ProphetDAG demo.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# ProphetDAG demo\n",
    "\n",
    "This notebook contains a simple demo of `ProphetDAG`. `ProphetDAG` helps you use Prophet for forecasting multiple variables at once - especially when you want to use the output of one forecast as a regressor column in another.\n",
    "\n",
    "Data set is daily Wikipedia pageviews for each page in the \"Signers of the US constitution\" category. Data from https://pageviews.toolforge.org/massviews/?project=en.wikipedia.org\n",
    "\n",
    "For this demo, we will forecast the total number of daily pageviews"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Title</th>\n",
       "      <th>2015-07-01</th>\n",
       "      <th>2015-07-02</th>\n",
       "      <th>2015-07-03</th>\n",
       "      <th>2015-07-04</th>\n",
       "      <th>2015-07-05</th>\n",
       "      <th>2015-07-06</th>\n",
       "      <th>2015-07-07</th>\n",
       "      <th>2015-07-08</th>\n",
       "      <th>2015-07-09</th>\n",
       "      <th>...</th>\n",
       "      <th>2020-10-04</th>\n",
       "      <th>2020-10-05</th>\n",
       "      <th>2020-10-06</th>\n",
       "      <th>2020-10-07</th>\n",
       "      <th>2020-10-08</th>\n",
       "      <th>2020-10-09</th>\n",
       "      <th>2020-10-10</th>\n",
       "      <th>2020-10-11</th>\n",
       "      <th>2020-10-12</th>\n",
       "      <th>2020-10-13</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Alexander Hamilton</td>\n",
       "      <td>4217</td>\n",
       "      <td>4218</td>\n",
       "      <td>4700</td>\n",
       "      <td>8999</td>\n",
       "      <td>7650</td>\n",
       "      <td>5187</td>\n",
       "      <td>4446</td>\n",
       "      <td>4815</td>\n",
       "      <td>5056</td>\n",
       "      <td>...</td>\n",
       "      <td>24151</td>\n",
       "      <td>18804</td>\n",
       "      <td>16400</td>\n",
       "      <td>17237</td>\n",
       "      <td>16606</td>\n",
       "      <td>18459</td>\n",
       "      <td>24045</td>\n",
       "      <td>26973</td>\n",
       "      <td>21599</td>\n",
       "      <td>19323</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>George Washington</td>\n",
       "      <td>9553</td>\n",
       "      <td>9766</td>\n",
       "      <td>11329</td>\n",
       "      <td>25459</td>\n",
       "      <td>21185</td>\n",
       "      <td>12457</td>\n",
       "      <td>10971</td>\n",
       "      <td>10665</td>\n",
       "      <td>9247</td>\n",
       "      <td>...</td>\n",
       "      <td>15012</td>\n",
       "      <td>16245</td>\n",
       "      <td>15998</td>\n",
       "      <td>16238</td>\n",
       "      <td>18156</td>\n",
       "      <td>16664</td>\n",
       "      <td>14343</td>\n",
       "      <td>15955</td>\n",
       "      <td>16133</td>\n",
       "      <td>16315</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Benjamin Franklin</td>\n",
       "      <td>10661</td>\n",
       "      <td>7308</td>\n",
       "      <td>7872</td>\n",
       "      <td>17024</td>\n",
       "      <td>13423</td>\n",
       "      <td>8802</td>\n",
       "      <td>8114</td>\n",
       "      <td>7259</td>\n",
       "      <td>8210</td>\n",
       "      <td>...</td>\n",
       "      <td>7231</td>\n",
       "      <td>8830</td>\n",
       "      <td>8943</td>\n",
       "      <td>9037</td>\n",
       "      <td>8864</td>\n",
       "      <td>8430</td>\n",
       "      <td>7167</td>\n",
       "      <td>7379</td>\n",
       "      <td>8569</td>\n",
       "      <td>8991</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>James Madison</td>\n",
       "      <td>2408</td>\n",
       "      <td>2971</td>\n",
       "      <td>4644</td>\n",
       "      <td>5789</td>\n",
       "      <td>5385</td>\n",
       "      <td>3234</td>\n",
       "      <td>2654</td>\n",
       "      <td>2493</td>\n",
       "      <td>2336</td>\n",
       "      <td>...</td>\n",
       "      <td>4732</td>\n",
       "      <td>5036</td>\n",
       "      <td>5343</td>\n",
       "      <td>4853</td>\n",
       "      <td>5311</td>\n",
       "      <td>5137</td>\n",
       "      <td>4457</td>\n",
       "      <td>4657</td>\n",
       "      <td>5197</td>\n",
       "      <td>5537</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Roger Sherman</td>\n",
       "      <td>252</td>\n",
       "      <td>4601</td>\n",
       "      <td>3414</td>\n",
       "      <td>1385</td>\n",
       "      <td>872</td>\n",
       "      <td>452</td>\n",
       "      <td>307</td>\n",
       "      <td>268</td>\n",
       "      <td>255</td>\n",
       "      <td>...</td>\n",
       "      <td>294</td>\n",
       "      <td>356</td>\n",
       "      <td>403</td>\n",
       "      <td>423</td>\n",
       "      <td>335</td>\n",
       "      <td>349</td>\n",
       "      <td>246</td>\n",
       "      <td>243</td>\n",
       "      <td>360</td>\n",
       "      <td>447</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5 rows × 1933 columns</p>\n",
       "</div>"
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      "text/plain": [
       "                Title  2015-07-01  2015-07-02  2015-07-03  2015-07-04  \\\n",
       "0  Alexander Hamilton        4217        4218        4700        8999   \n",
       "1   George Washington        9553        9766       11329       25459   \n",
       "2   Benjamin Franklin       10661        7308        7872       17024   \n",
       "3       James Madison        2408        2971        4644        5789   \n",
       "4       Roger Sherman         252        4601        3414        1385   \n",
       "\n",
       "   2015-07-05  2015-07-06  2015-07-07  2015-07-08  2015-07-09  ...  \\\n",
       "0        7650        5187        4446        4815        5056  ...   \n",
       "1       21185       12457       10971       10665        9247  ...   \n",
       "2       13423        8802        8114        7259        8210  ...   \n",
       "3        5385        3234        2654        2493        2336  ...   \n",
       "4         872         452         307         268         255  ...   \n",
       "\n",
       "   2020-10-04  2020-10-05  2020-10-06  2020-10-07  2020-10-08  2020-10-09  \\\n",
       "0       24151       18804       16400       17237       16606       18459   \n",
       "1       15012       16245       15998       16238       18156       16664   \n",
       "2        7231        8830        8943        9037        8864        8430   \n",
       "3        4732        5036        5343        4853        5311        5137   \n",
       "4         294         356         403         423         335         349   \n",
       "\n",
       "   2020-10-10  2020-10-11  2020-10-12  2020-10-13  \n",
       "0       24045       26973       21599       19323  \n",
       "1       14343       15955       16133       16315  \n",
       "2        7167        7379        8569        8991  \n",
       "3        4457        4657        5197        5537  \n",
       "4         246         243         360         447  \n",
       "\n",
       "[5 rows x 1933 columns]"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import pandas as pd\n",
    "raw = pd.read_csv(\"constitution-signatories-views.csv\")\n",
    "raw.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Irritatingly this has the pages as rows and the dates as columns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th>Title</th>\n",
       "      <th>Alexander Hamilton</th>\n",
       "      <th>George Washington</th>\n",
       "      <th>Benjamin Franklin</th>\n",
       "      <th>James Madison</th>\n",
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       "      <th>Gouverneur Morris</th>\n",
       "      <th>Rufus King</th>\n",
       "      <th>...</th>\n",
       "      <th>Daniel of St. Thomas Jenifer</th>\n",
       "      <th>George Read (American politician, born 1733)</th>\n",
       "      <th>Richard Dobbs Spaight</th>\n",
       "      <th>Thomas Fitzsimons</th>\n",
       "      <th>William Jackson (secretary)</th>\n",
       "      <th>Jacob Broom</th>\n",
       "      <th>David Brearley</th>\n",
       "      <th>Gunning Bedford Jr.</th>\n",
       "      <th>Richard Bassett (Delaware politician)</th>\n",
       "      <th>Template:United States Constitution signatories</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2015-07-01</th>\n",
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       "      <td>2408</td>\n",
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       "      <td>115</td>\n",
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       "    <tr>\n",
       "      <th>2015-07-02</th>\n",
       "      <td>4218</td>\n",
       "      <td>9766</td>\n",
       "      <td>7308</td>\n",
       "      <td>2971</td>\n",
       "      <td>4601</td>\n",
       "      <td>260</td>\n",
       "      <td>9</td>\n",
       "      <td>255</td>\n",
       "      <td>778</td>\n",
       "      <td>110</td>\n",
       "      <td>...</td>\n",
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       "      <td>0</td>\n",
       "      <td>0</td>\n",
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       "    <tr>\n",
       "      <th>2015-07-03</th>\n",
       "      <td>4700</td>\n",
       "      <td>11329</td>\n",
       "      <td>7872</td>\n",
       "      <td>4644</td>\n",
       "      <td>3414</td>\n",
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       "      <td>8</td>\n",
       "      <td>273</td>\n",
       "      <td>955</td>\n",
       "      <td>101</td>\n",
       "      <td>...</td>\n",
       "      <td>30</td>\n",
       "      <td>0</td>\n",
       "      <td>17</td>\n",
       "      <td>36</td>\n",
       "      <td>16</td>\n",
       "      <td>17</td>\n",
       "      <td>14</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2015-07-04</th>\n",
       "      <td>8999</td>\n",
       "      <td>25459</td>\n",
       "      <td>17024</td>\n",
       "      <td>5789</td>\n",
       "      <td>1385</td>\n",
       "      <td>776</td>\n",
       "      <td>138</td>\n",
       "      <td>838</td>\n",
       "      <td>460</td>\n",
       "      <td>168</td>\n",
       "      <td>...</td>\n",
       "      <td>45</td>\n",
       "      <td>0</td>\n",
       "      <td>40</td>\n",
       "      <td>42</td>\n",
       "      <td>22</td>\n",
       "      <td>45</td>\n",
       "      <td>25</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
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       "    <tr>\n",
       "      <th>2015-07-05</th>\n",
       "      <td>7650</td>\n",
       "      <td>21185</td>\n",
       "      <td>13423</td>\n",
       "      <td>5385</td>\n",
       "      <td>872</td>\n",
       "      <td>561</td>\n",
       "      <td>61</td>\n",
       "      <td>595</td>\n",
       "      <td>317</td>\n",
       "      <td>128</td>\n",
       "      <td>...</td>\n",
       "      <td>33</td>\n",
       "      <td>0</td>\n",
       "      <td>49</td>\n",
       "      <td>36</td>\n",
       "      <td>21</td>\n",
       "      <td>42</td>\n",
       "      <td>19</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
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       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
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       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2020-10-09</th>\n",
       "      <td>18459</td>\n",
       "      <td>16664</td>\n",
       "      <td>8430</td>\n",
       "      <td>5137</td>\n",
       "      <td>349</td>\n",
       "      <td>298</td>\n",
       "      <td>362</td>\n",
       "      <td>453</td>\n",
       "      <td>253</td>\n",
       "      <td>191</td>\n",
       "      <td>...</td>\n",
       "      <td>27</td>\n",
       "      <td>27</td>\n",
       "      <td>22</td>\n",
       "      <td>29</td>\n",
       "      <td>27</td>\n",
       "      <td>18</td>\n",
       "      <td>19</td>\n",
       "      <td>26</td>\n",
       "      <td>16</td>\n",
       "      <td>0</td>\n",
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       "    <tr>\n",
       "      <th>2020-10-10</th>\n",
       "      <td>24045</td>\n",
       "      <td>14343</td>\n",
       "      <td>7167</td>\n",
       "      <td>4457</td>\n",
       "      <td>246</td>\n",
       "      <td>210</td>\n",
       "      <td>269</td>\n",
       "      <td>293</td>\n",
       "      <td>205</td>\n",
       "      <td>159</td>\n",
       "      <td>...</td>\n",
       "      <td>19</td>\n",
       "      <td>26</td>\n",
       "      <td>16</td>\n",
       "      <td>19</td>\n",
       "      <td>19</td>\n",
       "      <td>10</td>\n",
       "      <td>6</td>\n",
       "      <td>11</td>\n",
       "      <td>12</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2020-10-11</th>\n",
       "      <td>26973</td>\n",
       "      <td>15955</td>\n",
       "      <td>7379</td>\n",
       "      <td>4657</td>\n",
       "      <td>243</td>\n",
       "      <td>245</td>\n",
       "      <td>282</td>\n",
       "      <td>357</td>\n",
       "      <td>220</td>\n",
       "      <td>179</td>\n",
       "      <td>...</td>\n",
       "      <td>19</td>\n",
       "      <td>27</td>\n",
       "      <td>16</td>\n",
       "      <td>14</td>\n",
       "      <td>15</td>\n",
       "      <td>19</td>\n",
       "      <td>11</td>\n",
       "      <td>22</td>\n",
       "      <td>19</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2020-10-12</th>\n",
       "      <td>21599</td>\n",
       "      <td>16133</td>\n",
       "      <td>8569</td>\n",
       "      <td>5197</td>\n",
       "      <td>360</td>\n",
       "      <td>290</td>\n",
       "      <td>349</td>\n",
       "      <td>668</td>\n",
       "      <td>285</td>\n",
       "      <td>217</td>\n",
       "      <td>...</td>\n",
       "      <td>32</td>\n",
       "      <td>33</td>\n",
       "      <td>14</td>\n",
       "      <td>29</td>\n",
       "      <td>18</td>\n",
       "      <td>10</td>\n",
       "      <td>25</td>\n",
       "      <td>27</td>\n",
       "      <td>26</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2020-10-13</th>\n",
       "      <td>19323</td>\n",
       "      <td>16315</td>\n",
       "      <td>8991</td>\n",
       "      <td>5537</td>\n",
       "      <td>447</td>\n",
       "      <td>339</td>\n",
       "      <td>440</td>\n",
       "      <td>923</td>\n",
       "      <td>315</td>\n",
       "      <td>206</td>\n",
       "      <td>...</td>\n",
       "      <td>26</td>\n",
       "      <td>47</td>\n",
       "      <td>20</td>\n",
       "      <td>31</td>\n",
       "      <td>13</td>\n",
       "      <td>22</td>\n",
       "      <td>16</td>\n",
       "      <td>29</td>\n",
       "      <td>24</td>\n",
       "      <td>0</td>\n",
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       "  </tbody>\n",
       "</table>\n",
       "<p>1932 rows × 41 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "Title      Alexander Hamilton George Washington Benjamin Franklin  \\\n",
       "2015-07-01               4217              9553             10661   \n",
       "2015-07-02               4218              9766              7308   \n",
       "2015-07-03               4700             11329              7872   \n",
       "2015-07-04               8999             25459             17024   \n",
       "2015-07-05               7650             21185             13423   \n",
       "...                       ...               ...               ...   \n",
       "2020-10-09              18459             16664              8430   \n",
       "2020-10-10              24045             14343              7167   \n",
       "2020-10-11              26973             15955              7379   \n",
       "2020-10-12              21599             16133              8569   \n",
       "2020-10-13              19323             16315              8991   \n",
       "\n",
       "Title      James Madison Roger Sherman Robert Morris (financier)  \\\n",
       "2015-07-01          2408           252                       269   \n",
       "2015-07-02          2971          4601                       260   \n",
       "2015-07-03          4644          3414                       327   \n",
       "2015-07-04          5789          1385                       776   \n",
       "2015-07-05          5385           872                       561   \n",
       "...                  ...           ...                       ...   \n",
       "2020-10-09          5137           349                       298   \n",
       "2020-10-10          4457           246                       210   \n",
       "2020-10-11          4657           243                       245   \n",
       "2020-10-12          5197           360                       290   \n",
       "2020-10-13          5537           447                       339   \n",
       "\n",
       "Title      John Dickinson John Rutledge Gouverneur Morris Rufus King  ...  \\\n",
       "2015-07-01             12           297               128        115  ...   \n",
       "2015-07-02              9           255               778        110  ...   \n",
       "2015-07-03              8           273               955        101  ...   \n",
       "2015-07-04            138           838               460        168  ...   \n",
       "2015-07-05             61           595               317        128  ...   \n",
       "...                   ...           ...               ...        ...  ...   \n",
       "2020-10-09            362           453               253        191  ...   \n",
       "2020-10-10            269           293               205        159  ...   \n",
       "2020-10-11            282           357               220        179  ...   \n",
       "2020-10-12            349           668               285        217  ...   \n",
       "2020-10-13            440           923               315        206  ...   \n",
       "\n",
       "Title      Daniel of St. Thomas Jenifer  \\\n",
       "2015-07-01                           27   \n",
       "2015-07-02                           19   \n",
       "2015-07-03                           30   \n",
       "2015-07-04                           45   \n",
       "2015-07-05                           33   \n",
       "...                                 ...   \n",
       "2020-10-09                           27   \n",
       "2020-10-10                           19   \n",
       "2020-10-11                           19   \n",
       "2020-10-12                           32   \n",
       "2020-10-13                           26   \n",
       "\n",
       "Title      George Read (American politician, born 1733) Richard Dobbs Spaight  \\\n",
       "2015-07-01                                            0                    25   \n",
       "2015-07-02                                            0                    16   \n",
       "2015-07-03                                            0                    17   \n",
       "2015-07-04                                            0                    40   \n",
       "2015-07-05                                            0                    49   \n",
       "...                                                 ...                   ...   \n",
       "2020-10-09                                           27                    22   \n",
       "2020-10-10                                           26                    16   \n",
       "2020-10-11                                           27                    16   \n",
       "2020-10-12                                           33                    14   \n",
       "2020-10-13                                           47                    20   \n",
       "\n",
       "Title      Thomas Fitzsimons William Jackson (secretary) Jacob Broom  \\\n",
       "2015-07-01                21                          16          20   \n",
       "2015-07-02                21                          22          15   \n",
       "2015-07-03                36                          16          17   \n",
       "2015-07-04                42                          22          45   \n",
       "2015-07-05                36                          21          42   \n",
       "...                      ...                         ...         ...   \n",
       "2020-10-09                29                          27          18   \n",
       "2020-10-10                19                          19          10   \n",
       "2020-10-11                14                          15          19   \n",
       "2020-10-12                29                          18          10   \n",
       "2020-10-13                31                          13          22   \n",
       "\n",
       "Title      David Brearley Gunning Bedford Jr.  \\\n",
       "2015-07-01             16                   0   \n",
       "2015-07-02             12                   0   \n",
       "2015-07-03             14                   0   \n",
       "2015-07-04             25                   0   \n",
       "2015-07-05             19                   0   \n",
       "...                   ...                 ...   \n",
       "2020-10-09             19                  26   \n",
       "2020-10-10              6                  11   \n",
       "2020-10-11             11                  22   \n",
       "2020-10-12             25                  27   \n",
       "2020-10-13             16                  29   \n",
       "\n",
       "Title      Richard Bassett (Delaware politician)  \\\n",
       "2015-07-01                                     0   \n",
       "2015-07-02                                     0   \n",
       "2015-07-03                                     0   \n",
       "2015-07-04                                     0   \n",
       "2015-07-05                                     0   \n",
       "...                                          ...   \n",
       "2020-10-09                                    16   \n",
       "2020-10-10                                    12   \n",
       "2020-10-11                                    19   \n",
       "2020-10-12                                    26   \n",
       "2020-10-13                                    24   \n",
       "\n",
       "Title      Template:United States Constitution signatories  \n",
       "2015-07-01                                               3  \n",
       "2015-07-02                                               0  \n",
       "2015-07-03                                               3  \n",
       "2015-07-04                                               2  \n",
       "2015-07-05                                               2  \n",
       "...                                                    ...  \n",
       "2020-10-09                                               0  \n",
       "2020-10-10                                               0  \n",
       "2020-10-11                                               1  \n",
       "2020-10-12                                               0  \n",
       "2020-10-13                                               0  \n",
       "\n",
       "[1932 rows x 41 columns]"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "transposed = raw.transpose(copy=True)\n",
    "transposed.columns = transposed.iloc[0]\n",
    "transposed = transposed.drop(['Title'], axis=0)\n",
    "transposed"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There are 41 pages in the category but some of them are much more important that others"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "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>pageviews</th>\n",
       "      <th>cumulative</th>\n",
       "      <th>cumulative_percentage</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Title</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Alexander Hamilton</th>\n",
       "      <td>39166341.0</td>\n",
       "      <td>39166341.0</td>\n",
       "      <td>0.409897</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>George Washington</th>\n",
       "      <td>26307376.0</td>\n",
       "      <td>65473717.0</td>\n",
       "      <td>0.685219</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Benjamin Franklin</th>\n",
       "      <td>16522462.0</td>\n",
       "      <td>81996179.0</td>\n",
       "      <td>0.858135</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>James Madison</th>\n",
       "      <td>7623497.0</td>\n",
       "      <td>89619676.0</td>\n",
       "      <td>0.937919</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Roger Sherman</th>\n",
       "      <td>656498.0</td>\n",
       "      <td>90276174.0</td>\n",
       "      <td>0.944790</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                     pageviews  cumulative  cumulative_percentage\n",
       "Title                                                            \n",
       "Alexander Hamilton  39166341.0  39166341.0               0.409897\n",
       "George Washington   26307376.0  65473717.0               0.685219\n",
       "Benjamin Franklin   16522462.0  81996179.0               0.858135\n",
       "James Madison        7623497.0  89619676.0               0.937919\n",
       "Roger Sherman         656498.0  90276174.0               0.944790"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "totals = pd.DataFrame({\"pageviews\":transposed.sum()})\n",
    "totals = totals.sort_values(by=\"pageviews\",ascending=False)\n",
    "totals['cumulative'] = totals[\"pageviews\"].cumsum()\n",
    "totals['cumulative_percentage'] = totals['cumulative']/totals['cumulative'].max()\n",
    "totals.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can cover >85% of the total with just three people.\n",
    "\n",
    "The big idea here is to build excellent individual forecast for those three - using specific events (like the launch of \"Hamilton\" the movie on Disney+) to make those forecasts as good as we can.\n",
    "\n",
    "Then we want to use the results of those three forecasts as input into our forecast of the total. When Benjamin Franklin is forecasted to have an increased number of pageviews this should increase the total too.\n",
    "\n",
    "Just adding the point estimate from those three forecasts as regressors in the forecast of the total can work well but uncertainties in the forecasted values won't be included then. The `ProphetDAG` class methods build the correct model for this to happen.\n",
    "\n",
    "First filter out the data we need:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "transposed['total'] = transposed.sum(axis=1)\n",
    "df = transposed[['Alexander Hamilton','George Washington','Benjamin Franklin','total']]\n",
    "df = df.reset_index()\n",
    "df = df.rename(columns={\"index\":\"ds\"})"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And import the necessary modules"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "from prophetDAG import ProphetDAG\n",
    "import networkx as nx\n",
    "from fbprophet import Prophet"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For `ProphetDAG` to work we need to describe the \"graph\" of dependencies between our variables.\n",
    "\n",
    "In this case it is fairly simple:\n",
    "1. Assume each of the signatories is independent of the others\n",
    "2. The total pageviews is dependent on all of them"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "graph = nx.DiGraph()\n",
    "graph.add_nodes_from([(1,{'name':'total'})\n",
    "                     ,(2,{'name':'Hamilton'})\n",
    "                     ,(3,{'name':'Washington'})\n",
    "                     ,(4,{'name':'Franklin'})])\n",
    "graph.add_edge(2,1)\n",
    "graph.add_edge(3,1)\n",
    "graph.add_edge(4,1)\n",
    "labels = nx.get_node_attributes(graph, 'name') \n",
    "nx.draw(graph, labels=labels, node_color='#00b4d9', font_weight='bold', node_size=2000)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next we must prepare the graph by adding data and a prophet model to each node.\n",
    "\n",
    "This is where you could get clever with adding extra regressors and seasonalities that would be specific for each signatory. But for this example we will keep it simple and just add US holidays and nothing else."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "history_dates = pd.to_datetime(pd.Series(df['ds'].unique(), name='ds')).sort_values()\n",
    "df['ds'] = pd.to_datetime(df['ds'])\n",
    "start = df['ds'].min()\n",
    "t_scale = df['ds'].max() - start\n",
    "total = df[['ds','total']].rename(columns={\"total\":\"y\"})\n",
    "hamilton = df[['ds','Alexander Hamilton']].rename(columns={\"Alexander Hamilton\":\"y\"})\n",
    "washington = df[['ds','George Washington']].rename(columns={\"George Washington\":\"y\"})\n",
    "franklin = df[['ds','Benjamin Franklin']].rename(columns={\"Benjamin Franklin\":\"y\"})\n",
    "\n",
    "for (i,d) in zip(graph.nodes,[total,hamilton,washington,franklin]):\n",
    "    graph.nodes[i]['df'] = d\n",
    "    m = Prophet()\n",
    "    m.add_country_holidays(country_name=\"US\")\n",
    "    m.history_dates = history_dates\n",
    "    m.start = start\n",
    "    m.t_scale = t_scale\n",
    "    future = m.make_future_dataframe(periods=365)\n",
    "    graph.nodes[i]['prophet'] = m\n",
    "    graph.nodes[i]['future'] = future\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now the graph is ready to be fitted. This can take a long time..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:fbprophet:Disabling daily seasonality. Run prophet with daily_seasonality=True to override this.\n",
      "INFO:fbprophet:Disabling daily seasonality. Run prophet with daily_seasonality=True to override this.\n",
      "INFO:fbprophet:Disabling daily seasonality. Run prophet with daily_seasonality=True to override this.\n",
      "INFO:fbprophet:Disabling daily seasonality. Run prophet with daily_seasonality=True to override this.\n",
      "INFO:pystan:COMPILING THE C++ CODE FOR MODEL anon_model_212810f865f60699dfc689ee4c288d14 NOW.\n"
     ]
    }
   ],
   "source": [
    "p = ProphetDAG()\n",
    "result = p.fit(graph)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The estimated forecast values for each node are in the `y_hat` attribute.\n",
    "\n",
    "You can also get 1000 samples for figuring out predictive intervals and the like from the `y_samples` key."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([104819.6502175 , 106554.30999696, 103974.5640673 , 106512.93026692,\n",
       "       111319.43028808, 115565.8098059 , 116123.94638747, 114868.13771192,\n",
       "       116835.07060756, 114296.62513599, 116682.23537505, 121144.600436  ,\n",
       "       124863.83181433, 124725.61390131, 122623.07783399, 123616.20192809,\n",
       "       120003.91035793, 121245.61333339, 124526.00740935, 127058.24986535,\n",
       "       125761.11371168, 122559.85421669, 122544.63097171, 118041.68705239,\n",
       "       118534.05663634, 121225.64518682, 123343.81820567, 121816.1231013 ,\n",
       "       121079.33441604, 118695.5528801 , 114507.92856597, 115477.1677434 ,\n",
       "       118788.26934415, 121645.24865772, 120948.57726642, 118596.61588929,\n",
       "       119644.86734899, 116378.2263554 , 118232.96528343, 122362.2615201 ,\n",
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       "       175923.28605021])"
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