{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "202599bf",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Crossvalidation and Regularization\n",
    "\n",
    "Peter Ralph\n",
    "\n",
    "https://uodsci.github.io/dsci345"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "733bfdf0",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "import matplotlib\n",
    "import matplotlib.pyplot as plt\n",
    "matplotlib.rcParams['figure.figsize'] = (15, 8)\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "from dsci345 import pretty\n",
    "\n",
    "rng = np.random.default_rng(123)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "88ec5c59",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "$$\\renewcommand{\\P}{\\mathbb{P}} \\newcommand{\\E}{\\mathbb{E}} \\newcommand{\\var}{\\text{var}} \\newcommand{\\sd}{\\text{sd}} \\newcommand{\\cov}{\\text{cov}} \\newcommand{\\cor}{\\text{cor}}$$\n",
    "This is here so we can use `\\P` and `\\E` and `\\var` and `\\cov` and `\\cor` and `\\sd` in LaTeX below."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2e6bfa48",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# A cautionary tale"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "38512175",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "import datetime\n",
    "full_covid = pd.read_csv(\"data/United_States_COVID-19_Cases_and_Deaths_by_State_over_Time.csv\")[[\"state\", \"tot_cases\", \"submission_date\"]]\n",
    "covid = full_covid.rename(columns={'submission_date': 'date', \"tot_cases\": \"cases\"})\n",
    "covid.date = pd.to_datetime(covid.date)\n",
    "covid = covid[covid.date < np.datetime64(\"2021-01-01\")]\n",
    "covid = covid[covid.date.dt.dayofweek == 0]\n",
    "states = ['AK', 'AL', 'AR', 'AZ', 'CA', 'CO', 'CT', 'DC', 'DE', 'FL',\n",
    "       'GA', 'GU', 'HI', 'IA', 'ID', 'IL', 'IN', 'KS', 'KY', 'LA',\n",
    "       'MA', 'MD', 'ME', 'MI', 'MN', 'MO', 'MS', 'MT', 'NC', 'ND',\n",
    "       'NE', 'NH', 'NJ', 'NM', 'NV', 'NY', 'OH', 'OK', 'OR', 'PA',\n",
    "       'PR', 'RI', 'SC', 'SD', 'TN', 'TX', 'UT', 'VA',\n",
    "       'VT', 'WA', 'WI', 'WV', 'WY']\n",
    "covid = covid[np.isin(covid.state, states)]\n",
    "covid = covid.pivot(index=\"date\", columns=\"state\")\n",
    "covid = covid.diff()[1:]\n",
    "covid.columns = [x[1] for x in covid.columns]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6408390e",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    " Here are weekly COVID case counts across the US states plus DC, PR, and GU for 2020,\n",
    " a 48 x 53 matrix:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "81101624",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
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       "        vertical-align: top;\n",
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       "    .dataframe thead th {\n",
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>AK</th>\n",
       "      <th>AL</th>\n",
       "      <th>AR</th>\n",
       "      <th>AZ</th>\n",
       "      <th>CA</th>\n",
       "      <th>CO</th>\n",
       "      <th>CT</th>\n",
       "      <th>DC</th>\n",
       "      <th>DE</th>\n",
       "      <th>FL</th>\n",
       "      <th>...</th>\n",
       "      <th>SD</th>\n",
       "      <th>TN</th>\n",
       "      <th>TX</th>\n",
       "      <th>UT</th>\n",
       "      <th>VA</th>\n",
       "      <th>VT</th>\n",
       "      <th>WA</th>\n",
       "      <th>WI</th>\n",
       "      <th>WV</th>\n",
       "      <th>WY</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>date</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
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       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2020-02-03</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>6.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>...</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
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       "    <tr>\n",
       "      <th>2020-02-10</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
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       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>0.0</td>\n",
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       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
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       "    <tr>\n",
       "      <th>2020-02-17</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>...</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
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       "    <tr>\n",
       "      <th>2020-02-24</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>17.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>...</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2020-03-02</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>14.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
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       "      <td>2.0</td>\n",
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       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2020-03-09</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>94.0</td>\n",
       "      <td>11.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>16.0</td>\n",
       "      <td>...</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>12.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>153.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2020-03-16</th>\n",
       "      <td>1.0</td>\n",
       "      <td>36.0</td>\n",
       "      <td>17.0</td>\n",
       "      <td>12.0</td>\n",
       "      <td>259.0</td>\n",
       "      <td>135.0</td>\n",
       "      <td>40.0</td>\n",
       "      <td>20.0</td>\n",
       "      <td>7.0</td>\n",
       "      <td>138.0</td>\n",
       "      <td>...</td>\n",
       "      <td>10.0</td>\n",
       "      <td>10.0</td>\n",
       "      <td>44.0</td>\n",
       "      <td>28.0</td>\n",
       "      <td>49.0</td>\n",
       "      <td>7.0</td>\n",
       "      <td>656.0</td>\n",
       "      <td>52.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>3.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2020-03-23</th>\n",
       "      <td>37.0</td>\n",
       "      <td>188.0</td>\n",
       "      <td>180.0</td>\n",
       "      <td>235.0</td>\n",
       "      <td>1341.0</td>\n",
       "      <td>582.0</td>\n",
       "      <td>374.0</td>\n",
       "      <td>115.0</td>\n",
       "      <td>58.0</td>\n",
       "      <td>1065.0</td>\n",
       "      <td>...</td>\n",
       "      <td>18.0</td>\n",
       "      <td>495.0</td>\n",
       "      <td>231.0</td>\n",
       "      <td>251.0</td>\n",
       "      <td>203.0</td>\n",
       "      <td>60.0</td>\n",
       "      <td>1212.0</td>\n",
       "      <td>363.0</td>\n",
       "      <td>20.0</td>\n",
       "      <td>23.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2020-03-30</th>\n",
       "      <td>80.0</td>\n",
       "      <td>770.0</td>\n",
       "      <td>307.0</td>\n",
       "      <td>904.0</td>\n",
       "      <td>4030.0</td>\n",
       "      <td>1890.0</td>\n",
       "      <td>2156.0</td>\n",
       "      <td>358.0</td>\n",
       "      <td>245.0</td>\n",
       "      <td>4408.0</td>\n",
       "      <td>...</td>\n",
       "      <td>73.0</td>\n",
       "      <td>1037.0</td>\n",
       "      <td>2587.0</td>\n",
       "      <td>526.0</td>\n",
       "      <td>766.0</td>\n",
       "      <td>168.0</td>\n",
       "      <td>2553.0</td>\n",
       "      <td>805.0</td>\n",
       "      <td>125.0</td>\n",
       "      <td>69.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2020-04-06</th>\n",
       "      <td>73.0</td>\n",
       "      <td>1076.0</td>\n",
       "      <td>411.0</td>\n",
       "      <td>1299.0</td>\n",
       "      <td>8573.0</td>\n",
       "      <td>2572.0</td>\n",
       "      <td>4335.0</td>\n",
       "      <td>602.0</td>\n",
       "      <td>475.0</td>\n",
       "      <td>7585.0</td>\n",
       "      <td>...</td>\n",
       "      <td>187.0</td>\n",
       "      <td>2117.0</td>\n",
       "      <td>4399.0</td>\n",
       "      <td>910.0</td>\n",
       "      <td>1858.0</td>\n",
       "      <td>274.0</td>\n",
       "      <td>3222.0</td>\n",
       "      <td>1219.0</td>\n",
       "      <td>200.0</td>\n",
       "      <td>117.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2020-04-13</th>\n",
       "      <td>86.0</td>\n",
       "      <td>1789.0</td>\n",
       "      <td>495.0</td>\n",
       "      <td>1246.0</td>\n",
       "      <td>8012.0</td>\n",
       "      <td>2719.0</td>\n",
       "      <td>6475.0</td>\n",
       "      <td>858.0</td>\n",
       "      <td>921.0</td>\n",
       "      <td>6979.0</td>\n",
       "      <td>...</td>\n",
       "      <td>580.0</td>\n",
       "      <td>1730.0</td>\n",
       "      <td>6633.0</td>\n",
       "      <td>676.0</td>\n",
       "      <td>2869.0</td>\n",
       "      <td>191.0</td>\n",
       "      <td>2303.0</td>\n",
       "      <td>988.0</td>\n",
       "      <td>281.0</td>\n",
       "      <td>161.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2020-04-20</th>\n",
       "      <td>44.0</td>\n",
       "      <td>1288.0</td>\n",
       "      <td>554.0</td>\n",
       "      <td>1362.0</td>\n",
       "      <td>8630.0</td>\n",
       "      <td>2390.0</td>\n",
       "      <td>6434.0</td>\n",
       "      <td>972.0</td>\n",
       "      <td>1097.0</td>\n",
       "      <td>5966.0</td>\n",
       "      <td>...</td>\n",
       "      <td>817.0</td>\n",
       "      <td>1721.0</td>\n",
       "      <td>5552.0</td>\n",
       "      <td>867.0</td>\n",
       "      <td>3243.0</td>\n",
       "      <td>55.0</td>\n",
       "      <td>1899.0</td>\n",
       "      <td>1071.0</td>\n",
       "      <td>276.0</td>\n",
       "      <td>55.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2020-04-27</th>\n",
       "      <td>24.0</td>\n",
       "      <td>1457.0</td>\n",
       "      <td>1091.0</td>\n",
       "      <td>1652.0</td>\n",
       "      <td>12486.0</td>\n",
       "      <td>3779.0</td>\n",
       "      <td>6182.0</td>\n",
       "      <td>965.0</td>\n",
       "      <td>1448.0</td>\n",
       "      <td>5545.0</td>\n",
       "      <td>...</td>\n",
       "      <td>560.0</td>\n",
       "      <td>2556.0</td>\n",
       "      <td>5839.0</td>\n",
       "      <td>1048.0</td>\n",
       "      <td>4545.0</td>\n",
       "      <td>31.0</td>\n",
       "      <td>1706.0</td>\n",
       "      <td>1582.0</td>\n",
       "      <td>175.0</td>\n",
       "      <td>92.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2020-05-04</th>\n",
       "      <td>25.0</td>\n",
       "      <td>1581.0</td>\n",
       "      <td>414.0</td>\n",
       "      <td>2203.0</td>\n",
       "      <td>11473.0</td>\n",
       "      <td>3364.0</td>\n",
       "      <td>3976.0</td>\n",
       "      <td>1278.0</td>\n",
       "      <td>1310.0</td>\n",
       "      <td>4489.0</td>\n",
       "      <td>...</td>\n",
       "      <td>423.0</td>\n",
       "      <td>3516.0</td>\n",
       "      <td>7035.0</td>\n",
       "      <td>1099.0</td>\n",
       "      <td>5957.0</td>\n",
       "      <td>42.0</td>\n",
       "      <td>1855.0</td>\n",
       "      <td>2155.0</td>\n",
       "      <td>147.0</td>\n",
       "      <td>76.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2020-05-11</th>\n",
       "      <td>11.0</td>\n",
       "      <td>2053.0</td>\n",
       "      <td>574.0</td>\n",
       "      <td>2461.0</td>\n",
       "      <td>13002.0</td>\n",
       "      <td>2809.0</td>\n",
       "      <td>3792.0</td>\n",
       "      <td>1219.0</td>\n",
       "      <td>1498.0</td>\n",
       "      <td>3991.0</td>\n",
       "      <td>...</td>\n",
       "      <td>946.0</td>\n",
       "      <td>1836.0</td>\n",
       "      <td>7537.0</td>\n",
       "      <td>989.0</td>\n",
       "      <td>5578.0</td>\n",
       "      <td>23.0</td>\n",
       "      <td>1681.0</td>\n",
       "      <td>2182.0</td>\n",
       "      <td>145.0</td>\n",
       "      <td>73.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2020-05-18</th>\n",
       "      <td>20.0</td>\n",
       "      <td>2175.0</td>\n",
       "      <td>770.0</td>\n",
       "      <td>2790.0</td>\n",
       "      <td>12491.0</td>\n",
       "      <td>2394.0</td>\n",
       "      <td>4351.0</td>\n",
       "      <td>881.0</td>\n",
       "      <td>1104.0</td>\n",
       "      <td>5238.0</td>\n",
       "      <td>...</td>\n",
       "      <td>413.0</td>\n",
       "      <td>2753.0</td>\n",
       "      <td>8824.0</td>\n",
       "      <td>1064.0</td>\n",
       "      <td>6070.0</td>\n",
       "      <td>12.0</td>\n",
       "      <td>1435.0</td>\n",
       "      <td>2269.0</td>\n",
       "      <td>133.0</td>\n",
       "      <td>97.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2020-05-25</th>\n",
       "      <td>10.0</td>\n",
       "      <td>2870.0</td>\n",
       "      <td>1216.0</td>\n",
       "      <td>2391.0</td>\n",
       "      <td>14128.0</td>\n",
       "      <td>2207.0</td>\n",
       "      <td>2757.0</td>\n",
       "      <td>955.0</td>\n",
       "      <td>820.0</td>\n",
       "      <td>5146.0</td>\n",
       "      <td>...</td>\n",
       "      <td>559.0</td>\n",
       "      <td>2451.0</td>\n",
       "      <td>7278.0</td>\n",
       "      <td>1125.0</td>\n",
       "      <td>6587.0</td>\n",
       "      <td>22.0</td>\n",
       "      <td>1455.0</td>\n",
       "      <td>2897.0</td>\n",
       "      <td>280.0</td>\n",
       "      <td>77.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2020-06-01</th>\n",
       "      <td>59.0</td>\n",
       "      <td>3213.0</td>\n",
       "      <td>1414.0</td>\n",
       "      <td>3562.0</td>\n",
       "      <td>18448.0</td>\n",
       "      <td>2087.0</td>\n",
       "      <td>1867.0</td>\n",
       "      <td>632.0</td>\n",
       "      <td>638.0</td>\n",
       "      <td>5239.0</td>\n",
       "      <td>...</td>\n",
       "      <td>448.0</td>\n",
       "      <td>3051.0</td>\n",
       "      <td>8909.0</td>\n",
       "      <td>1517.0</td>\n",
       "      <td>7671.0</td>\n",
       "      <td>21.0</td>\n",
       "      <td>1863.0</td>\n",
       "      <td>2959.0</td>\n",
       "      <td>246.0</td>\n",
       "      <td>67.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2020-06-08</th>\n",
       "      <td>97.0</td>\n",
       "      <td>2739.0</td>\n",
       "      <td>2297.0</td>\n",
       "      <td>7555.0</td>\n",
       "      <td>18313.0</td>\n",
       "      <td>1578.0</td>\n",
       "      <td>1352.0</td>\n",
       "      <td>532.0</td>\n",
       "      <td>396.0</td>\n",
       "      <td>8321.0</td>\n",
       "      <td>...</td>\n",
       "      <td>437.0</td>\n",
       "      <td>3228.0</td>\n",
       "      <td>10736.0</td>\n",
       "      <td>2328.0</td>\n",
       "      <td>5853.0</td>\n",
       "      <td>84.0</td>\n",
       "      <td>1997.0</td>\n",
       "      <td>2495.0</td>\n",
       "      <td>133.0</td>\n",
       "      <td>50.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2020-06-15</th>\n",
       "      <td>101.0</td>\n",
       "      <td>5209.0</td>\n",
       "      <td>3177.0</td>\n",
       "      <td>9033.0</td>\n",
       "      <td>20133.0</td>\n",
       "      <td>1163.0</td>\n",
       "      <td>1143.0</td>\n",
       "      <td>410.0</td>\n",
       "      <td>388.0</td>\n",
       "      <td>13687.0</td>\n",
       "      <td>...</td>\n",
       "      <td>457.0</td>\n",
       "      <td>3793.0</td>\n",
       "      <td>13492.0</td>\n",
       "      <td>2397.0</td>\n",
       "      <td>3635.0</td>\n",
       "      <td>50.0</td>\n",
       "      <td>2096.0</td>\n",
       "      <td>4442.0</td>\n",
       "      <td>161.0</td>\n",
       "      <td>119.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2020-06-22</th>\n",
       "      <td>99.0</td>\n",
       "      <td>4266.0</td>\n",
       "      <td>3166.0</td>\n",
       "      <td>17888.0</td>\n",
       "      <td>26602.0</td>\n",
       "      <td>1524.0</td>\n",
       "      <td>547.0</td>\n",
       "      <td>259.0</td>\n",
       "      <td>397.0</td>\n",
       "      <td>23612.0</td>\n",
       "      <td>...</td>\n",
       "      <td>398.0</td>\n",
       "      <td>4547.0</td>\n",
       "      <td>25773.0</td>\n",
       "      <td>3309.0</td>\n",
       "      <td>3579.0</td>\n",
       "      <td>36.0</td>\n",
       "      <td>2725.0</td>\n",
       "      <td>2358.0</td>\n",
       "      <td>249.0</td>\n",
       "      <td>151.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2020-06-29</th>\n",
       "      <td>141.0</td>\n",
       "      <td>6797.0</td>\n",
       "      <td>4174.0</td>\n",
       "      <td>19954.0</td>\n",
       "      <td>38496.0</td>\n",
       "      <td>1788.0</td>\n",
       "      <td>580.0</td>\n",
       "      <td>234.0</td>\n",
       "      <td>666.0</td>\n",
       "      <td>48535.0</td>\n",
       "      <td>...</td>\n",
       "      <td>390.0</td>\n",
       "      <td>5434.0</td>\n",
       "      <td>38130.0</td>\n",
       "      <td>4128.0</td>\n",
       "      <td>3724.0</td>\n",
       "      <td>31.0</td>\n",
       "      <td>3204.0</td>\n",
       "      <td>3195.0</td>\n",
       "      <td>299.0</td>\n",
       "      <td>220.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2020-07-06</th>\n",
       "      <td>260.0</td>\n",
       "      <td>7295.0</td>\n",
       "      <td>3996.0</td>\n",
       "      <td>26915.0</td>\n",
       "      <td>55134.0</td>\n",
       "      <td>1982.0</td>\n",
       "      <td>614.0</td>\n",
       "      <td>223.0</td>\n",
       "      <td>851.0</td>\n",
       "      <td>59914.0</td>\n",
       "      <td>...</td>\n",
       "      <td>389.0</td>\n",
       "      <td>10877.0</td>\n",
       "      <td>47546.0</td>\n",
       "      <td>3741.0</td>\n",
       "      <td>3913.0</td>\n",
       "      <td>41.0</td>\n",
       "      <td>4659.0</td>\n",
       "      <td>4197.0</td>\n",
       "      <td>572.0</td>\n",
       "      <td>225.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2020-07-13</th>\n",
       "      <td>369.0</td>\n",
       "      <td>11142.0</td>\n",
       "      <td>4686.0</td>\n",
       "      <td>22390.0</td>\n",
       "      <td>57478.0</td>\n",
       "      <td>2988.0</td>\n",
       "      <td>534.0</td>\n",
       "      <td>391.0</td>\n",
       "      <td>891.0</td>\n",
       "      <td>76760.0</td>\n",
       "      <td>...</td>\n",
       "      <td>419.0</td>\n",
       "      <td>11915.0</td>\n",
       "      <td>63756.0</td>\n",
       "      <td>4718.0</td>\n",
       "      <td>5540.0</td>\n",
       "      <td>45.0</td>\n",
       "      <td>4881.0</td>\n",
       "      <td>5152.0</td>\n",
       "      <td>871.0</td>\n",
       "      <td>228.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2020-07-20</th>\n",
       "      <td>417.0</td>\n",
       "      <td>13038.0</td>\n",
       "      <td>4988.0</td>\n",
       "      <td>21366.0</td>\n",
       "      <td>62376.0</td>\n",
       "      <td>3350.0</td>\n",
       "      <td>545.0</td>\n",
       "      <td>433.0</td>\n",
       "      <td>692.0</td>\n",
       "      <td>76510.0</td>\n",
       "      <td>...</td>\n",
       "      <td>419.0</td>\n",
       "      <td>14570.0</td>\n",
       "      <td>68121.0</td>\n",
       "      <td>4362.0</td>\n",
       "      <td>6733.0</td>\n",
       "      <td>54.0</td>\n",
       "      <td>5958.0</td>\n",
       "      <td>6293.0</td>\n",
       "      <td>829.0</td>\n",
       "      <td>284.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2020-07-27</th>\n",
       "      <td>672.0</td>\n",
       "      <td>11976.0</td>\n",
       "      <td>5520.0</td>\n",
       "      <td>18651.0</td>\n",
       "      <td>69012.0</td>\n",
       "      <td>4095.0</td>\n",
       "      <td>928.0</td>\n",
       "      <td>519.0</td>\n",
       "      <td>767.0</td>\n",
       "      <td>70503.0</td>\n",
       "      <td>...</td>\n",
       "      <td>501.0</td>\n",
       "      <td>16021.0</td>\n",
       "      <td>53489.0</td>\n",
       "      <td>3831.0</td>\n",
       "      <td>7697.0</td>\n",
       "      <td>40.0</td>\n",
       "      <td>5513.0</td>\n",
       "      <td>6606.0</td>\n",
       "      <td>912.0</td>\n",
       "      <td>333.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2020-08-03</th>\n",
       "      <td>707.0</td>\n",
       "      <td>11206.0</td>\n",
       "      <td>5150.0</td>\n",
       "      <td>15677.0</td>\n",
       "      <td>54351.0</td>\n",
       "      <td>3680.0</td>\n",
       "      <td>1079.0</td>\n",
       "      <td>455.0</td>\n",
       "      <td>668.0</td>\n",
       "      <td>53915.0</td>\n",
       "      <td>...</td>\n",
       "      <td>576.0</td>\n",
       "      <td>14060.0</td>\n",
       "      <td>56091.0</td>\n",
       "      <td>3238.0</td>\n",
       "      <td>7034.0</td>\n",
       "      <td>21.0</td>\n",
       "      <td>5670.0</td>\n",
       "      <td>6120.0</td>\n",
       "      <td>919.0</td>\n",
       "      <td>328.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2020-08-10</th>\n",
       "      <td>455.0</td>\n",
       "      <td>9842.0</td>\n",
       "      <td>5431.0</td>\n",
       "      <td>8033.0</td>\n",
       "      <td>47010.0</td>\n",
       "      <td>2986.0</td>\n",
       "      <td>505.0</td>\n",
       "      <td>494.0</td>\n",
       "      <td>474.0</td>\n",
       "      <td>44277.0</td>\n",
       "      <td>...</td>\n",
       "      <td>643.0</td>\n",
       "      <td>13014.0</td>\n",
       "      <td>48803.0</td>\n",
       "      <td>2853.0</td>\n",
       "      <td>7643.0</td>\n",
       "      <td>31.0</td>\n",
       "      <td>4872.0</td>\n",
       "      <td>5955.0</td>\n",
       "      <td>781.0</td>\n",
       "      <td>194.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2020-08-17</th>\n",
       "      <td>527.0</td>\n",
       "      <td>6662.0</td>\n",
       "      <td>3049.0</td>\n",
       "      <td>6489.0</td>\n",
       "      <td>66120.0</td>\n",
       "      <td>2209.0</td>\n",
       "      <td>700.0</td>\n",
       "      <td>466.0</td>\n",
       "      <td>511.0</td>\n",
       "      <td>36154.0</td>\n",
       "      <td>...</td>\n",
       "      <td>697.0</td>\n",
       "      <td>11112.0</td>\n",
       "      <td>52133.0</td>\n",
       "      <td>2481.0</td>\n",
       "      <td>6672.0</td>\n",
       "      <td>58.0</td>\n",
       "      <td>4193.0</td>\n",
       "      <td>5359.0</td>\n",
       "      <td>878.0</td>\n",
       "      <td>289.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2020-08-24</th>\n",
       "      <td>517.0</td>\n",
       "      <td>6911.0</td>\n",
       "      <td>3817.0</td>\n",
       "      <td>4416.0</td>\n",
       "      <td>40584.0</td>\n",
       "      <td>2138.0</td>\n",
       "      <td>744.0</td>\n",
       "      <td>366.0</td>\n",
       "      <td>471.0</td>\n",
       "      <td>24946.0</td>\n",
       "      <td>...</td>\n",
       "      <td>1065.0</td>\n",
       "      <td>10106.0</td>\n",
       "      <td>37434.0</td>\n",
       "      <td>2566.0</td>\n",
       "      <td>6209.0</td>\n",
       "      <td>36.0</td>\n",
       "      <td>3913.0</td>\n",
       "      <td>4904.0</td>\n",
       "      <td>680.0</td>\n",
       "      <td>272.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2020-08-31</th>\n",
       "      <td>458.0</td>\n",
       "      <td>10366.0</td>\n",
       "      <td>4330.0</td>\n",
       "      <td>3428.0</td>\n",
       "      <td>35470.0</td>\n",
       "      <td>2091.0</td>\n",
       "      <td>868.0</td>\n",
       "      <td>353.0</td>\n",
       "      <td>651.0</td>\n",
       "      <td>24465.0</td>\n",
       "      <td>...</td>\n",
       "      <td>2084.0</td>\n",
       "      <td>10075.0</td>\n",
       "      <td>32585.0</td>\n",
       "      <td>2739.0</td>\n",
       "      <td>6964.0</td>\n",
       "      <td>50.0</td>\n",
       "      <td>3344.0</td>\n",
       "      <td>4949.0</td>\n",
       "      <td>938.0</td>\n",
       "      <td>239.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2020-09-07</th>\n",
       "      <td>520.0</td>\n",
       "      <td>5695.0</td>\n",
       "      <td>5056.0</td>\n",
       "      <td>4136.0</td>\n",
       "      <td>31150.0</td>\n",
       "      <td>2159.0</td>\n",
       "      <td>486.0</td>\n",
       "      <td>323.0</td>\n",
       "      <td>697.0</td>\n",
       "      <td>18770.0</td>\n",
       "      <td>...</td>\n",
       "      <td>1791.0</td>\n",
       "      <td>10229.0</td>\n",
       "      <td>27401.0</td>\n",
       "      <td>2951.0</td>\n",
       "      <td>6977.0</td>\n",
       "      <td>31.0</td>\n",
       "      <td>3163.0</td>\n",
       "      <td>6360.0</td>\n",
       "      <td>1325.0</td>\n",
       "      <td>190.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2020-09-14</th>\n",
       "      <td>541.0</td>\n",
       "      <td>6336.0</td>\n",
       "      <td>4347.0</td>\n",
       "      <td>2768.0</td>\n",
       "      <td>22543.0</td>\n",
       "      <td>2404.0</td>\n",
       "      <td>1530.0</td>\n",
       "      <td>307.0</td>\n",
       "      <td>692.0</td>\n",
       "      <td>18268.0</td>\n",
       "      <td>...</td>\n",
       "      <td>1501.0</td>\n",
       "      <td>8427.0</td>\n",
       "      <td>23034.0</td>\n",
       "      <td>3540.0</td>\n",
       "      <td>7000.0</td>\n",
       "      <td>44.0</td>\n",
       "      <td>2717.0</td>\n",
       "      <td>8569.0</td>\n",
       "      <td>1245.0</td>\n",
       "      <td>360.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2020-09-21</th>\n",
       "      <td>580.0</td>\n",
       "      <td>6609.0</td>\n",
       "      <td>5737.0</td>\n",
       "      <td>5533.0</td>\n",
       "      <td>23916.0</td>\n",
       "      <td>3760.0</td>\n",
       "      <td>1129.0</td>\n",
       "      <td>356.0</td>\n",
       "      <td>681.0</td>\n",
       "      <td>18630.0</td>\n",
       "      <td>...</td>\n",
       "      <td>2068.0</td>\n",
       "      <td>10994.0</td>\n",
       "      <td>34983.0</td>\n",
       "      <td>5111.0</td>\n",
       "      <td>6567.0</td>\n",
       "      <td>24.0</td>\n",
       "      <td>2907.0</td>\n",
       "      <td>13091.0</td>\n",
       "      <td>1351.0</td>\n",
       "      <td>552.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2020-09-28</th>\n",
       "      <td>733.0</td>\n",
       "      <td>6905.0</td>\n",
       "      <td>5685.0</td>\n",
       "      <td>3266.0</td>\n",
       "      <td>23569.0</td>\n",
       "      <td>4354.0</td>\n",
       "      <td>1123.0</td>\n",
       "      <td>286.0</td>\n",
       "      <td>732.0</td>\n",
       "      <td>16536.0</td>\n",
       "      <td>...</td>\n",
       "      <td>2869.0</td>\n",
       "      <td>9406.0</td>\n",
       "      <td>40835.0</td>\n",
       "      <td>7048.0</td>\n",
       "      <td>5455.0</td>\n",
       "      <td>21.0</td>\n",
       "      <td>3947.0</td>\n",
       "      <td>15629.0</td>\n",
       "      <td>1341.0</td>\n",
       "      <td>810.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2020-10-05</th>\n",
       "      <td>982.0</td>\n",
       "      <td>7010.0</td>\n",
       "      <td>5381.0</td>\n",
       "      <td>3567.0</td>\n",
       "      <td>21521.0</td>\n",
       "      <td>4319.0</td>\n",
       "      <td>1973.0</td>\n",
       "      <td>283.0</td>\n",
       "      <td>958.0</td>\n",
       "      <td>15795.0</td>\n",
       "      <td>...</td>\n",
       "      <td>2860.0</td>\n",
       "      <td>8763.0</td>\n",
       "      <td>30081.0</td>\n",
       "      <td>7281.0</td>\n",
       "      <td>5964.0</td>\n",
       "      <td>64.0</td>\n",
       "      <td>3829.0</td>\n",
       "      <td>17438.0</td>\n",
       "      <td>1230.0</td>\n",
       "      <td>875.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2020-10-12</th>\n",
       "      <td>1258.0</td>\n",
       "      <td>6911.0</td>\n",
       "      <td>6057.0</td>\n",
       "      <td>4987.0</td>\n",
       "      <td>23244.0</td>\n",
       "      <td>5803.0</td>\n",
       "      <td>2257.0</td>\n",
       "      <td>475.0</td>\n",
       "      <td>948.0</td>\n",
       "      <td>18209.0</td>\n",
       "      <td>...</td>\n",
       "      <td>4327.0</td>\n",
       "      <td>14216.0</td>\n",
       "      <td>25823.0</td>\n",
       "      <td>8109.0</td>\n",
       "      <td>7013.0</td>\n",
       "      <td>54.0</td>\n",
       "      <td>4271.0</td>\n",
       "      <td>18676.0</td>\n",
       "      <td>1539.0</td>\n",
       "      <td>1173.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2020-10-19</th>\n",
       "      <td>1322.0</td>\n",
       "      <td>7452.0</td>\n",
       "      <td>6110.0</td>\n",
       "      <td>5854.0</td>\n",
       "      <td>20763.0</td>\n",
       "      <td>8035.0</td>\n",
       "      <td>2644.0</td>\n",
       "      <td>373.0</td>\n",
       "      <td>909.0</td>\n",
       "      <td>21336.0</td>\n",
       "      <td>...</td>\n",
       "      <td>4911.0</td>\n",
       "      <td>13443.0</td>\n",
       "      <td>33401.0</td>\n",
       "      <td>8730.0</td>\n",
       "      <td>7258.0</td>\n",
       "      <td>69.0</td>\n",
       "      <td>4557.0</td>\n",
       "      <td>22811.0</td>\n",
       "      <td>2012.0</td>\n",
       "      <td>1509.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2020-10-26</th>\n",
       "      <td>2166.0</td>\n",
       "      <td>11592.0</td>\n",
       "      <td>7130.0</td>\n",
       "      <td>7074.0</td>\n",
       "      <td>30219.0</td>\n",
       "      <td>11308.0</td>\n",
       "      <td>4078.0</td>\n",
       "      <td>417.0</td>\n",
       "      <td>944.0</td>\n",
       "      <td>25682.0</td>\n",
       "      <td>...</td>\n",
       "      <td>5905.0</td>\n",
       "      <td>18277.0</td>\n",
       "      <td>38548.0</td>\n",
       "      <td>10521.0</td>\n",
       "      <td>7447.0</td>\n",
       "      <td>139.0</td>\n",
       "      <td>5089.0</td>\n",
       "      <td>28786.0</td>\n",
       "      <td>1930.0</td>\n",
       "      <td>2166.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2020-11-02</th>\n",
       "      <td>2716.0</td>\n",
       "      <td>9513.0</td>\n",
       "      <td>6914.0</td>\n",
       "      <td>9211.0</td>\n",
       "      <td>29618.0</td>\n",
       "      <td>15715.0</td>\n",
       "      <td>5759.0</td>\n",
       "      <td>626.0</td>\n",
       "      <td>1127.0</td>\n",
       "      <td>29906.0</td>\n",
       "      <td>...</td>\n",
       "      <td>8109.0</td>\n",
       "      <td>13939.0</td>\n",
       "      <td>110710.0</td>\n",
       "      <td>11623.0</td>\n",
       "      <td>9143.0</td>\n",
       "      <td>134.0</td>\n",
       "      <td>6119.0</td>\n",
       "      <td>33000.0</td>\n",
       "      <td>3012.0</td>\n",
       "      <td>2690.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2020-11-09</th>\n",
       "      <td>3239.0</td>\n",
       "      <td>10609.0</td>\n",
       "      <td>9170.0</td>\n",
       "      <td>11581.0</td>\n",
       "      <td>41223.0</td>\n",
       "      <td>25028.0</td>\n",
       "      <td>7605.0</td>\n",
       "      <td>649.0</td>\n",
       "      <td>1552.0</td>\n",
       "      <td>34832.0</td>\n",
       "      <td>...</td>\n",
       "      <td>8461.0</td>\n",
       "      <td>21972.0</td>\n",
       "      <td>61179.0</td>\n",
       "      <td>17162.0</td>\n",
       "      <td>10059.0</td>\n",
       "      <td>216.0</td>\n",
       "      <td>9421.0</td>\n",
       "      <td>41452.0</td>\n",
       "      <td>3570.0</td>\n",
       "      <td>3843.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2020-11-16</th>\n",
       "      <td>4071.0</td>\n",
       "      <td>14028.0</td>\n",
       "      <td>11537.0</td>\n",
       "      <td>17234.0</td>\n",
       "      <td>57384.0</td>\n",
       "      <td>34597.0</td>\n",
       "      <td>11821.0</td>\n",
       "      <td>977.0</td>\n",
       "      <td>2273.0</td>\n",
       "      <td>44342.0</td>\n",
       "      <td>...</td>\n",
       "      <td>9967.0</td>\n",
       "      <td>28019.0</td>\n",
       "      <td>77266.0</td>\n",
       "      <td>20911.0</td>\n",
       "      <td>11160.0</td>\n",
       "      <td>620.0</td>\n",
       "      <td>13727.0</td>\n",
       "      <td>48182.0</td>\n",
       "      <td>5655.0</td>\n",
       "      <td>5183.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2020-11-23</th>\n",
       "      <td>3932.0</td>\n",
       "      <td>15812.0</td>\n",
       "      <td>11842.0</td>\n",
       "      <td>25433.0</td>\n",
       "      <td>81135.0</td>\n",
       "      <td>37795.0</td>\n",
       "      <td>13456.0</td>\n",
       "      <td>1226.0</td>\n",
       "      <td>2999.0</td>\n",
       "      <td>54578.0</td>\n",
       "      <td>...</td>\n",
       "      <td>7570.0</td>\n",
       "      <td>28054.0</td>\n",
       "      <td>85027.0</td>\n",
       "      <td>23641.0</td>\n",
       "      <td>16401.0</td>\n",
       "      <td>677.0</td>\n",
       "      <td>15029.0</td>\n",
       "      <td>45131.0</td>\n",
       "      <td>6654.0</td>\n",
       "      <td>6238.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2020-11-30</th>\n",
       "      <td>4443.0</td>\n",
       "      <td>15860.0</td>\n",
       "      <td>11169.0</td>\n",
       "      <td>24514.0</td>\n",
       "      <td>102598.0</td>\n",
       "      <td>32762.0</td>\n",
       "      <td>10555.0</td>\n",
       "      <td>1262.0</td>\n",
       "      <td>3426.0</td>\n",
       "      <td>53444.0</td>\n",
       "      <td>...</td>\n",
       "      <td>6616.0</td>\n",
       "      <td>27143.0</td>\n",
       "      <td>77175.0</td>\n",
       "      <td>16286.0</td>\n",
       "      <td>16797.0</td>\n",
       "      <td>460.0</td>\n",
       "      <td>18941.0</td>\n",
       "      <td>32037.0</td>\n",
       "      <td>6728.0</td>\n",
       "      <td>3874.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2020-12-07</th>\n",
       "      <td>4903.0</td>\n",
       "      <td>23381.0</td>\n",
       "      <td>14683.0</td>\n",
       "      <td>39047.0</td>\n",
       "      <td>153467.0</td>\n",
       "      <td>34561.0</td>\n",
       "      <td>18549.0</td>\n",
       "      <td>1767.0</td>\n",
       "      <td>5055.0</td>\n",
       "      <td>64630.0</td>\n",
       "      <td>...</td>\n",
       "      <td>6036.0</td>\n",
       "      <td>32250.0</td>\n",
       "      <td>106372.0</td>\n",
       "      <td>21932.0</td>\n",
       "      <td>21035.0</td>\n",
       "      <td>752.0</td>\n",
       "      <td>17031.0</td>\n",
       "      <td>31659.0</td>\n",
       "      <td>8286.0</td>\n",
       "      <td>3680.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2020-12-14</th>\n",
       "      <td>3908.0</td>\n",
       "      <td>24904.0</td>\n",
       "      <td>15015.0</td>\n",
       "      <td>54426.0</td>\n",
       "      <td>218609.0</td>\n",
       "      <td>26619.0</td>\n",
       "      <td>18148.0</td>\n",
       "      <td>1719.0</td>\n",
       "      <td>5818.0</td>\n",
       "      <td>69233.0</td>\n",
       "      <td>...</td>\n",
       "      <td>4854.0</td>\n",
       "      <td>55834.0</td>\n",
       "      <td>97337.0</td>\n",
       "      <td>18234.0</td>\n",
       "      <td>26279.0</td>\n",
       "      <td>713.0</td>\n",
       "      <td>23549.0</td>\n",
       "      <td>27896.0</td>\n",
       "      <td>8266.0</td>\n",
       "      <td>2790.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2020-12-21</th>\n",
       "      <td>2383.0</td>\n",
       "      <td>27509.0</td>\n",
       "      <td>16050.0</td>\n",
       "      <td>41118.0</td>\n",
       "      <td>307304.0</td>\n",
       "      <td>18576.0</td>\n",
       "      <td>13385.0</td>\n",
       "      <td>1702.0</td>\n",
       "      <td>4735.0</td>\n",
       "      <td>77384.0</td>\n",
       "      <td>...</td>\n",
       "      <td>3720.0</td>\n",
       "      <td>64380.0</td>\n",
       "      <td>109807.0</td>\n",
       "      <td>16911.0</td>\n",
       "      <td>25741.0</td>\n",
       "      <td>648.0</td>\n",
       "      <td>15917.0</td>\n",
       "      <td>23068.0</td>\n",
       "      <td>8943.0</td>\n",
       "      <td>2343.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2020-12-28</th>\n",
       "      <td>1839.0</td>\n",
       "      <td>21699.0</td>\n",
       "      <td>13421.0</td>\n",
       "      <td>43099.0</td>\n",
       "      <td>263628.0</td>\n",
       "      <td>14576.0</td>\n",
       "      <td>13823.0</td>\n",
       "      <td>1602.0</td>\n",
       "      <td>4504.0</td>\n",
       "      <td>67592.0</td>\n",
       "      <td>...</td>\n",
       "      <td>2583.0</td>\n",
       "      <td>40264.0</td>\n",
       "      <td>91478.0</td>\n",
       "      <td>13807.0</td>\n",
       "      <td>25285.0</td>\n",
       "      <td>544.0</td>\n",
       "      <td>12829.0</td>\n",
       "      <td>15784.0</td>\n",
       "      <td>8099.0</td>\n",
       "      <td>1586.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>48 rows × 53 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "                AK       AL       AR       AZ        CA       CO       CT  \\\n",
       "date                                                                        \n",
       "2020-02-03     0.0      0.0      0.0      0.0       6.0      0.0      0.0   \n",
       "2020-02-10     0.0      0.0      0.0      0.0       0.0      0.0      0.0   \n",
       "2020-02-17     0.0      0.0      0.0      0.0       2.0      0.0      0.0   \n",
       "2020-02-24     0.0      0.0      0.0      0.0      17.0      0.0      0.0   \n",
       "2020-03-02     0.0      0.0      0.0      0.0      14.0      1.0      0.0   \n",
       "2020-03-09     0.0      0.0      0.0      5.0      94.0     11.0      1.0   \n",
       "2020-03-16     1.0     36.0     17.0     12.0     259.0    135.0     40.0   \n",
       "2020-03-23    37.0    188.0    180.0    235.0    1341.0    582.0    374.0   \n",
       "2020-03-30    80.0    770.0    307.0    904.0    4030.0   1890.0   2156.0   \n",
       "2020-04-06    73.0   1076.0    411.0   1299.0    8573.0   2572.0   4335.0   \n",
       "2020-04-13    86.0   1789.0    495.0   1246.0    8012.0   2719.0   6475.0   \n",
       "2020-04-20    44.0   1288.0    554.0   1362.0    8630.0   2390.0   6434.0   \n",
       "2020-04-27    24.0   1457.0   1091.0   1652.0   12486.0   3779.0   6182.0   \n",
       "2020-05-04    25.0   1581.0    414.0   2203.0   11473.0   3364.0   3976.0   \n",
       "2020-05-11    11.0   2053.0    574.0   2461.0   13002.0   2809.0   3792.0   \n",
       "2020-05-18    20.0   2175.0    770.0   2790.0   12491.0   2394.0   4351.0   \n",
       "2020-05-25    10.0   2870.0   1216.0   2391.0   14128.0   2207.0   2757.0   \n",
       "2020-06-01    59.0   3213.0   1414.0   3562.0   18448.0   2087.0   1867.0   \n",
       "2020-06-08    97.0   2739.0   2297.0   7555.0   18313.0   1578.0   1352.0   \n",
       "2020-06-15   101.0   5209.0   3177.0   9033.0   20133.0   1163.0   1143.0   \n",
       "2020-06-22    99.0   4266.0   3166.0  17888.0   26602.0   1524.0    547.0   \n",
       "2020-06-29   141.0   6797.0   4174.0  19954.0   38496.0   1788.0    580.0   \n",
       "2020-07-06   260.0   7295.0   3996.0  26915.0   55134.0   1982.0    614.0   \n",
       "2020-07-13   369.0  11142.0   4686.0  22390.0   57478.0   2988.0    534.0   \n",
       "2020-07-20   417.0  13038.0   4988.0  21366.0   62376.0   3350.0    545.0   \n",
       "2020-07-27   672.0  11976.0   5520.0  18651.0   69012.0   4095.0    928.0   \n",
       "2020-08-03   707.0  11206.0   5150.0  15677.0   54351.0   3680.0   1079.0   \n",
       "2020-08-10   455.0   9842.0   5431.0   8033.0   47010.0   2986.0    505.0   \n",
       "2020-08-17   527.0   6662.0   3049.0   6489.0   66120.0   2209.0    700.0   \n",
       "2020-08-24   517.0   6911.0   3817.0   4416.0   40584.0   2138.0    744.0   \n",
       "2020-08-31   458.0  10366.0   4330.0   3428.0   35470.0   2091.0    868.0   \n",
       "2020-09-07   520.0   5695.0   5056.0   4136.0   31150.0   2159.0    486.0   \n",
       "2020-09-14   541.0   6336.0   4347.0   2768.0   22543.0   2404.0   1530.0   \n",
       "2020-09-21   580.0   6609.0   5737.0   5533.0   23916.0   3760.0   1129.0   \n",
       "2020-09-28   733.0   6905.0   5685.0   3266.0   23569.0   4354.0   1123.0   \n",
       "2020-10-05   982.0   7010.0   5381.0   3567.0   21521.0   4319.0   1973.0   \n",
       "2020-10-12  1258.0   6911.0   6057.0   4987.0   23244.0   5803.0   2257.0   \n",
       "2020-10-19  1322.0   7452.0   6110.0   5854.0   20763.0   8035.0   2644.0   \n",
       "2020-10-26  2166.0  11592.0   7130.0   7074.0   30219.0  11308.0   4078.0   \n",
       "2020-11-02  2716.0   9513.0   6914.0   9211.0   29618.0  15715.0   5759.0   \n",
       "2020-11-09  3239.0  10609.0   9170.0  11581.0   41223.0  25028.0   7605.0   \n",
       "2020-11-16  4071.0  14028.0  11537.0  17234.0   57384.0  34597.0  11821.0   \n",
       "2020-11-23  3932.0  15812.0  11842.0  25433.0   81135.0  37795.0  13456.0   \n",
       "2020-11-30  4443.0  15860.0  11169.0  24514.0  102598.0  32762.0  10555.0   \n",
       "2020-12-07  4903.0  23381.0  14683.0  39047.0  153467.0  34561.0  18549.0   \n",
       "2020-12-14  3908.0  24904.0  15015.0  54426.0  218609.0  26619.0  18148.0   \n",
       "2020-12-21  2383.0  27509.0  16050.0  41118.0  307304.0  18576.0  13385.0   \n",
       "2020-12-28  1839.0  21699.0  13421.0  43099.0  263628.0  14576.0  13823.0   \n",
       "\n",
       "                DC      DE       FL  ...      SD       TN        TX       UT  \\\n",
       "date                                 ...                                       \n",
       "2020-02-03     0.0     1.0      0.0  ...     0.0      0.0       0.0      0.0   \n",
       "2020-02-10     0.0     2.0      0.0  ...     0.0      0.0       0.0      0.0   \n",
       "2020-02-17     0.0     2.0      0.0  ...     0.0      0.0       0.0      0.0   \n",
       "2020-02-24     0.0     2.0      0.0  ...     0.0      0.0       0.0      0.0   \n",
       "2020-03-02     0.0     0.0      2.0  ...     0.0      0.0       0.0      0.0   \n",
       "2020-03-09     2.0     0.0     16.0  ...     0.0      0.0      12.0      1.0   \n",
       "2020-03-16    20.0     7.0    138.0  ...    10.0     10.0      44.0     28.0   \n",
       "2020-03-23   115.0    58.0   1065.0  ...    18.0    495.0     231.0    251.0   \n",
       "2020-03-30   358.0   245.0   4408.0  ...    73.0   1037.0    2587.0    526.0   \n",
       "2020-04-06   602.0   475.0   7585.0  ...   187.0   2117.0    4399.0    910.0   \n",
       "2020-04-13   858.0   921.0   6979.0  ...   580.0   1730.0    6633.0    676.0   \n",
       "2020-04-20   972.0  1097.0   5966.0  ...   817.0   1721.0    5552.0    867.0   \n",
       "2020-04-27   965.0  1448.0   5545.0  ...   560.0   2556.0    5839.0   1048.0   \n",
       "2020-05-04  1278.0  1310.0   4489.0  ...   423.0   3516.0    7035.0   1099.0   \n",
       "2020-05-11  1219.0  1498.0   3991.0  ...   946.0   1836.0    7537.0    989.0   \n",
       "2020-05-18   881.0  1104.0   5238.0  ...   413.0   2753.0    8824.0   1064.0   \n",
       "2020-05-25   955.0   820.0   5146.0  ...   559.0   2451.0    7278.0   1125.0   \n",
       "2020-06-01   632.0   638.0   5239.0  ...   448.0   3051.0    8909.0   1517.0   \n",
       "2020-06-08   532.0   396.0   8321.0  ...   437.0   3228.0   10736.0   2328.0   \n",
       "2020-06-15   410.0   388.0  13687.0  ...   457.0   3793.0   13492.0   2397.0   \n",
       "2020-06-22   259.0   397.0  23612.0  ...   398.0   4547.0   25773.0   3309.0   \n",
       "2020-06-29   234.0   666.0  48535.0  ...   390.0   5434.0   38130.0   4128.0   \n",
       "2020-07-06   223.0   851.0  59914.0  ...   389.0  10877.0   47546.0   3741.0   \n",
       "2020-07-13   391.0   891.0  76760.0  ...   419.0  11915.0   63756.0   4718.0   \n",
       "2020-07-20   433.0   692.0  76510.0  ...   419.0  14570.0   68121.0   4362.0   \n",
       "2020-07-27   519.0   767.0  70503.0  ...   501.0  16021.0   53489.0   3831.0   \n",
       "2020-08-03   455.0   668.0  53915.0  ...   576.0  14060.0   56091.0   3238.0   \n",
       "2020-08-10   494.0   474.0  44277.0  ...   643.0  13014.0   48803.0   2853.0   \n",
       "2020-08-17   466.0   511.0  36154.0  ...   697.0  11112.0   52133.0   2481.0   \n",
       "2020-08-24   366.0   471.0  24946.0  ...  1065.0  10106.0   37434.0   2566.0   \n",
       "2020-08-31   353.0   651.0  24465.0  ...  2084.0  10075.0   32585.0   2739.0   \n",
       "2020-09-07   323.0   697.0  18770.0  ...  1791.0  10229.0   27401.0   2951.0   \n",
       "2020-09-14   307.0   692.0  18268.0  ...  1501.0   8427.0   23034.0   3540.0   \n",
       "2020-09-21   356.0   681.0  18630.0  ...  2068.0  10994.0   34983.0   5111.0   \n",
       "2020-09-28   286.0   732.0  16536.0  ...  2869.0   9406.0   40835.0   7048.0   \n",
       "2020-10-05   283.0   958.0  15795.0  ...  2860.0   8763.0   30081.0   7281.0   \n",
       "2020-10-12   475.0   948.0  18209.0  ...  4327.0  14216.0   25823.0   8109.0   \n",
       "2020-10-19   373.0   909.0  21336.0  ...  4911.0  13443.0   33401.0   8730.0   \n",
       "2020-10-26   417.0   944.0  25682.0  ...  5905.0  18277.0   38548.0  10521.0   \n",
       "2020-11-02   626.0  1127.0  29906.0  ...  8109.0  13939.0  110710.0  11623.0   \n",
       "2020-11-09   649.0  1552.0  34832.0  ...  8461.0  21972.0   61179.0  17162.0   \n",
       "2020-11-16   977.0  2273.0  44342.0  ...  9967.0  28019.0   77266.0  20911.0   \n",
       "2020-11-23  1226.0  2999.0  54578.0  ...  7570.0  28054.0   85027.0  23641.0   \n",
       "2020-11-30  1262.0  3426.0  53444.0  ...  6616.0  27143.0   77175.0  16286.0   \n",
       "2020-12-07  1767.0  5055.0  64630.0  ...  6036.0  32250.0  106372.0  21932.0   \n",
       "2020-12-14  1719.0  5818.0  69233.0  ...  4854.0  55834.0   97337.0  18234.0   \n",
       "2020-12-21  1702.0  4735.0  77384.0  ...  3720.0  64380.0  109807.0  16911.0   \n",
       "2020-12-28  1602.0  4504.0  67592.0  ...  2583.0  40264.0   91478.0  13807.0   \n",
       "\n",
       "                 VA     VT       WA       WI      WV      WY  \n",
       "date                                                          \n",
       "2020-02-03      0.0    0.0      0.0      0.0     0.0     0.0  \n",
       "2020-02-10      0.0    0.0      0.0      0.0     0.0     0.0  \n",
       "2020-02-17      0.0    0.0      0.0      0.0     0.0     0.0  \n",
       "2020-02-24      0.0    0.0      0.0      0.0     0.0     0.0  \n",
       "2020-03-02      0.0    0.0      0.0      0.0     0.0     0.0  \n",
       "2020-03-09      2.0    1.0    153.0      1.0     0.0     0.0  \n",
       "2020-03-16     49.0    7.0    656.0     52.0     0.0     3.0  \n",
       "2020-03-23    203.0   60.0   1212.0    363.0    20.0    23.0  \n",
       "2020-03-30    766.0  168.0   2553.0    805.0   125.0    69.0  \n",
       "2020-04-06   1858.0  274.0   3222.0   1219.0   200.0   117.0  \n",
       "2020-04-13   2869.0  191.0   2303.0    988.0   281.0   161.0  \n",
       "2020-04-20   3243.0   55.0   1899.0   1071.0   276.0    55.0  \n",
       "2020-04-27   4545.0   31.0   1706.0   1582.0   175.0    92.0  \n",
       "2020-05-04   5957.0   42.0   1855.0   2155.0   147.0    76.0  \n",
       "2020-05-11   5578.0   23.0   1681.0   2182.0   145.0    73.0  \n",
       "2020-05-18   6070.0   12.0   1435.0   2269.0   133.0    97.0  \n",
       "2020-05-25   6587.0   22.0   1455.0   2897.0   280.0    77.0  \n",
       "2020-06-01   7671.0   21.0   1863.0   2959.0   246.0    67.0  \n",
       "2020-06-08   5853.0   84.0   1997.0   2495.0   133.0    50.0  \n",
       "2020-06-15   3635.0   50.0   2096.0   4442.0   161.0   119.0  \n",
       "2020-06-22   3579.0   36.0   2725.0   2358.0   249.0   151.0  \n",
       "2020-06-29   3724.0   31.0   3204.0   3195.0   299.0   220.0  \n",
       "2020-07-06   3913.0   41.0   4659.0   4197.0   572.0   225.0  \n",
       "2020-07-13   5540.0   45.0   4881.0   5152.0   871.0   228.0  \n",
       "2020-07-20   6733.0   54.0   5958.0   6293.0   829.0   284.0  \n",
       "2020-07-27   7697.0   40.0   5513.0   6606.0   912.0   333.0  \n",
       "2020-08-03   7034.0   21.0   5670.0   6120.0   919.0   328.0  \n",
       "2020-08-10   7643.0   31.0   4872.0   5955.0   781.0   194.0  \n",
       "2020-08-17   6672.0   58.0   4193.0   5359.0   878.0   289.0  \n",
       "2020-08-24   6209.0   36.0   3913.0   4904.0   680.0   272.0  \n",
       "2020-08-31   6964.0   50.0   3344.0   4949.0   938.0   239.0  \n",
       "2020-09-07   6977.0   31.0   3163.0   6360.0  1325.0   190.0  \n",
       "2020-09-14   7000.0   44.0   2717.0   8569.0  1245.0   360.0  \n",
       "2020-09-21   6567.0   24.0   2907.0  13091.0  1351.0   552.0  \n",
       "2020-09-28   5455.0   21.0   3947.0  15629.0  1341.0   810.0  \n",
       "2020-10-05   5964.0   64.0   3829.0  17438.0  1230.0   875.0  \n",
       "2020-10-12   7013.0   54.0   4271.0  18676.0  1539.0  1173.0  \n",
       "2020-10-19   7258.0   69.0   4557.0  22811.0  2012.0  1509.0  \n",
       "2020-10-26   7447.0  139.0   5089.0  28786.0  1930.0  2166.0  \n",
       "2020-11-02   9143.0  134.0   6119.0  33000.0  3012.0  2690.0  \n",
       "2020-11-09  10059.0  216.0   9421.0  41452.0  3570.0  3843.0  \n",
       "2020-11-16  11160.0  620.0  13727.0  48182.0  5655.0  5183.0  \n",
       "2020-11-23  16401.0  677.0  15029.0  45131.0  6654.0  6238.0  \n",
       "2020-11-30  16797.0  460.0  18941.0  32037.0  6728.0  3874.0  \n",
       "2020-12-07  21035.0  752.0  17031.0  31659.0  8286.0  3680.0  \n",
       "2020-12-14  26279.0  713.0  23549.0  27896.0  8266.0  2790.0  \n",
       "2020-12-21  25741.0  648.0  15917.0  23068.0  8943.0  2343.0  \n",
       "2020-12-28  25285.0  544.0  12829.0  15784.0  8099.0  1586.0  \n",
       "\n",
       "[48 rows x 53 columns]"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "covid"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6188eae7",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "**Question:** Can we predict, say, Oregon's case counts\n",
    "using the other states?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "9e19935e",
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.linear_model import LinearRegression as lm\n",
    "other_states = covid.loc[:,covid.columns != \"OR\"]\n",
    "obs_OR = covid.loc[:,\"OR\"]\n",
    "OR_fit = lm().fit(other_states, obs_OR)\n",
    "est_OR = OR_fit.predict(other_states)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "4404ae71",
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1500x800 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(covid.index, obs_OR, label=\"observed\")\n",
    "plt.plot(covid.index, est_OR, label=\"estimated\", linestyle=\"--\")\n",
    "plt.legend(); plt.xlabel(\"date\"); plt.ylabel(\"OR case counts\");"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6bd16937",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Gee, we can predict the case counts *perfectly*?\n",
    "Does that seem very likely? What's going on?"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8f599ead",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Let's think about what we're trying to do here.\n",
    "We're trying to find coefficients $b_1, \\ldots, b_k$\n",
    "so that the the linear combination of the columns of $X$\n",
    "$$  \\hat y = b_1 X_{\\cdot 1} + \\cdots + b_k X_{\\cdot k} $$\n",
    "is as close to $y$ as possible."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9d270f78",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Well, when is it possible to find $b$ so that $\\hat y = y$?\n",
    "It is possible if $y$ is in the column space of $X$.\n",
    "\n",
    "Recall that $X$ is an $n \\times k$ matrix.\n",
    "If $n \\le k$ then the columns of $X$ span then *entire* space $\\mathbb{R}^n$\n",
    "(unless for instance some columns are identical)."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "edd74bd2",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "*Takeaway:* if you have more variables than observations\n",
    "(the problem is *singular* and)\n",
    "it is always possible to *exactly* predict the response.\n",
    "\n",
    "*However,* these predictions are unlikely to be *generalizable*."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "40db9c8d",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Crossvalidation"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "259b8fcf",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "How to tell how good your model is?\n",
    "\n",
    "*See how well it predicts \"new\" data.*"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2119178a",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "To do $k$-fold crossvalidation:\n",
    "\n",
    "1. Split your dataset into $k$ chunks (these should be independent!), and\n",
    "2. for each chunk in turn, put it aside for \"testing\"\n",
    "    and train your model on the remaining $k-1$ chunks.\n",
    "3. Compare \"test error\" to \"training error\".\n",
    "\n",
    "Predictions for data used to fit the model (\"training error\")\n",
    "should not be much further off than for data held out (\"test error\")."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a0844f33",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "This can be used either as an indication of *overfitting*\n",
    "or to compare different models to each other."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2effe8f5",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Crossvalidation set-up"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "24d48de8",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Here's a pretty 'easy' prediction problem:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "aa6d5ddc",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1500x800 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n = 100\n",
    "x = np.array([\n",
    "    rng.uniform(low=0, high=10, size=n),\n",
    "    rng.normal(size=n),\n",
    "]).T\n",
    "y = 2.5 + 1.5 * x[:,0] - 4.2 * x[:,1] + rng.normal(size=n)\n",
    "\n",
    "fig, (ax0, ax1) = plt.subplots(1, 2)\n",
    "ax0.scatter(x[:,0], y); ax0.set_xlabel(\"x0\"); ax0.set_ylabel(\"y\")\n",
    "ax1.scatter(x[:,1], y); ax1.set_xlabel(\"x1\"); ax1.set_ylabel(\"y\");"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ae605053",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Let's (a) fit a linear model\n",
    "and (b) do crossvalidation to look for evidence of overfitting."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "64c3c531",
   "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>test</th>\n",
       "      <th>train</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1.002842</td>\n",
       "      <td>1.102181</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1.280119</td>\n",
       "      <td>1.030386</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1.342009</td>\n",
       "      <td>1.017593</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1.042074</td>\n",
       "      <td>1.093432</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.939767</td>\n",
       "      <td>1.114522</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       test     train\n",
       "0  1.002842  1.102181\n",
       "1  1.280119  1.030386\n",
       "2  1.342009  1.017593\n",
       "3  1.042074  1.093432\n",
       "4  0.939767  1.114522"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def rmse(X, y, model):\n",
    "    # root mean squared error, comparing y\n",
    "    # to the value predicted by `model` using `x`\n",
    "    yhat = model.predict(X)\n",
    "    resids = y - yhat\n",
    "    return np.sqrt(np.mean(resids ** 2))\n",
    "\n",
    "def kfold(k, X, y, model):\n",
    "    # x: matrix, y: vector with same number of entries as rows of x\n",
    "    # model is something with .fit() and .predict() methods\n",
    "    n  = len(y)\n",
    "    folds = np.repeat(np.arange(k), np.ceil(n / k))[:n]\n",
    "    rng.shuffle(folds)\n",
    "    test_rmse = []\n",
    "    train_rmse = []\n",
    "    for ik in range(k):\n",
    "        test_X = X[folds == ik]\n",
    "        test_y = y[folds == ik]\n",
    "        train_X = X[folds != ik]\n",
    "        train_y = y[folds != ik]\n",
    "        model.fit(train_X, train_y)\n",
    "        test_rmse.append(rmse(test_X, test_y, model))\n",
    "        train_rmse.append(rmse(train_X, train_y, model))\n",
    "    return pd.DataFrame({\n",
    "        \"test\" : test_rmse,\n",
    "        \"train\" : train_rmse,\n",
    "    })\n",
    "\n",
    "crossval = kfold(5, x, y, lm())\n",
    "crossval"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2a92ef41-163b-45c6-a75c-3ae4142b457e",
   "metadata": {},
   "source": [
    "*Conclusion:* test error was higher than training error,\n",
    "but not much; there is (unsurprisingly) no evidence of (serious) overfitting."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "95f4dc05",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# When you've got too many variables"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c7f4ca9e",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "We're going to *add more variables* -\n",
    "these will be *independent* of everything else, so they should *not*\n",
    "give us meaningful predictive power for $y$.\n",
    "However, by chance each is a little correlated with $y$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "854326c0",
   "metadata": {},
   "outputs": [],
   "source": [
    "crossval = pd.DataFrame()\n",
    "for new_vars in np.linspace(0, 80, 9):\n",
    "    new_x = rng.normal(size=(n, int(new_vars)))\n",
    "    X = np.column_stack([x, new_x])\n",
    "    xval = kfold(5, X, y, lm())\n",
    "    xval[\"new_vars\"] = int(new_vars)\n",
    "    crossval = pd.concat([crossval, xval])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "2a4f739a",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/tmp/ipykernel_74939/268185597.py:1: FutureWarning: The provided callable <function mean at 0x7f29f98e0720> is currently using DataFrameGroupBy.mean. In a future version of pandas, the provided callable will be used directly. To keep current behavior pass the string \"mean\" instead.\n",
      "  crossval.groupby(\"new_vars\").agg(np.mean).plot();\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1500x800 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "crossval.groupby(\"new_vars\").agg(np.mean).plot();"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "12b56d9b-0180-49c0-ae07-e03677d05d69",
   "metadata": {},
   "source": [
    "*Conclusion:* as the number of variables increases, the training error decreases - even though we *know* there's no new information being added!\n",
    "The model is overfitting, which leads to increasing test (i.e., out-of-sample) error - the thing we generally care about."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2fa6bdde",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Regularization"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f65fabd2",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Recall that, somewhat mysteriously,\n",
    "scikit-learn's method to fit a Binomial GLM with a logistic link function\n",
    "[has a \"penalty\" option](https://scikit-learn.org/stable/modules/generated/sklearn.linear_model.LogisticRegression.html).\n",
    "What's that?\n",
    "\n",
    "Well, method finds $b$ to maximize the likelihood under the following model:\n",
    "$$ Y_i \\sim \\text{Binomial}(N, p(X_i \\cdot b)), $$\n",
    "where $p(\\cdot)$ is the logistic function.\n",
    "The terms in the log-likelihood that depend on $b$ are\n",
    "$$\n",
    "    \\sum_{i=1}^n \\left\\{\n",
    "        Y_i \\log(p(X_i \\cdot b)) + (N_i - Y_i) \\log(1 - p(X_i \\cdot b))\n",
    "    \\right\\} .\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4713898f",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "The problem we had above\n",
    "was that the variables that didn't matter\n",
    "had small but nonzero estimated parameters;\n",
    "and there were so many of them,\n",
    "that together they added up to something big.\n",
    "\n",
    "*Solution:* \"encourage\" them to be small."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8658c015",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "So, with a \"penalty\" the method instead maximizes the log-likelihood **minus**\n",
    "a \"regularization\" term that does the \"encouraging\".\n",
    "Options:\n",
    "$$\\begin{aligned}\n",
    "  \\sum_j |b_j| \\qquad & \\text{\"L1\" or \"$\\ell_1$\" or \"lasso\"}\\\\\n",
    "  \\sum_j b_j^2 \\qquad & \\text{\"L2\" or \"$\\ell_2$\" or \"ridge\" or \"Tikhonov\"}\n",
    "\\end{aligned}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "42b08b74-8d23-43e3-b658-57d307ba6988",
   "metadata": {},
   "source": [
    "```\n",
    "sklearn.linear_model.LogisticRegression(penalty=\"l1\")\n",
    "```\n",
    "therefore finds the $b$ that maximizes\n",
    "$$\n",
    "    \\sum_{i=1}^n \\left\\{\n",
    "        Y_i \\log(p(X_i \\cdot b)) + (N_i - Y_i) \\log(1 - p(X_i \\cdot b))\n",
    "    \\right\\}  - \\sum_j |b_j| .\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c2a88a5a-0b4a-47ea-9fe4-fccf16c738f4",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# The Lasso"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "25ebdf5a",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Let's try out this scheme on our example data, using [the Lasso](https://scikit-learn.org/stable/modules/generated/sklearn.linear_model.Lasso.html),\n",
    "which fits a standard least-squares linear model but with a L1 penalty, minimizing\n",
    "$$ \\sum_i (y_i - X_i \\cdot b)^2 + \\alpha \\sum_j |b_j| . $$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "dfa99130",
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.linear_model import Lasso\n",
    "\n",
    "ridge_crossval = pd.DataFrame()\n",
    "for new_vars in np.linspace(0, 80, 9):\n",
    "    new_x = rng.normal(size=(len(y), int(new_vars)))\n",
    "    X = np.column_stack([x, new_x])\n",
    "    xval = kfold(5, X, y, Lasso(alpha=.3))\n",
    "    xval[\"new_vars\"] = int(new_vars)\n",
    "    ridge_crossval = pd.concat([ridge_crossval, xval])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "57aafe5d",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/tmp/ipykernel_74939/3745485892.py:1: FutureWarning: The provided callable <function mean at 0x7f29f98e0720> is currently using DataFrameGroupBy.mean. In a future version of pandas, the provided callable will be used directly. To keep current behavior pass the string \"mean\" instead.\n",
      "  ridge_crossval.groupby(\"new_vars\").agg(np.mean).plot();\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1500x800 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ridge_crossval.groupby(\"new_vars\").agg(np.mean).plot();"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "87e963c6-228e-4040-a24e-460d3d8a3e48",
   "metadata": {},
   "source": [
    "Test error is still consistently higher than training error - as we'd expect - but only slightly."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4173181f",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Exercise"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3553056e",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Let's use *crossvalidation* to choose the *strength of regularization*\n",
    "(i.e., the $\\alpha$ parameter in the lasso).\n",
    "\n",
    "We'll apply it to the `covid` data above."
   ]
  }
 ],
 "metadata": {
  "celltoolbar": "Slideshow",
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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": "3.11.8"
  },
  "rise": {
   "scroll": true,
   "transition": "none"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}