notebook/Stochastic Variational Inference (predict cancer mortality rate).ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "needed-aerospace",
   "metadata": {},
   "source": [
    "# Stochastic Variational Inference\n",
    "\n",
    "Implementation of Stochastic Variational Inference (SVI) using [PyTorch](https://pytorch.org/), for the purpose of uncertainty quantification.\n",
    "\n",
    "We'll consider the [OLS Regression Challenge](https://data.world/nrippner/ols-regression-challenge), which aims at predicting cancer mortality rates for US counties.\n",
    "\n",
    "## Data Dictionary\n",
    "\n",
    "* **TARGET_deathRate**: Dependent variable. Mean per capita (100,000) cancer mortalities (a)\n",
    "* **avgAnnCount**: Mean number of reported cases of cancer diagnosed annually (a)\n",
    "* **avgDeathsPerYear**: Mean number of reported mortalities due to cancer (a)\n",
    "* **incidenceRate**: Mean per capita (100,000) cancer diagoses (a)\n",
    "* **medianIncome**: Median income per county (b)\n",
    "* **popEst2015**: Population of county (b)\n",
    "* **povertyPercent**: Percent of populace in poverty (b)\n",
    "* **studyPerCap**: Per capita number of cancer-related clinical trials per county (a)\n",
    "* **binnedInc**: Median income per capita binned by decile (b)\n",
    "* **MedianAge**: Median age of county residents (b)\n",
    "* **MedianAgeMale**: Median age of male county residents (b)\n",
    "* **MedianAgeFemale**: Median age of female county residents (b)\n",
    "* **Geography**: County name (b)\n",
    "* **AvgHouseholdSize**: Mean household size of county (b)\n",
    "* **PercentMarried**: Percent of county residents who are married (b)\n",
    "* **PctNoHS18_24**: Percent of county residents ages 18-24 highest education attained: less than high school (b)\n",
    "* **PctHS18_24**: Percent of county residents ages 18-24 highest education attained: high school diploma (b)\n",
    "* **PctSomeCol18_24**: Percent of county residents ages 18-24 highest education attained: some college (b)\n",
    "* **PctBachDeg18_24**: Percent of county residents ages 18-24 highest education attained: bachelor's degree (b)\n",
    "* **PctHS25_Over**: Percent of county residents ages 25 and over highest education attained: high school diploma (b)\n",
    "* **PctBachDeg25_Over**: Percent of county residents ages 25 and over highest education attained: bachelor's degree (b)\n",
    "* **PctEmployed16_Over**: Percent of county residents ages 16 and over employed (b)\n",
    "* **PctUnemployed16_Over**: Percent of county residents ages 16 and over unemployed (b)\n",
    "* **PctPrivateCoverage**: Percent of county residents with private health coverage (b)\n",
    "* **PctPrivateCoverageAlone**: Percent of county residents with private health coverage alone (no public assistance) (b)\n",
    "* **PctEmpPrivCoverage**: Percent of county residents with employee-provided private health coverage (b)\n",
    "* **PctPublicCoverage**: Percent of county residents with government-provided health coverage (b)\n",
    "* **PctPubliceCoverageAlone**: Percent of county residents with government-provided health coverage alone (b)\n",
    "* **PctWhite**: Percent of county residents who identify as White (b)\n",
    "* **PctBlack**: Percent of county residents who identify as Black (b)\n",
    "* **PctAsian**: Percent of county residents who identify as Asian (b)\n",
    "* **PctOtherRace**: Percent of county residents who identify in a category which is not White, Black, or Asian (b)\n",
    "* **PctMarriedHouseholds**: Percent of married households (b)\n",
    "* **BirthRate**: Number of live births relative to number of women in county (b)\n",
    "\n",
    "Notes:\n",
    "* (a): years 2010-2016\n",
    "* (b): 2013 Census Estimates"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "alien-charger",
   "metadata": {},
   "outputs": [],
   "source": [
    "import os\n",
    "from os.path import join\n",
    "\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "import torch\n",
    "import torch.nn.functional as F\n",
    "from sklearn.metrics import r2_score\n",
    "from sklearn.model_selection import train_test_split\n",
    "from scipy.stats import binned_statistic\n",
    "\n",
    "cwd = os.getcwd()\n",
    "if cwd.endswith('notebook'):\n",
    "    os.chdir('..')\n",
    "    cwd = os.getcwd()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "physical-memphis",
   "metadata": {},
   "outputs": [],
   "source": [
    "sns.set(palette='colorblind', font_scale=1.3)\n",
    "palette = sns.color_palette()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "consolidated-person",
   "metadata": {},
   "outputs": [],
   "source": [
    "seed = 444\n",
    "np.random.seed(seed);\n",
    "torch.manual_seed(seed);\n",
    "torch.set_default_dtype(torch.float64)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "unexpected-enterprise",
   "metadata": {},
   "source": [
    "## Dataset\n",
    "\n",
    "### Load"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "elect-camera",
   "metadata": {},
   "outputs": [
    {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>avgAnnCount</th>\n",
       "      <th>avgDeathsPerYear</th>\n",
       "      <th>TARGET_deathRate</th>\n",
       "      <th>incidenceRate</th>\n",
       "      <th>medIncome</th>\n",
       "      <th>popEst2015</th>\n",
       "      <th>povertyPercent</th>\n",
       "      <th>studyPerCap</th>\n",
       "      <th>binnedInc</th>\n",
       "      <th>MedianAge</th>\n",
       "      <th>...</th>\n",
       "      <th>PctPrivateCoverageAlone</th>\n",
       "      <th>PctEmpPrivCoverage</th>\n",
       "      <th>PctPublicCoverage</th>\n",
       "      <th>PctPublicCoverageAlone</th>\n",
       "      <th>PctWhite</th>\n",
       "      <th>PctBlack</th>\n",
       "      <th>PctAsian</th>\n",
       "      <th>PctOtherRace</th>\n",
       "      <th>PctMarriedHouseholds</th>\n",
       "      <th>BirthRate</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1397.0</td>\n",
       "      <td>469</td>\n",
       "      <td>164.9</td>\n",
       "      <td>489.8</td>\n",
       "      <td>61898</td>\n",
       "      <td>260131</td>\n",
       "      <td>11.2</td>\n",
       "      <td>499.748204</td>\n",
       "      <td>(61494.5, 125635]</td>\n",
       "      <td>39.3</td>\n",
       "      <td>...</td>\n",
       "      <td>NaN</td>\n",
       "      <td>41.6</td>\n",
       "      <td>32.9</td>\n",
       "      <td>14.0</td>\n",
       "      <td>81.780529</td>\n",
       "      <td>2.594728</td>\n",
       "      <td>4.821857</td>\n",
       "      <td>1.843479</td>\n",
       "      <td>52.856076</td>\n",
       "      <td>6.118831</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>173.0</td>\n",
       "      <td>70</td>\n",
       "      <td>161.3</td>\n",
       "      <td>411.6</td>\n",
       "      <td>48127</td>\n",
       "      <td>43269</td>\n",
       "      <td>18.6</td>\n",
       "      <td>23.111234</td>\n",
       "      <td>(48021.6, 51046.4]</td>\n",
       "      <td>33.0</td>\n",
       "      <td>...</td>\n",
       "      <td>53.8</td>\n",
       "      <td>43.6</td>\n",
       "      <td>31.1</td>\n",
       "      <td>15.3</td>\n",
       "      <td>89.228509</td>\n",
       "      <td>0.969102</td>\n",
       "      <td>2.246233</td>\n",
       "      <td>3.741352</td>\n",
       "      <td>45.372500</td>\n",
       "      <td>4.333096</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>102.0</td>\n",
       "      <td>50</td>\n",
       "      <td>174.7</td>\n",
       "      <td>349.7</td>\n",
       "      <td>49348</td>\n",
       "      <td>21026</td>\n",
       "      <td>14.6</td>\n",
       "      <td>47.560164</td>\n",
       "      <td>(48021.6, 51046.4]</td>\n",
       "      <td>45.0</td>\n",
       "      <td>...</td>\n",
       "      <td>43.5</td>\n",
       "      <td>34.9</td>\n",
       "      <td>42.1</td>\n",
       "      <td>21.1</td>\n",
       "      <td>90.922190</td>\n",
       "      <td>0.739673</td>\n",
       "      <td>0.465898</td>\n",
       "      <td>2.747358</td>\n",
       "      <td>54.444868</td>\n",
       "      <td>3.729488</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>427.0</td>\n",
       "      <td>202</td>\n",
       "      <td>194.8</td>\n",
       "      <td>430.4</td>\n",
       "      <td>44243</td>\n",
       "      <td>75882</td>\n",
       "      <td>17.1</td>\n",
       "      <td>342.637253</td>\n",
       "      <td>(42724.4, 45201]</td>\n",
       "      <td>42.8</td>\n",
       "      <td>...</td>\n",
       "      <td>40.3</td>\n",
       "      <td>35.0</td>\n",
       "      <td>45.3</td>\n",
       "      <td>25.0</td>\n",
       "      <td>91.744686</td>\n",
       "      <td>0.782626</td>\n",
       "      <td>1.161359</td>\n",
       "      <td>1.362643</td>\n",
       "      <td>51.021514</td>\n",
       "      <td>4.603841</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>57.0</td>\n",
       "      <td>26</td>\n",
       "      <td>144.4</td>\n",
       "      <td>350.1</td>\n",
       "      <td>49955</td>\n",
       "      <td>10321</td>\n",
       "      <td>12.5</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>(48021.6, 51046.4]</td>\n",
       "      <td>48.3</td>\n",
       "      <td>...</td>\n",
       "      <td>43.9</td>\n",
       "      <td>35.1</td>\n",
       "      <td>44.0</td>\n",
       "      <td>22.7</td>\n",
       "      <td>94.104024</td>\n",
       "      <td>0.270192</td>\n",
       "      <td>0.665830</td>\n",
       "      <td>0.492135</td>\n",
       "      <td>54.027460</td>\n",
       "      <td>6.796657</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5 rows × 34 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "   avgAnnCount  avgDeathsPerYear  TARGET_deathRate  incidenceRate  medIncome  \\\n",
       "0       1397.0               469             164.9          489.8      61898   \n",
       "1        173.0                70             161.3          411.6      48127   \n",
       "2        102.0                50             174.7          349.7      49348   \n",
       "3        427.0               202             194.8          430.4      44243   \n",
       "4         57.0                26             144.4          350.1      49955   \n",
       "\n",
       "   popEst2015  povertyPercent  studyPerCap           binnedInc  MedianAge  \\\n",
       "0      260131            11.2   499.748204   (61494.5, 125635]       39.3   \n",
       "1       43269            18.6    23.111234  (48021.6, 51046.4]       33.0   \n",
       "2       21026            14.6    47.560164  (48021.6, 51046.4]       45.0   \n",
       "3       75882            17.1   342.637253    (42724.4, 45201]       42.8   \n",
       "4       10321            12.5     0.000000  (48021.6, 51046.4]       48.3   \n",
       "\n",
       "   ...  PctPrivateCoverageAlone  PctEmpPrivCoverage PctPublicCoverage  \\\n",
       "0  ...                      NaN                41.6              32.9   \n",
       "1  ...                     53.8                43.6              31.1   \n",
       "2  ...                     43.5                34.9              42.1   \n",
       "3  ...                     40.3                35.0              45.3   \n",
       "4  ...                     43.9                35.1              44.0   \n",
       "\n",
       "   PctPublicCoverageAlone   PctWhite  PctBlack  PctAsian  PctOtherRace  \\\n",
       "0                    14.0  81.780529  2.594728  4.821857      1.843479   \n",
       "1                    15.3  89.228509  0.969102  2.246233      3.741352   \n",
       "2                    21.1  90.922190  0.739673  0.465898      2.747358   \n",
       "3                    25.0  91.744686  0.782626  1.161359      1.362643   \n",
       "4                    22.7  94.104024  0.270192  0.665830      0.492135   \n",
       "\n",
       "   PctMarriedHouseholds  BirthRate  \n",
       "0             52.856076   6.118831  \n",
       "1             45.372500   4.333096  \n",
       "2             54.444868   3.729488  \n",
       "3             51.021514   4.603841  \n",
       "4             54.027460   6.796657  \n",
       "\n",
       "[5 rows x 34 columns]"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = pd.read_csv(join(cwd, 'data/cancer_reg.csv'))\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "difficult-fighter",
   "metadata": {},
   "source": [
    "### Describe"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "changed-princess",
   "metadata": {},
   "outputs": [
    {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>avgAnnCount</th>\n",
       "      <th>avgDeathsPerYear</th>\n",
       "      <th>TARGET_deathRate</th>\n",
       "      <th>incidenceRate</th>\n",
       "      <th>medIncome</th>\n",
       "      <th>popEst2015</th>\n",
       "      <th>povertyPercent</th>\n",
       "      <th>studyPerCap</th>\n",
       "      <th>MedianAge</th>\n",
       "      <th>MedianAgeMale</th>\n",
       "      <th>...</th>\n",
       "      <th>PctPrivateCoverageAlone</th>\n",
       "      <th>PctEmpPrivCoverage</th>\n",
       "      <th>PctPublicCoverage</th>\n",
       "      <th>PctPublicCoverageAlone</th>\n",
       "      <th>PctWhite</th>\n",
       "      <th>PctBlack</th>\n",
       "      <th>PctAsian</th>\n",
       "      <th>PctOtherRace</th>\n",
       "      <th>PctMarriedHouseholds</th>\n",
       "      <th>BirthRate</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>3047.000000</td>\n",
       "      <td>3047.000000</td>\n",
       "      <td>3047.000000</td>\n",
       "      <td>3047.000000</td>\n",
       "      <td>3047.000000</td>\n",
       "      <td>3.047000e+03</td>\n",
       "      <td>3047.000000</td>\n",
       "      <td>3047.000000</td>\n",
       "      <td>3047.000000</td>\n",
       "      <td>3047.000000</td>\n",
       "      <td>...</td>\n",
       "      <td>2438.000000</td>\n",
       "      <td>3047.000000</td>\n",
       "      <td>3047.000000</td>\n",
       "      <td>3047.000000</td>\n",
       "      <td>3047.000000</td>\n",
       "      <td>3047.000000</td>\n",
       "      <td>3047.000000</td>\n",
       "      <td>3047.000000</td>\n",
       "      <td>3047.000000</td>\n",
       "      <td>3047.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>606.338544</td>\n",
       "      <td>185.965868</td>\n",
       "      <td>178.664063</td>\n",
       "      <td>448.268586</td>\n",
       "      <td>47063.281917</td>\n",
       "      <td>1.026374e+05</td>\n",
       "      <td>16.878175</td>\n",
       "      <td>155.399415</td>\n",
       "      <td>45.272333</td>\n",
       "      <td>39.570725</td>\n",
       "      <td>...</td>\n",
       "      <td>48.453774</td>\n",
       "      <td>41.196324</td>\n",
       "      <td>36.252642</td>\n",
       "      <td>19.240072</td>\n",
       "      <td>83.645286</td>\n",
       "      <td>9.107978</td>\n",
       "      <td>1.253965</td>\n",
       "      <td>1.983523</td>\n",
       "      <td>51.243872</td>\n",
       "      <td>5.640306</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>1416.356223</td>\n",
       "      <td>504.134286</td>\n",
       "      <td>27.751511</td>\n",
       "      <td>54.560733</td>\n",
       "      <td>12040.090836</td>\n",
       "      <td>3.290592e+05</td>\n",
       "      <td>6.409087</td>\n",
       "      <td>529.628366</td>\n",
       "      <td>45.304480</td>\n",
       "      <td>5.226017</td>\n",
       "      <td>...</td>\n",
       "      <td>10.083006</td>\n",
       "      <td>9.447687</td>\n",
       "      <td>7.841741</td>\n",
       "      <td>6.113041</td>\n",
       "      <td>16.380025</td>\n",
       "      <td>14.534538</td>\n",
       "      <td>2.610276</td>\n",
       "      <td>3.517710</td>\n",
       "      <td>6.572814</td>\n",
       "      <td>1.985816</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>6.000000</td>\n",
       "      <td>3.000000</td>\n",
       "      <td>59.700000</td>\n",
       "      <td>201.300000</td>\n",
       "      <td>22640.000000</td>\n",
       "      <td>8.270000e+02</td>\n",
       "      <td>3.200000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>22.300000</td>\n",
       "      <td>22.400000</td>\n",
       "      <td>...</td>\n",
       "      <td>15.700000</td>\n",
       "      <td>13.500000</td>\n",
       "      <td>11.200000</td>\n",
       "      <td>2.600000</td>\n",
       "      <td>10.199155</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>22.992490</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>76.000000</td>\n",
       "      <td>28.000000</td>\n",
       "      <td>161.200000</td>\n",
       "      <td>420.300000</td>\n",
       "      <td>38882.500000</td>\n",
       "      <td>1.168400e+04</td>\n",
       "      <td>12.150000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>37.700000</td>\n",
       "      <td>36.350000</td>\n",
       "      <td>...</td>\n",
       "      <td>41.000000</td>\n",
       "      <td>34.500000</td>\n",
       "      <td>30.900000</td>\n",
       "      <td>14.850000</td>\n",
       "      <td>77.296180</td>\n",
       "      <td>0.620675</td>\n",
       "      <td>0.254199</td>\n",
       "      <td>0.295172</td>\n",
       "      <td>47.763063</td>\n",
       "      <td>4.521419</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>171.000000</td>\n",
       "      <td>61.000000</td>\n",
       "      <td>178.100000</td>\n",
       "      <td>453.549422</td>\n",
       "      <td>45207.000000</td>\n",
       "      <td>2.664300e+04</td>\n",
       "      <td>15.900000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>41.000000</td>\n",
       "      <td>39.600000</td>\n",
       "      <td>...</td>\n",
       "      <td>48.700000</td>\n",
       "      <td>41.100000</td>\n",
       "      <td>36.300000</td>\n",
       "      <td>18.800000</td>\n",
       "      <td>90.059774</td>\n",
       "      <td>2.247576</td>\n",
       "      <td>0.549812</td>\n",
       "      <td>0.826185</td>\n",
       "      <td>51.669941</td>\n",
       "      <td>5.381478</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>518.000000</td>\n",
       "      <td>149.000000</td>\n",
       "      <td>195.200000</td>\n",
       "      <td>480.850000</td>\n",
       "      <td>52492.000000</td>\n",
       "      <td>6.867100e+04</td>\n",
       "      <td>20.400000</td>\n",
       "      <td>83.650776</td>\n",
       "      <td>44.000000</td>\n",
       "      <td>42.500000</td>\n",
       "      <td>...</td>\n",
       "      <td>55.600000</td>\n",
       "      <td>47.700000</td>\n",
       "      <td>41.550000</td>\n",
       "      <td>23.100000</td>\n",
       "      <td>95.451693</td>\n",
       "      <td>10.509732</td>\n",
       "      <td>1.221037</td>\n",
       "      <td>2.177960</td>\n",
       "      <td>55.395132</td>\n",
       "      <td>6.493677</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>38150.000000</td>\n",
       "      <td>14010.000000</td>\n",
       "      <td>362.800000</td>\n",
       "      <td>1206.900000</td>\n",
       "      <td>125635.000000</td>\n",
       "      <td>1.017029e+07</td>\n",
       "      <td>47.400000</td>\n",
       "      <td>9762.308998</td>\n",
       "      <td>624.000000</td>\n",
       "      <td>64.700000</td>\n",
       "      <td>...</td>\n",
       "      <td>78.900000</td>\n",
       "      <td>70.700000</td>\n",
       "      <td>65.100000</td>\n",
       "      <td>46.600000</td>\n",
       "      <td>100.000000</td>\n",
       "      <td>85.947799</td>\n",
       "      <td>42.619425</td>\n",
       "      <td>41.930251</td>\n",
       "      <td>78.075397</td>\n",
       "      <td>21.326165</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>8 rows × 32 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "        avgAnnCount  avgDeathsPerYear  TARGET_deathRate  incidenceRate  \\\n",
       "count   3047.000000       3047.000000       3047.000000    3047.000000   \n",
       "mean     606.338544        185.965868        178.664063     448.268586   \n",
       "std     1416.356223        504.134286         27.751511      54.560733   \n",
       "min        6.000000          3.000000         59.700000     201.300000   \n",
       "25%       76.000000         28.000000        161.200000     420.300000   \n",
       "50%      171.000000         61.000000        178.100000     453.549422   \n",
       "75%      518.000000        149.000000        195.200000     480.850000   \n",
       "max    38150.000000      14010.000000        362.800000    1206.900000   \n",
       "\n",
       "           medIncome    popEst2015  povertyPercent  studyPerCap    MedianAge  \\\n",
       "count    3047.000000  3.047000e+03     3047.000000  3047.000000  3047.000000   \n",
       "mean    47063.281917  1.026374e+05       16.878175   155.399415    45.272333   \n",
       "std     12040.090836  3.290592e+05        6.409087   529.628366    45.304480   \n",
       "min     22640.000000  8.270000e+02        3.200000     0.000000    22.300000   \n",
       "25%     38882.500000  1.168400e+04       12.150000     0.000000    37.700000   \n",
       "50%     45207.000000  2.664300e+04       15.900000     0.000000    41.000000   \n",
       "75%     52492.000000  6.867100e+04       20.400000    83.650776    44.000000   \n",
       "max    125635.000000  1.017029e+07       47.400000  9762.308998   624.000000   \n",
       "\n",
       "       MedianAgeMale  ...  PctPrivateCoverageAlone  PctEmpPrivCoverage  \\\n",
       "count    3047.000000  ...              2438.000000         3047.000000   \n",
       "mean       39.570725  ...                48.453774           41.196324   \n",
       "std         5.226017  ...                10.083006            9.447687   \n",
       "min        22.400000  ...                15.700000           13.500000   \n",
       "25%        36.350000  ...                41.000000           34.500000   \n",
       "50%        39.600000  ...                48.700000           41.100000   \n",
       "75%        42.500000  ...                55.600000           47.700000   \n",
       "max        64.700000  ...                78.900000           70.700000   \n",
       "\n",
       "       PctPublicCoverage  PctPublicCoverageAlone     PctWhite     PctBlack  \\\n",
       "count        3047.000000             3047.000000  3047.000000  3047.000000   \n",
       "mean           36.252642               19.240072    83.645286     9.107978   \n",
       "std             7.841741                6.113041    16.380025    14.534538   \n",
       "min            11.200000                2.600000    10.199155     0.000000   \n",
       "25%            30.900000               14.850000    77.296180     0.620675   \n",
       "50%            36.300000               18.800000    90.059774     2.247576   \n",
       "75%            41.550000               23.100000    95.451693    10.509732   \n",
       "max            65.100000               46.600000   100.000000    85.947799   \n",
       "\n",
       "          PctAsian  PctOtherRace  PctMarriedHouseholds    BirthRate  \n",
       "count  3047.000000   3047.000000           3047.000000  3047.000000  \n",
       "mean      1.253965      1.983523             51.243872     5.640306  \n",
       "std       2.610276      3.517710              6.572814     1.985816  \n",
       "min       0.000000      0.000000             22.992490     0.000000  \n",
       "25%       0.254199      0.295172             47.763063     4.521419  \n",
       "50%       0.549812      0.826185             51.669941     5.381478  \n",
       "75%       1.221037      2.177960             55.395132     6.493677  \n",
       "max      42.619425     41.930251             78.075397    21.326165  \n",
       "\n",
       "[8 rows x 32 columns]"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.describe()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "adjustable-premises",
   "metadata": {},
   "source": [
    "### Plot distribution of target variable"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "academic-lincoln",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "_, ax = plt.subplots(1, 1, figsize=(10, 5))\n",
    "df['TARGET_deathRate'].hist(bins=50, ax=ax);\n",
    "ax.set_title('Distribution of cancer death rate per 100,000 people');\n",
    "ax.set_xlabel('Cancer death rate in county (per 100,000 people)');\n",
    "ax.set_ylabel('Count');"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "clear-printing",
   "metadata": {},
   "source": [
    "### Define feature & target variables"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "certain-clearing",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "28 features\n"
     ]
    }
   ],
   "source": [
    "target = 'TARGET_deathRate'\n",
    "features = [\n",
    "    col for col in df.columns\n",
    "    if col not in [\n",
    "        target, \n",
    "        'Geography',                # Label describing the county - each row has a different one\n",
    "        'binnedInc',                # Redundant with median income?\n",
    "        'PctSomeCol18_24',          # contains null values - ignoring for now\n",
    "        'PctEmployed16_Over',       # contains null values - ignoring for now\n",
    "        'PctPrivateCoverageAlone',  # contains null values - ignoring for now\n",
    "    ]\n",
    "]\n",
    "print(len(features), 'features')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "normal-newsletter",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(3047, 28) (3047, 1)\n"
     ]
    }
   ],
   "source": [
    "x = df[features].values\n",
    "y = df[[target]].values\n",
    "print(x.shape, y.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "parliamentary-festival",
   "metadata": {},
   "source": [
    "## Define model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "aboriginal-worker",
   "metadata": {},
   "outputs": [],
   "source": [
    "class VariationalModel(torch.nn.Module):\n",
    "    def __init__(\n",
    "        self, \n",
    "        n_inputs,\n",
    "        n_hidden,\n",
    "        priors,\n",
    "        x_scaler, \n",
    "        y_scaler,\n",
    "        n_shared_layers=1,\n",
    "    ):\n",
    "        super().__init__()\n",
    "        \n",
    "        self.priors = priors\n",
    "        self.x_scaler = x_scaler\n",
    "        self.y_scaler = y_scaler\n",
    "        self.jitter = 1e-6\n",
    "        \n",
    "        # Shared layers\n",
    "        self.shared_layers = [\n",
    "            torch.nn.Linear(n_inputs, n_hidden)\n",
    "        ]\n",
    "        if n_shared_layers > 1:\n",
    "            for _ in range(n_shared_layers - 1):\n",
    "                self.shared_layers.append(\n",
    "                    torch.nn.Linear(n_hidden, n_hidden)\n",
    "                )\n",
    "        \n",
    "        # Parameters for the mean \n",
    "        self.mean_loc_hidden = torch.nn.Linear(n_hidden, n_hidden)\n",
    "        self.mean_loc = torch.nn.Linear(n_hidden, 1)\n",
    "        self.mean_scale_hidden = torch.nn.Linear(n_hidden, n_hidden)\n",
    "        self.mean_scale = torch.nn.Linear(n_hidden, 1)\n",
    "        \n",
    "        # Parameters for the standard deviation\n",
    "        self.std_loc_hidden = torch.nn.Linear(n_hidden, n_hidden)\n",
    "        self.std_loc = torch.nn.Linear(n_hidden, 1)\n",
    "        self.std_scale_hidden = torch.nn.Linear(n_hidden, n_hidden)\n",
    "        self.std_scale = torch.nn.Linear(n_hidden, 1)\n",
    "        \n",
    "    def encoder(self, x):\n",
    "        shared = self.x_scaler(x)\n",
    "        \n",
    "        for layer in self.shared_layers:\n",
    "            shared = layer(shared)\n",
    "            shared = F.relu(shared)\n",
    "            #shared = self.dropout(shared)\n",
    "        \n",
    "        # Parametrization of the mean (normal)\n",
    "        mean_loc = self.mean_loc_hidden(shared)\n",
    "        mean_loc = F.relu(mean_loc)\n",
    "        mean_loc = self.mean_loc(mean_loc)\n",
    "        \n",
    "        mean_scale = self.mean_scale_hidden(shared)\n",
    "        mean_scale = F.relu(mean_scale)\n",
    "        mean_scale = F.softplus(self.mean_scale(mean_scale)) + self.jitter\n",
    "        \n",
    "        # Parametrization of the standard deviation (log normal)\n",
    "        std_loc = self.std_loc_hidden(shared)\n",
    "        std_loc = F.relu(std_loc)\n",
    "        std_loc = self.std_loc(std_loc)\n",
    "        \n",
    "        std_scale = self.std_scale_hidden(shared)\n",
    "        std_scale = F.relu(std_scale)\n",
    "        std_scale = F.softplus(self.std_scale(std_scale)) + self.jitter    \n",
    "        \n",
    "        return (\n",
    "            torch.distributions.Normal(mean_loc, mean_scale),\n",
    "            torch.distributions.LogNormal(std_loc, std_scale)\n",
    "        )\n",
    "    \n",
    "    def decoder(self, mean, std):\n",
    "        return torch.distributions.Normal(mean, std)\n",
    "    \n",
    "    def forward(self, x, sample_shape=torch.Size([])):\n",
    "        mean_dist, std_dist = self.encoder(x)\n",
    "        \n",
    "        mean = mean_dist.rsample(sample_shape)\n",
    "        std = std_dist.rsample(sample_shape) + self.jitter\n",
    "        \n",
    "        y_hat = self.decoder(mean, std)\n",
    "        \n",
    "        kl_divergence = None\n",
    "        if self.priors is not None:\n",
    "            kl_divergence1 = torch.distributions.kl.kl_divergence(mean_dist, self.priors[0])\n",
    "            kl_divergence2 = torch.distributions.kl.kl_divergence(std_dist, self.priors[1])\n",
    "            kl_divergence = kl_divergence1 + kl_divergence2\n",
    "            \n",
    "        return y_hat, kl_divergence\n",
    "\n",
    "\n",
    "def compute_loss(model, x, y, kl_reg=0.1):\n",
    "    \"\"\"\n",
    "    ELBO loss - https://en.wikipedia.org/wiki/Evidence_lower_bound\n",
    "    \"\"\"\n",
    "    y_scaled = model.y_scaler(y)\n",
    "    \n",
    "    y_hat, kl_divergence = model(x)\n",
    "    \n",
    "    neg_log_likelihood = -y_hat.log_prob(y_scaled)\n",
    "    \n",
    "    if kl_divergence is not None:\n",
    "        neg_log_likelihood += kl_reg * kl_divergence\n",
    "\n",
    "    return torch.mean(neg_log_likelihood)\n",
    "\n",
    "\n",
    "def compute_rmse(model, x_test, y_test):\n",
    "    model.eval()\n",
    "    y_hat, _ = model(x_test)\n",
    "    pred = model.y_scaler.inverse_transform(y_hat.mean)\n",
    "    return torch.sqrt(torch.mean((pred - y_test)**2))\n",
    "\n",
    "\n",
    "def train_one_step(model, optimizer, x_batch, y_batch):\n",
    "    model.train()\n",
    "    optimizer.zero_grad()\n",
    "    loss = compute_loss(model, x_batch, y_batch)\n",
    "    loss.backward()\n",
    "    optimizer.step()\n",
    "    return loss"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "tribal-trainer",
   "metadata": {},
   "outputs": [],
   "source": [
    "def train(model, optimizer, x_train, x_val, y_train, y_val, n_epochs, batch_size, scheduler=None, print_every=10):\n",
    "    train_losses, val_losses = [], []\n",
    "    for epoch in range(n_epochs):\n",
    "        batch_indices = sample_batch_indices(x_train, y_train, batch_size)\n",
    "        \n",
    "        batch_losses_t, batch_losses_v, batch_rmse_v = [], [], []\n",
    "        for batch_ix in batch_indices:\n",
    "            b_train_loss = train_one_step(model, optimizer, x_train[batch_ix], y_train[batch_ix])\n",
    "\n",
    "            model.eval()\n",
    "            b_val_loss = compute_loss(model, x_val, y_val)\n",
    "            b_val_rmse = compute_rmse(model, x_val, y_val)\n",
    "\n",
    "            batch_losses_t.append(b_train_loss.detach().numpy())\n",
    "            batch_losses_v.append(b_val_loss.detach().numpy())\n",
    "            batch_rmse_v.append(b_val_rmse.detach().numpy())\n",
    "            \n",
    "        if scheduler is not None:\n",
    "            scheduler.step()\n",
    "            \n",
    "        train_loss = np.mean(batch_losses_t)\n",
    "        val_loss = np.mean(batch_losses_v)\n",
    "        val_rmse = np.mean(batch_rmse_v)\n",
    "        \n",
    "        train_losses.append(train_loss)\n",
    "        val_losses.append(val_loss)\n",
    "\n",
    "        if epoch == 0 or (epoch + 1) % print_every == 0:\n",
    "            print(f'Epoch {epoch+1} | Validation loss = {val_loss:.4f} | Validation RMSE = {val_rmse:.4f}')\n",
    "        \n",
    "    _, ax = plt.subplots(1, 1, figsize=(12, 6))\n",
    "    ax.plot(range(1, n_epochs + 1), train_losses, label='Train loss')\n",
    "    ax.plot(range(1, n_epochs + 1), val_losses, label='Validation loss')\n",
    "    ax.set_xlabel('Epoch')\n",
    "    ax.set_ylabel('Loss')\n",
    "    ax.set_title('Training Overview')\n",
    "    ax.legend()\n",
    "    \n",
    "    return train_losses, val_losses\n",
    "\n",
    "\n",
    "def sample_batch_indices(x, y, batch_size, rs=None):\n",
    "    if rs is None:\n",
    "        rs = np.random.RandomState()\n",
    "    \n",
    "    train_ix = np.arange(len(x))\n",
    "    rs.shuffle(train_ix)\n",
    "    \n",
    "    n_batches = int(np.ceil(len(x) / batch_size))\n",
    "    \n",
    "    batch_indices = []\n",
    "    for i in range(n_batches):\n",
    "        start = i + batch_size\n",
    "        end = start + batch_size\n",
    "        batch_indices.append(\n",
    "            train_ix[start:end].tolist()\n",
    "        )\n",
    "\n",
    "    return batch_indices"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "right-county",
   "metadata": {},
   "outputs": [],
   "source": [
    "class StandardScaler(object):\n",
    "    \"\"\"\n",
    "    Standardize data by removing the mean and scaling to unit variance.\n",
    "    \"\"\"\n",
    "    def __init__(self):\n",
    "        self.mean = None\n",
    "        self.scale = None\n",
    "\n",
    "    def fit(self, sample):\n",
    "        self.mean = sample.mean(0, keepdim=True)\n",
    "        self.scale = sample.std(0, unbiased=False, keepdim=True)\n",
    "        return self\n",
    "\n",
    "    def __call__(self, sample):\n",
    "        return self.transform(sample)\n",
    "    \n",
    "    def transform(self, sample):\n",
    "        return (sample - self.mean) / self.scale\n",
    "\n",
    "    def inverse_transform(self, sample):\n",
    "        return sample * self.scale + self.mean"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "soviet-senegal",
   "metadata": {},
   "source": [
    "## Split between training and validation sets"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "fresh-gazette",
   "metadata": {},
   "outputs": [],
   "source": [
    "def compute_train_test_split(x, y, test_size):\n",
    "    x_train, x_test, y_train, y_test = train_test_split(x, y, test_size=test_size)\n",
    "    return (\n",
    "        torch.from_numpy(x_train),\n",
    "        torch.from_numpy(x_test),\n",
    "        torch.from_numpy(y_train),\n",
    "        torch.from_numpy(y_test),\n",
    "    )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "defensive-affairs",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "torch.Size([2437, 28]) torch.Size([2437, 1])\n",
      "torch.Size([610, 28]) torch.Size([610, 1])\n"
     ]
    }
   ],
   "source": [
    "x_train, x_val, y_train, y_val = compute_train_test_split(x, y, test_size=0.2)\n",
    "\n",
    "print(x_train.shape, y_train.shape)\n",
    "print(x_val.shape, y_val.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "second-clause",
   "metadata": {},
   "source": [
    "## Train model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "square-municipality",
   "metadata": {},
   "outputs": [],
   "source": [
    "x_scaler = StandardScaler().fit(torch.from_numpy(x))\n",
    "y_scaler = StandardScaler().fit(torch.from_numpy(y))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "fitted-participant",
   "metadata": {},
   "outputs": [],
   "source": [
    "def lr_steep_schedule(epoch):\n",
    "    threshold = 5\n",
    "    if epoch < threshold:\n",
    "        return 1.0\n",
    "    \n",
    "    multiplier = 2 / 10\n",
    "    step_change = (epoch - threshold) // 300\n",
    "    \n",
    "    return multiplier * 0.5 ** (step_change)\n",
    "\n",
    "\n",
    "def lr_simple_schedule(epoch):\n",
    "    return 0.5 ** (epoch // 200)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "changing-campaign",
   "metadata": {},
   "outputs": [],
   "source": [
    "def make_priors(y_train, y_scaler):\n",
    "    std = torch.Tensor((0.5,))\n",
    "    scale = torch.Tensor((0.2,))\n",
    "    \n",
    "    std_loc = torch.log(std**2 / torch.sqrt(std**2 + scale**2))\n",
    "    std_scale = torch.sqrt(torch.log(1 + scale**2 / std**2))\n",
    "    \n",
    "    return [\n",
    "        torch.distributions.Normal(0, 1),\n",
    "        torch.distributions.LogNormal(std_loc, std_scale),\n",
    "    ]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "brutal-script",
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "40,804 trainable parameters\n",
      "\n",
      "Epoch 1 | Validation loss = 2.1251 | Validation RMSE = 31.5151\n",
      "Epoch 50 | Validation loss = 1.3677 | Validation RMSE = 20.3201\n",
      "Epoch 100 | Validation loss = 1.2999 | Validation RMSE = 19.8506\n",
      "Epoch 150 | Validation loss = 1.2854 | Validation RMSE = 19.5741\n",
      "Epoch 200 | Validation loss = 1.2695 | Validation RMSE = 19.4597\n",
      "Epoch 250 | Validation loss = 1.2747 | Validation RMSE = 19.3205\n",
      "Epoch 300 | Validation loss = 1.3003 | Validation RMSE = 19.5134\n",
      "Epoch 350 | Validation loss = 1.2617 | Validation RMSE = 19.0837\n",
      "Epoch 400 | Validation loss = 1.2400 | Validation RMSE = 18.8530\n",
      "Epoch 450 | Validation loss = 1.2662 | Validation RMSE = 18.9906\n",
      "Epoch 500 | Validation loss = 1.2509 | Validation RMSE = 18.9645\n",
      "Epoch 550 | Validation loss = 1.2512 | Validation RMSE = 18.8079\n",
      "Epoch 600 | Validation loss = 1.2602 | Validation RMSE = 18.9772\n",
      "Epoch 650 | Validation loss = 1.2475 | Validation RMSE = 18.8599\n",
      "Epoch 700 | Validation loss = 1.2661 | Validation RMSE = 18.8974\n",
      "CPU times: user 3min 55s, sys: 41.4 s, total: 4min 37s\n",
      "Wall time: 4min 20s\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%%time\n",
    "\n",
    "learning_rate = 1e-3\n",
    "momentum = 0.9\n",
    "weight_decay = 1e-4\n",
    "\n",
    "n_epochs = 700\n",
    "batch_size = 64\n",
    "print_every = 50\n",
    "\n",
    "n_hidden = 100\n",
    "n_shared_layers = 1\n",
    "\n",
    "priors = make_priors(y_train, y_scaler)\n",
    "\n",
    "model = VariationalModel(\n",
    "    n_inputs=x.shape[1],\n",
    "    n_hidden=n_hidden,\n",
    "    priors=priors,\n",
    "    n_shared_layers=n_shared_layers,\n",
    "    x_scaler=x_scaler, \n",
    "    y_scaler=y_scaler,\n",
    ")\n",
    "\n",
    "pytorch_total_params = sum(p.numel() for p in model.parameters() if p.requires_grad)\n",
    "print(f'{pytorch_total_params:,} trainable parameters')\n",
    "print()\n",
    "\n",
    "optimizer = torch.optim.SGD(\n",
    "    model.parameters(), \n",
    "    lr=learning_rate, \n",
    "    momentum=momentum, \n",
    "    nesterov=True,\n",
    "    weight_decay=weight_decay,\n",
    ")\n",
    "scheduler = torch.optim.lr_scheduler.LambdaLR(\n",
    "    optimizer, \n",
    "    lr_lambda=lr_steep_schedule,\n",
    ")\n",
    "\n",
    "train_losses, val_losses = train(\n",
    "    model, \n",
    "    optimizer, \n",
    "    x_train, \n",
    "    x_val, \n",
    "    y_train, \n",
    "    y_val, \n",
    "    n_epochs=n_epochs, \n",
    "    batch_size=batch_size, \n",
    "    scheduler=scheduler, \n",
    "    print_every=print_every,\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "involved-korean",
   "metadata": {},
   "source": [
    "### Validation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "legitimate-microphone",
   "metadata": {},
   "outputs": [],
   "source": [
    "y_dist, _ = model(x_val)\n",
    "y_hat = model.y_scaler.inverse_transform(y_dist.mean)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "monthly-andrew",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Validation RMSE = 18.59\n"
     ]
    }
   ],
   "source": [
    "val_rmse = float(compute_rmse(model, x_val, y_val).detach().numpy())\n",
    "print(f'Validation RMSE = {val_rmse:.2f}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "religious-feeding",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Validation $R^2$ = 0.53\n"
     ]
    }
   ],
   "source": [
    "val_r2 = r2_score(\n",
    "    y_val.detach().numpy().flatten(),\n",
    "    y_hat.detach().numpy().flatten(),\n",
    ")\n",
    "print(f'Validation $R^2$ = {val_r2:.2f}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "starting-daily",
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_results(y_true, y_pred):\n",
    "    _, ax = plt.subplots(1, 1, figsize=(7, 7))\n",
    "    palette = sns.color_palette()\n",
    "    \n",
    "    min_value = min(np.amin(y_true), np.amin(y_pred))\n",
    "    max_value = max(np.amax(y_true), np.amax(y_pred))\n",
    "    y_mid = np.linspace(min_value, max_value)\n",
    "    \n",
    "    ax.plot(y_mid, y_mid, '--', color=palette[1])\n",
    "    ax.scatter(y_true, y_pred, color=palette[0], alpha=0.5);\n",
    "    \n",
    "    return ax"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "experimental-exhibit",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x504 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ax = plot_results(\n",
    "    y_val.detach().numpy().flatten(),\n",
    "    y_hat.detach().numpy().flatten(),\n",
    ");\n",
    "\n",
    "ax.text(270, 120, f'$R^2 = {val_r2:.2f}$')\n",
    "ax.text(270, 100, f'$RMSE = {val_rmse:.2f}$')\n",
    "    \n",
    "ax.set_xlabel('Actuals');\n",
    "ax.set_ylabel('Predictions');\n",
    "ax.set_title('Regression results on validation set');"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "returning-concept",
   "metadata": {},
   "source": [
    "## Uncertainty"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "accomplished-monday",
   "metadata": {},
   "outputs": [],
   "source": [
    "def make_predictions(model, x):\n",
    "    mean_dist, std_dist = model.encoder(x)\n",
    "    \n",
    "    inv_tr = model.y_scaler.inverse_transform\n",
    "    \n",
    "    y_hat = inv_tr(mean_dist.mean)\n",
    "    \n",
    "    # Recover standard deviation's original scale\n",
    "    std_from_mean_dist = inv_tr(mean_dist.mean + mean_dist.stddev) - y_hat\n",
    "    std_from_std_dist = inv_tr(mean_dist.mean + std_dist.mean + std_dist.stddev) - y_hat\n",
    "    \n",
    "    return y_hat, std_from_mean_dist, std_from_std_dist"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "harmful-referral",
   "metadata": {},
   "outputs": [],
   "source": [
    "y_hat, std_from_mean_dist , std_from_std_dist = make_predictions(model, x_val)\n",
    "std = std_from_mean_dist + std_from_std_dist"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "difficult-finnish",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(y_hat.detach().numpy().flatten(), bins=50);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "incomplete-adobe",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(std_from_mean_dist.detach().numpy().flatten(), bins=50);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "successful-cartridge",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(std_from_std_dist.detach().numpy().flatten(), bins=50);"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "sublime-child",
   "metadata": {},
   "source": [
    "### Plot absolute error against uncertainty"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "id": "pursuant-farming",
   "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>error</th>\n",
       "      <th>uncertainty</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>error</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.314829</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>uncertainty</th>\n",
       "      <td>0.314829</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                error  uncertainty\n",
       "error        1.000000     0.314829\n",
       "uncertainty  0.314829     1.000000"
      ]
     },
     "execution_count": 71,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "absolute_errors = torch.abs(y_hat - y_val).detach().numpy().flatten()\n",
    "stds = std.detach().numpy().flatten()\n",
    "\n",
    "df = pd.DataFrame.from_dict({\n",
    "    'error': absolute_errors,\n",
    "    'uncertainty': stds\n",
    "})\n",
    "df.corr()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "id": "satisfied-kruger",
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_absolute_error_vs_uncertainty(y_val, y_hat, std, binned):\n",
    "    absolute_errors = torch.abs(y_hat - y_val).detach().numpy().flatten()\n",
    "    stds = std.detach().numpy().flatten()\n",
    "    \n",
    "    \n",
    "    if binned:\n",
    "        ret = binned_statistic(absolute_errors, stds, bins=100)\n",
    "        a = ret.bin_edges[1:]\n",
    "        b = ret.statistic\n",
    "        alpha = 1.0\n",
    "    else:\n",
    "        a = absolute_errors\n",
    "        b = stds\n",
    "        alpha = 0.3\n",
    "    \n",
    "    _, ax = plt.subplots(1, 1, figsize=(8, 8))\n",
    "    ax.scatter(a, b, alpha=alpha)\n",
    "    \n",
    "    return ax"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "id": "altered-buffalo",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x576 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ax = plot_absolute_error_vs_uncertainty(y_val, y_hat, std, binned=True)\n",
    "\n",
    "ax.set_title('Absolute error vs uncertainty (binned & averaged)');\n",
    "ax.set_xlabel('Absolute error (binned)');\n",
    "ax.set_ylabel('Uncertainty (average within bin)');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "id": "least-place",
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_results_with_uncertainty(y_true, y_pred, y_pred_std, subset):\n",
    "    _, ax = plt.subplots(1, 1, figsize=(7, 7))\n",
    "    palette = sns.color_palette()\n",
    "    \n",
    "    min_value = min(np.amin(y_true), np.amin(y_pred))\n",
    "    max_value = max(np.amax(y_true), np.amax(y_pred))\n",
    "    y_mid = np.linspace(min_value, max_value)\n",
    "    \n",
    "    ax.plot(y_mid, y_mid, '--', color=palette[1])\n",
    "    \n",
    "    ax.scatter(y_true, y_pred, color=palette[0], alpha=0.1);\n",
    "    \n",
    "    ax.errorbar(y_true[subset], y_pred[subset], yerr=y_pred_std[subset], color=palette[0], fmt='o')\n",
    "    \n",
    "    return ax"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "id": "associate-shooting",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x504 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ix = [i for i, v in enumerate(stds) if v > stds.mean() + 3 * stds.std()]\n",
    "\n",
    "plot_results_with_uncertainty(\n",
    "    y_val.detach().numpy().flatten(),\n",
    "    y_hat.detach().numpy().flatten(),\n",
    "    std.detach().numpy().flatten(),\n",
    "    subset=ix,\n",
    ");"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "marine-diving",
   "metadata": {},
   "source": [
    "### Uncertainty on an input not yet seen & very different from the rest of the dataset\n",
    "\n",
    "We'll consider an input composed of the maximum of all features."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 111,
   "id": "bibliographic-sullivan",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "torch.Size([1, 28])"
      ]
     },
     "execution_count": 111,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "random_input_np = np.zeros((1, x_val.shape[1]))\n",
    "for i in range(x_val.shape[1]):\n",
    "    fn = torch.amax\n",
    "    random_input_np[0, i] = fn(x_val[:, i]) * 2\n",
    "    \n",
    "random_input = torch.from_numpy(random_input_np)\n",
    "random_input.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 116,
   "id": "standard-discovery",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Uncertainty on made up input: 863.15\n"
     ]
    }
   ],
   "source": [
    "_, std_epistemic, std_aleatoric = make_predictions(model, random_input)\n",
    "uncertainty = float((std_epistemic + std_aleatoric).detach().numpy())\n",
    "print(f'Uncertainty on made up input: {uncertainty:.2f}')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "several-evening",
   "metadata": {},
   "source": [
    "Uncertainty is high, which is what we want!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "behind-manual",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.9"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}