u001b[0;32m-> 1224\u001b[0;31m           ctx, args, cancellation_manager=cancellation_manager)\n\u001b[0m\u001b[1;32m   1225\u001b[0m     \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1226\u001b[0m       \u001b[0mgradient_name\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_delayed_rewrite_functions\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mregister\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/.pyenv/versions/3.7.3/lib/python3.7/site-packages/tensorflow_core/python/eager/function.py\u001b[0m in \u001b[0;36mcall\u001b[0;34m(self, ctx, args, cancellation_manager)\u001b[0m\n\u001b[1;32m    509\u001b[0m               \u001b[0minputs\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    510\u001b[0m               \u001b[0mattrs\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"executor_type\"\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mexecutor_type\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m\"config_proto\"\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mconfig\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 511\u001b[0;31m               ctx=ctx)\n\u001b[0m\u001b[1;32m    512\u001b[0m         \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    513\u001b[0m           outputs = execute.execute_with_cancellation(\n",
      "\u001b[0;32m~/.pyenv/versions/3.7.3/lib/python3.7/site-packages/tensorflow_core/python/eager/execute.py\u001b[0m in \u001b[0;36mquick_execute\u001b[0;34m(op_name, num_outputs, inputs, attrs, ctx, name)\u001b[0m\n\u001b[1;32m     59\u001b[0m     tensors = pywrap_tensorflow.TFE_Py_Execute(ctx._handle, device_name,\n\u001b[1;32m     60\u001b[0m                                                \u001b[0mop_name\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0minputs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mattrs\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 61\u001b[0;31m                                                num_outputs)\n\u001b[0m\u001b[1;32m     62\u001b[0m   \u001b[0;32mexcept\u001b[0m \u001b[0mcore\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_NotOkStatusException\u001b[0m \u001b[0;32mas\u001b[0m \u001b[0me\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     63\u001b[0m     \u001b[0;32mif\u001b[0m \u001b[0mname\u001b[0m \u001b[0;32mis\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0;32mNone\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mKeyboardInterrupt\u001b[0m: "
     ]
    }
   ],
   "source": [
    "history2 = model.fit(\n",
    "    normed_train_data, \n",
    "    train_labels,\n",
    "    epochs=2_000, \n",
    "    validation_split = 0.2, \n",
    "    verbose=0,\n",
    "    callbacks=[PrintDot()]\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "ename": "NameError",
     "evalue": "name 'history2' is not defined",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mNameError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-38-06329efc019a>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mhist2\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mpd\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mDataFrame\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mhistory2\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mhistory\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      2\u001b[0m \u001b[0mhist2\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m'epoch'\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mhistory2\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mepoch\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      3\u001b[0m \u001b[0mhist2\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m'epoch'\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mhist2\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m'epoch'\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0mEPOCHS\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      4\u001b[0m \u001b[0mhist2\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mtail\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mNameError\u001b[0m: name 'history2' is not defined"
     ]
    }
   ],
   "source": [
    "hist2 = pd.DataFrame(history2.history)\n",
    "hist2['epoch'] = history2.epoch\n",
    "hist2['epoch'] = hist2['epoch'] + EPOCHS\n",
    "hist2.tail()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [],
   "source": [
    "combined_hist = pd.concat([hist, hist2])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_history(combined_hist)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Use a list comprehension to predict over each test instance 100 times.\n",
    "yhats = [model.predict(normed_test_data).flatten() for _ in range(100)]\n",
    "\n",
    "df = pd.DataFrame(yhats).T\n",
    "df['y'] = test_labels.values\n",
    "\n",
    "sample_preds = list(itertools.chain.from_iterable([[(j, x[-1]) for j in x if j != x[-1]] for x in df.values]))\n",
    "\n",
    "a = plt.axes(aspect='equal')\n",
    "plt.scatter([x[1] for x in sample_preds], [x[0] for x in sample_preds], alpha=0.1)\n",
    "plt.xlabel('True Values [MPG]')\n",
    "plt.ylabel('Predictions [MPG]')\n",
    "lims = [0, 50]\n",
    "plt.xlim(lims)\n",
    "plt.ylim(lims)\n",
    "_ = plt.plot(lims, lims)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "error = [x[0] - x[1] for x in sample_preds]\n",
    "plt.hist(error, bins = 25)\n",
    "plt.xlabel(\"Prediction Error [MPG]\")\n",
    "_ = plt.ylabel(\"Count\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Takeaways:\n",
    "- TensorFlow Probability offers a `layers` submodule with a selection of `tf.keras`-compatible neural network layers that are _probabilistic_.\n",
    "- These layers interoperate cleanly with existing neural network architectures (up to a point -- sometimes they need explicit priors or other arguments to be provided for them).\n",
    "- Probabilistic neural networks (those with probabilistic layers specifying distributions over their weights) are substantially less prone to overfitting than neural networks that merely fit point estimates.\n",
    "- The `predict` method on these models pulls a _random draw_ from the distributions that specify the weights of the model.\n",
    "- If we run many predictions, we draw a Monte Carlo sample from the model and obtain true estimates of its _uncertainty_."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The point on probabilistic neural networks being less prone to overfitting is a good one that's been explored in some depth. It's beyond the scope of this talk, but I refer the interested reader to _Gal & Ghahramani (2016)_, below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<iframe src=\"https://arxiv.org/pdf/1506.02142.pdf\" width=\"900\" height=\"1000\"></iframe>\n"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
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   ],
   "source": [
    "%%HTML\n",
    "<iframe src=\"https://arxiv.org/pdf/1506.02142.pdf\" width=\"900\" height=\"1000\"></iframe>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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