├── .gitignore
├── 1.2 - Simpsons Paradox.ipynb
├── 1.3 - Probability and Statistics.ipynb
├── 1.4 - Graphs.ipynb
├── 1.5 - Structural Causal Models.ipynb
├── 2.2 - Chains and Forks.ipynb
├── 2.3 - Colliders.ipynb
├── 2.4 - d-separation.ipynb
├── 2.5 - Model Testing and Causal Search.ipynb
├── 3.1 - Interventions.ipynb
├── 3.2 - The Adjustment Formula.ipynb
├── 3.3 - Backdoor Criterion.ipynb
├── 3.4 - Front-Door Criterion.ipynb
├── 3.5 - Conditional Interventions and Covariate-Specific Effects.ipynb
├── 3.6 - Inverse Probability Weighing.ipynb
├── 3.7 - Mediation.ipynb
├── CausalModel.py
├── LICENSE
├── README.md
├── d4sci.mplstyle
├── dags
    ├── Causality.Fig.1.2.dot
    ├── Primer.Fig.1.10.dot
    ├── Primer.Fig.1.6.dot
    ├── Primer.Fig.1.7a.dot
    ├── Primer.Fig.1.8.dot
    ├── Primer.Fig.1.9.dot
    ├── Primer.Fig.2.1.dot
    ├── Primer.Fig.2.2.dot
    ├── Primer.Fig.2.3.dot
    ├── Primer.Fig.2.5.dot
    ├── Primer.Fig.2.6.dot
    ├── Primer.Fig.2.7.dot
    ├── Primer.Fig.2.8.dot
    ├── Primer.Fig.2.9.dot
    ├── Primer.Fig.3.1.dot
    ├── Primer.Fig.3.10b.dot
    ├── Primer.Fig.3.11.dot
    ├── Primer.Fig.3.12.dot
    ├── Primer.Fig.3.2.dot
    ├── Primer.Fig.3.3.dot
    ├── Primer.Fig.3.4.dot
    ├── Primer.Fig.3.5.dot
    ├── Primer.Fig.3.6.dot
    ├── Primer.Fig.3.7.dot
    ├── Primer.Fig.3.8.dot
    └── Primer.SCM.1.5.3.dot
├── data
    ├── D4Sci_logo_ball.png
    ├── D4Sci_logo_full.png
    ├── book2.jpeg
    ├── causality.jpeg
    ├── iris.csv
    └── newsletter.png
└── environment.yml


/.gitignore:
--------------------------------------------------------------------------------
  1 | figures/
  2 | # Byte-compiled / optimized / DLL files
  3 | __pycache__/
  4 | *.py[cod]
  5 | *$py.class
  6 | 
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 10 | # Distribution / packaging
 11 | .Python
 12 | build/
 13 | develop-eggs/
 14 | dist/
 15 | downloads/
 16 | eggs/
 17 | .eggs/
 18 | lib/
 19 | lib64/
 20 | parts/
 21 | sdist/
 22 | var/
 23 | wheels/
 24 | pip-wheel-metadata/
 25 | share/python-wheels/
 26 | *.egg-info/
 27 | .installed.cfg
 28 | *.egg
 29 | MANIFEST
 30 | 
 31 | # PyInstaller
 32 | #  Usually these files are written by a python script from a template
 33 | #  before PyInstaller builds the exe, so as to inject date/other infos into it.
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 35 | *.spec
 36 | 
 37 | # Installer logs
 38 | pip-log.txt
 39 | pip-delete-this-directory.txt
 40 | 
 41 | # Unit test / coverage reports
 42 | htmlcov/
 43 | .tox/
 44 | .nox/
 45 | .coverage
 46 | .coverage.*
 47 | .cache
 48 | nosetests.xml
 49 | coverage.xml
 50 | *.cover
 51 | *.py,cover
 52 | .hypothesis/
 53 | .pytest_cache/
 54 | 
 55 | # Translations
 56 | *.mo
 57 | *.pot
 58 | 
 59 | # Django stuff:
 60 | *.log
 61 | local_settings.py
 62 | db.sqlite3
 63 | db.sqlite3-journal
 64 | 
 65 | # Flask stuff:
 66 | instance/
 67 | .webassets-cache
 68 | 
 69 | # Scrapy stuff:
 70 | .scrapy
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 72 | # Sphinx documentation
 73 | docs/_build/
 74 | 
 75 | # PyBuilder
 76 | target/
 77 | 
 78 | # Jupyter Notebook
 79 | .ipynb_checkpoints
 80 | 
 81 | # IPython
 82 | profile_default/
 83 | ipython_config.py
 84 | 
 85 | # pyenv
 86 | .python-version
 87 | 
 88 | # pipenv
 89 | #   According to pypa/pipenv#598, it is recommended to include Pipfile.lock in version control.
 90 | #   However, in case of collaboration, if having platform-specific dependencies or dependencies
 91 | #   having no cross-platform support, pipenv may install dependencies that don't work, or not
 92 | #   install all needed dependencies.
 93 | #Pipfile.lock
 94 | 
 95 | # PEP 582; used by e.g. github.com/David-OConnor/pyflow
 96 | __pypackages__/
 97 | 
 98 | # Celery stuff
 99 | celerybeat-schedule
100 | celerybeat.pid
101 | 
102 | # SageMath parsed files
103 | *.sage.py
104 | 
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106 | .env
107 | .venv
108 | env/
109 | venv/
110 | ENV/
111 | env.bak/
112 | venv.bak/
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115 | .spyderproject
116 | .spyproject
117 | 
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119 | .ropeproject
120 | 
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122 | /site
123 | 
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125 | .mypy_cache/
126 | .dmypy.json
127 | dmypy.json
128 | 
129 | # Pyre type checker
130 | .pyre/
131 | 


--------------------------------------------------------------------------------
/1.3 - Probability and Statistics.ipynb:
--------------------------------------------------------------------------------
  1 | {
  2 |  "cells": [
  3 |   {
  4 |    "cell_type": "markdown",
  5 |    "metadata": {},
  6 |    "source": [
  7 |     "<div style=\"width: 100%; overflow: hidden;\">\n",
  8 |     "    <div style=\"width: 150px; float: left;\"> <img src=\"https://raw.githubusercontent.com/DataForScience/Networks/master/data/D4Sci_logo_ball.png\" alt=\"Data For Science, Inc\" align=\"left\" border=\"0\" width=150px> </div>\n",
  9 |     "    <div style=\"float: left; margin-left: 10px;\"> <h1>Causal Inference In Statistics - A Primer</h1>\n",
 10 |     "        <h1>1.3 Probability and Statistics</h1>\n",
 11 |     "        <p>Bruno Gonçalves<br/>\n",
 12 |     "        <a href=\"http://www.data4sci.com/\">www.data4sci.com</a><br/>\n",
 13 |     "            @bgoncalves, @data4sci</p></div>\n",
 14 |     "    <div style=\"float: right; margin-right:10px;\"> <p><a href=\"https://amzn.to/3gsFlkO\" target=_blank><img src='data/causality.jpeg' width='100px'>\n",
 15 |     "        <!--Amazon Affiliate Link--></a></p></div>\n",
 16 |     "</div>"
 17 |    ]
 18 |   },
 19 |   {
 20 |    "cell_type": "code",
 21 |    "execution_count": 1,
 22 |    "metadata": {},
 23 |    "outputs": [],
 24 |    "source": [
 25 |     "from collections import Counter\n",
 26 |     "from pprint import pprint\n",
 27 |     "\n",
 28 |     "import pandas as pd\n",
 29 |     "import numpy as np\n",
 30 |     "import matplotlib.pyplot as plt \n",
 31 |     "\n",
 32 |     "import watermark\n",
 33 |     "\n",
 34 |     "%load_ext watermark\n",
 35 |     "%matplotlib inline"
 36 |    ]
 37 |   },
 38 |   {
 39 |    "cell_type": "markdown",
 40 |    "metadata": {},
 41 |    "source": [
 42 |     "We start by print out the versions of the libraries we're using for future reference"
 43 |    ]
 44 |   },
 45 |   {
 46 |    "cell_type": "code",
 47 |    "execution_count": 2,
 48 |    "metadata": {},
 49 |    "outputs": [
 50 |     {
 51 |      "name": "stdout",
 52 |      "output_type": "stream",
 53 |      "text": [
 54 |       "watermark 2.0.2\n",
 55 |       "json      2.0.9\n",
 56 |       "numpy     1.18.1\n",
 57 |       "autopep8  1.5\n",
 58 |       "pandas    1.0.1\n",
 59 |       "Fri Jul 24 2020 \n",
 60 |       "\n",
 61 |       "CPython 3.7.3\n",
 62 |       "IPython 6.2.1\n",
 63 |       "\n",
 64 |       "compiler   : Clang 4.0.1 (tags/RELEASE_401/final)\n",
 65 |       "system     : Darwin\n",
 66 |       "release    : 19.5.0\n",
 67 |       "machine    : x86_64\n",
 68 |       "processor  : i386\n",
 69 |       "CPU cores  : 8\n",
 70 |       "interpreter: 64bit\n",
 71 |       "Git hash   : 7bb21d92754ca48aa8a201cf2e70b750085be46b\n"
 72 |      ]
 73 |     }
 74 |    ],
 75 |    "source": [
 76 |     "%watermark -n -v -m -g -iv"
 77 |    ]
 78 |   },
 79 |   {
 80 |    "cell_type": "markdown",
 81 |    "metadata": {},
 82 |    "source": [
 83 |     "Load default figure style"
 84 |    ]
 85 |   },
 86 |   {
 87 |    "cell_type": "code",
 88 |    "execution_count": 3,
 89 |    "metadata": {},
 90 |    "outputs": [],
 91 |    "source": [
 92 |     "plt.style.use('./d4sci.mplstyle')"
 93 |    ]
 94 |   },
 95 |   {
 96 |    "cell_type": "markdown",
 97 |    "metadata": {},
 98 |    "source": [
 99 |     "## Probability"
100 |    ]
101 |   },
102 |   {
103 |    "cell_type": "code",
104 |    "execution_count": 4,
105 |    "metadata": {},
106 |    "outputs": [],
107 |    "source": [
108 |     "data = pd.DataFrame({\n",
109 |     "    'Gender': ['Male', 'Male', 'Male', 'Male', 'Female', 'Female', 'Female', 'Female'],\n",
110 |     "    'Education': ['No High School', 'High School', 'College', 'Grad School', 'No High School', 'High School', 'College', 'Grad School'],\n",
111 |     "    'Occurrence': [112, 231, 595, 242, 136, 189, 763, 172]\n",
112 |     "})"
113 |    ]
114 |   },
115 |   {
116 |    "cell_type": "code",
117 |    "execution_count": 5,
118 |    "metadata": {},
119 |    "outputs": [],
120 |    "source": [
121 |     "data.set_index(['Gender', 'Education'], inplace=True)"
122 |    ]
123 |   },
124 |   {
125 |    "cell_type": "code",
126 |    "execution_count": 6,
127 |    "metadata": {},
128 |    "outputs": [
129 |     {
130 |      "data": {
131 |       "text/plain": [
132 |        "Occurrence    2440\n",
133 |        "dtype: int64"
134 |       ]
135 |      },
136 |      "execution_count": 6,
137 |      "metadata": {},
138 |      "output_type": "execute_result"
139 |     }
140 |    ],
141 |    "source": [
142 |     "data.sum()"
143 |    ]
144 |   },
145 |   {
146 |    "cell_type": "code",
147 |    "execution_count": 7,
148 |    "metadata": {},
149 |    "outputs": [],
150 |    "source": [
151 |     "P = data/data.sum()"
152 |    ]
153 |   },
154 |   {
155 |    "cell_type": "code",
156 |    "execution_count": 8,
157 |    "metadata": {},
158 |    "outputs": [
159 |     {
160 |      "data": {
161 |       "text/html": [
162 |        "<div>\n",
163 |        "<style scoped>\n",
164 |        "    .dataframe tbody tr th:only-of-type {\n",
165 |        "        vertical-align: middle;\n",
166 |        "    }\n",
167 |        "\n",
168 |        "    .dataframe tbody tr th {\n",
169 |        "        vertical-align: top;\n",
170 |        "    }\n",
171 |        "\n",
172 |        "    .dataframe thead th {\n",
173 |        "        text-align: right;\n",
174 |        "    }\n",
175 |        "</style>\n",
176 |        "<table border=\"1\" class=\"dataframe\">\n",
177 |        "  <thead>\n",
178 |        "    <tr style=\"text-align: right;\">\n",
179 |        "      <th></th>\n",
180 |        "      <th></th>\n",
181 |        "      <th>Occurrence</th>\n",
182 |        "    </tr>\n",
183 |        "    <tr>\n",
184 |        "      <th>Gender</th>\n",
185 |        "      <th>Education</th>\n",
186 |        "      <th></th>\n",
187 |        "    </tr>\n",
188 |        "  </thead>\n",
189 |        "  <tbody>\n",
190 |        "    <tr>\n",
191 |        "      <th rowspan=\"4\" valign=\"top\">Male</th>\n",
192 |        "      <th>No High School</th>\n",
193 |        "      <td>0.045902</td>\n",
194 |        "    </tr>\n",
195 |        "    <tr>\n",
196 |        "      <th>High School</th>\n",
197 |        "      <td>0.094672</td>\n",
198 |        "    </tr>\n",
199 |        "    <tr>\n",
200 |        "      <th>College</th>\n",
201 |        "      <td>0.243852</td>\n",
202 |        "    </tr>\n",
203 |        "    <tr>\n",
204 |        "      <th>Grad School</th>\n",
205 |        "      <td>0.099180</td>\n",
206 |        "    </tr>\n",
207 |        "    <tr>\n",
208 |        "      <th rowspan=\"4\" valign=\"top\">Female</th>\n",
209 |        "      <th>No High School</th>\n",
210 |        "      <td>0.055738</td>\n",
211 |        "    </tr>\n",
212 |        "    <tr>\n",
213 |        "      <th>High School</th>\n",
214 |        "      <td>0.077459</td>\n",
215 |        "    </tr>\n",
216 |        "    <tr>\n",
217 |        "      <th>College</th>\n",
218 |        "      <td>0.312705</td>\n",
219 |        "    </tr>\n",
220 |        "    <tr>\n",
221 |        "      <th>Grad School</th>\n",
222 |        "      <td>0.070492</td>\n",
223 |        "    </tr>\n",
224 |        "  </tbody>\n",
225 |        "</table>\n",
226 |        "</div>"
227 |       ],
228 |       "text/plain": [
229 |        "                       Occurrence\n",
230 |        "Gender Education                 \n",
231 |        "Male   No High School    0.045902\n",
232 |        "       High School       0.094672\n",
233 |        "       College           0.243852\n",
234 |        "       Grad School       0.099180\n",
235 |        "Female No High School    0.055738\n",
236 |        "       High School       0.077459\n",
237 |        "       College           0.312705\n",
238 |        "       Grad School       0.070492"
239 |       ]
240 |      },
241 |      "execution_count": 8,
242 |      "metadata": {},
243 |      "output_type": "execute_result"
244 |     }
245 |    ],
246 |    "source": [
247 |     "P"
248 |    ]
249 |   },
250 |   {
251 |    "cell_type": "code",
252 |    "execution_count": 9,
253 |    "metadata": {},
254 |    "outputs": [
255 |     {
256 |      "data": {
257 |       "text/plain": [
258 |        "Occurrence    0.172131\n",
259 |        "dtype: float64"
260 |       ]
261 |      },
262 |      "execution_count": 9,
263 |      "metadata": {},
264 |      "output_type": "execute_result"
265 |     }
266 |    ],
267 |    "source": [
268 |     "P.loc[(slice(None), 'High School'), :].sum()"
269 |    ]
270 |   },
271 |   {
272 |    "cell_type": "code",
273 |    "execution_count": 10,
274 |    "metadata": {},
275 |    "outputs": [
276 |     {
277 |      "data": {
278 |       "text/plain": [
279 |        "Occurrence    0.611066\n",
280 |        "dtype: float64"
281 |       ]
282 |      },
283 |      "execution_count": 10,
284 |      "metadata": {},
285 |      "output_type": "execute_result"
286 |     }
287 |    ],
288 |    "source": [
289 |     "P.loc['Female'].sum() + P.loc[(slice(None), 'High School'), :].sum() - P.loc[('Female', 'High School')]"
290 |    ]
291 |   },
292 |   {
293 |    "cell_type": "code",
294 |    "execution_count": 11,
295 |    "metadata": {},
296 |    "outputs": [
297 |     {
298 |      "data": {
299 |       "text/plain": [
300 |        "Occurrence    231\n",
301 |        "Name: (Male, High School), dtype: int64"
302 |       ]
303 |      },
304 |      "execution_count": 11,
305 |      "metadata": {},
306 |      "output_type": "execute_result"
307 |     }
308 |    ],
309 |    "source": [
310 |     "data.loc[('Male', 'High School')]"
311 |    ]
312 |   },
313 |   {
314 |    "cell_type": "code",
315 |    "execution_count": 12,
316 |    "metadata": {},
317 |    "outputs": [],
318 |    "source": [
319 |     "P_Female = data.loc['Female'].sum()/data.sum()"
320 |    ]
321 |   },
322 |   {
323 |    "cell_type": "code",
324 |    "execution_count": 13,
325 |    "metadata": {},
326 |    "outputs": [
327 |     {
328 |      "data": {
329 |       "text/plain": [
330 |        "Occurrence    0.611066\n",
331 |        "dtype: float64"
332 |       ]
333 |      },
334 |      "execution_count": 13,
335 |      "metadata": {},
336 |      "output_type": "execute_result"
337 |     }
338 |    ],
339 |    "source": [
340 |     "(data.loc[('Male', 'High School')] + data.loc['Female'].sum())/data.sum()"
341 |    ]
342 |   },
343 |   {
344 |    "cell_type": "code",
345 |    "execution_count": 14,
346 |    "metadata": {},
347 |    "outputs": [],
348 |    "source": [
349 |     "idx = pd.IndexSlice"
350 |    ]
351 |   },
352 |   {
353 |    "cell_type": "code",
354 |    "execution_count": 15,
355 |    "metadata": {},
356 |    "outputs": [
357 |     {
358 |      "data": {
359 |       "text/plain": [
360 |        "Occurrence    0.172131\n",
361 |        "dtype: float64"
362 |       ]
363 |      },
364 |      "execution_count": 15,
365 |      "metadata": {},
366 |      "output_type": "execute_result"
367 |     }
368 |    ],
369 |    "source": [
370 |     "data.loc[(slice(None), 'High School'), :].sum()/data.sum()"
371 |    ]
372 |   },
373 |   {
374 |    "cell_type": "code",
375 |    "execution_count": 16,
376 |    "metadata": {},
377 |    "outputs": [
378 |     {
379 |      "data": {
380 |       "text/plain": [
381 |        "Occurrence    0.077459\n",
382 |        "dtype: float64"
383 |       ]
384 |      },
385 |      "execution_count": 16,
386 |      "metadata": {},
387 |      "output_type": "execute_result"
388 |     }
389 |    ],
390 |    "source": [
391 |     "data.loc[('Female', 'High School')]/data.sum()"
392 |    ]
393 |   },
394 |   {
395 |    "cell_type": "code",
396 |    "execution_count": 17,
397 |    "metadata": {},
398 |    "outputs": [],
399 |    "source": [
400 |     "table = pd.pivot_table(data.reset_index(), index='Gender', columns='Education')"
401 |    ]
402 |   },
403 |   {
404 |    "cell_type": "code",
405 |    "execution_count": 18,
406 |    "metadata": {},
407 |    "outputs": [
408 |     {
409 |      "data": {
410 |       "text/html": [
411 |        "<div>\n",
412 |        "<style scoped>\n",
413 |        "    .dataframe tbody tr th:only-of-type {\n",
414 |        "        vertical-align: middle;\n",
415 |        "    }\n",
416 |        "\n",
417 |        "    .dataframe tbody tr th {\n",
418 |        "        vertical-align: top;\n",
419 |        "    }\n",
420 |        "\n",
421 |        "    .dataframe thead tr th {\n",
422 |        "        text-align: left;\n",
423 |        "    }\n",
424 |        "\n",
425 |        "    .dataframe thead tr:last-of-type th {\n",
426 |        "        text-align: right;\n",
427 |        "    }\n",
428 |        "</style>\n",
429 |        "<table border=\"1\" class=\"dataframe\">\n",
430 |        "  <thead>\n",
431 |        "    <tr>\n",
432 |        "      <th></th>\n",
433 |        "      <th colspan=\"4\" halign=\"left\">Occurrence</th>\n",
434 |        "    </tr>\n",
435 |        "    <tr>\n",
436 |        "      <th>Education</th>\n",
437 |        "      <th>College</th>\n",
438 |        "      <th>Grad School</th>\n",
439 |        "      <th>High School</th>\n",
440 |        "      <th>No High School</th>\n",
441 |        "    </tr>\n",
442 |        "    <tr>\n",
443 |        "      <th>Gender</th>\n",
444 |        "      <th></th>\n",
445 |        "      <th></th>\n",
446 |        "      <th></th>\n",
447 |        "      <th></th>\n",
448 |        "    </tr>\n",
449 |        "  </thead>\n",
450 |        "  <tbody>\n",
451 |        "    <tr>\n",
452 |        "      <th>Female</th>\n",
453 |        "      <td>763</td>\n",
454 |        "      <td>172</td>\n",
455 |        "      <td>189</td>\n",
456 |        "      <td>136</td>\n",
457 |        "    </tr>\n",
458 |        "    <tr>\n",
459 |        "      <th>Male</th>\n",
460 |        "      <td>595</td>\n",
461 |        "      <td>242</td>\n",
462 |        "      <td>231</td>\n",
463 |        "      <td>112</td>\n",
464 |        "    </tr>\n",
465 |        "  </tbody>\n",
466 |        "</table>\n",
467 |        "</div>"
468 |       ],
469 |       "text/plain": [
470 |        "          Occurrence                                       \n",
471 |        "Education    College Grad School High School No High School\n",
472 |        "Gender                                                     \n",
473 |        "Female           763         172         189            136\n",
474 |        "Male             595         242         231            112"
475 |       ]
476 |      },
477 |      "execution_count": 18,
478 |      "metadata": {},
479 |      "output_type": "execute_result"
480 |     }
481 |    ],
482 |    "source": [
483 |     "table"
484 |    ]
485 |   },
486 |   {
487 |    "cell_type": "code",
488 |    "execution_count": 19,
489 |    "metadata": {},
490 |    "outputs": [],
491 |    "source": [
492 |     "table.loc['Total'] = table.sum()\n",
493 |     "table['Total'] = table.sum(axis=1)"
494 |    ]
495 |   },
496 |   {
497 |    "cell_type": "code",
498 |    "execution_count": 20,
499 |    "metadata": {},
500 |    "outputs": [
501 |     {
502 |      "data": {
503 |       "text/html": [
504 |        "<div>\n",
505 |        "<style scoped>\n",
506 |        "    .dataframe tbody tr th:only-of-type {\n",
507 |        "        vertical-align: middle;\n",
508 |        "    }\n",
509 |        "\n",
510 |        "    .dataframe tbody tr th {\n",
511 |        "        vertical-align: top;\n",
512 |        "    }\n",
513 |        "\n",
514 |        "    .dataframe thead tr th {\n",
515 |        "        text-align: left;\n",
516 |        "    }\n",
517 |        "\n",
518 |        "    .dataframe thead tr:last-of-type th {\n",
519 |        "        text-align: right;\n",
520 |        "    }\n",
521 |        "</style>\n",
522 |        "<table border=\"1\" class=\"dataframe\">\n",
523 |        "  <thead>\n",
524 |        "    <tr>\n",
525 |        "      <th></th>\n",
526 |        "      <th colspan=\"4\" halign=\"left\">Occurrence</th>\n",
527 |        "      <th>Total</th>\n",
528 |        "    </tr>\n",
529 |        "    <tr>\n",
530 |        "      <th>Education</th>\n",
531 |        "      <th>College</th>\n",
532 |        "      <th>Grad School</th>\n",
533 |        "      <th>High School</th>\n",
534 |        "      <th>No High School</th>\n",
535 |        "      <th></th>\n",
536 |        "    </tr>\n",
537 |        "    <tr>\n",
538 |        "      <th>Gender</th>\n",
539 |        "      <th></th>\n",
540 |        "      <th></th>\n",
541 |        "      <th></th>\n",
542 |        "      <th></th>\n",
543 |        "      <th></th>\n",
544 |        "    </tr>\n",
545 |        "  </thead>\n",
546 |        "  <tbody>\n",
547 |        "    <tr>\n",
548 |        "      <th>Female</th>\n",
549 |        "      <td>763</td>\n",
550 |        "      <td>172</td>\n",
551 |        "      <td>189</td>\n",
552 |        "      <td>136</td>\n",
553 |        "      <td>1260</td>\n",
554 |        "    </tr>\n",
555 |        "    <tr>\n",
556 |        "      <th>Male</th>\n",
557 |        "      <td>595</td>\n",
558 |        "      <td>242</td>\n",
559 |        "      <td>231</td>\n",
560 |        "      <td>112</td>\n",
561 |        "      <td>1180</td>\n",
562 |        "    </tr>\n",
563 |        "    <tr>\n",
564 |        "      <th>Total</th>\n",
565 |        "      <td>1358</td>\n",
566 |        "      <td>414</td>\n",
567 |        "      <td>420</td>\n",
568 |        "      <td>248</td>\n",
569 |        "      <td>2440</td>\n",
570 |        "    </tr>\n",
571 |        "  </tbody>\n",
572 |        "</table>\n",
573 |        "</div>"
574 |       ],
575 |       "text/plain": [
576 |        "          Occurrence                                        Total\n",
577 |        "Education    College Grad School High School No High School      \n",
578 |        "Gender                                                           \n",
579 |        "Female           763         172         189            136  1260\n",
580 |        "Male             595         242         231            112  1180\n",
581 |        "Total           1358         414         420            248  2440"
582 |       ]
583 |      },
584 |      "execution_count": 20,
585 |      "metadata": {},
586 |      "output_type": "execute_result"
587 |     }
588 |    ],
589 |    "source": [
590 |     "table"
591 |    ]
592 |   },
593 |   {
594 |    "cell_type": "markdown",
595 |    "metadata": {},
596 |    "source": [
597 |     "<div style=\"width: 100%; overflow: hidden;\">\n",
598 |     "     <img src=\"data/D4Sci_logo_full.png\" alt=\"Data For Science, Inc\" align=\"center\" border=\"0\" width=300px> \n",
599 |     "</div>"
600 |    ]
601 |   }
602 |  ],
603 |  "metadata": {
604 |   "kernelspec": {
605 |    "display_name": "Python 3",
606 |    "language": "python",
607 |    "name": "python3"
608 |   },
609 |   "language_info": {
610 |    "codemirror_mode": {
611 |     "name": "ipython",
612 |     "version": 3
613 |    },
614 |    "file_extension": ".py",
615 |    "mimetype": "text/x-python",
616 |    "name": "python",
617 |    "nbconvert_exporter": "python",
618 |    "pygments_lexer": "ipython3",
619 |    "version": "3.8.5"
620 |   },
621 |   "toc": {
622 |    "base_numbering": 1,
623 |    "nav_menu": {},
624 |    "number_sections": true,
625 |    "sideBar": true,
626 |    "skip_h1_title": true,
627 |    "title_cell": "Table of Contents",
628 |    "title_sidebar": "Contents",
629 |    "toc_cell": false,
630 |    "toc_position": {},
631 |    "toc_section_display": true,
632 |    "toc_window_display": false
633 |   },
634 |   "varInspector": {
635 |    "cols": {
636 |     "lenName": 16,
637 |     "lenType": 16,
638 |     "lenVar": 40
639 |    },
640 |    "kernels_config": {
641 |     "python": {
642 |      "delete_cmd_postfix": "",
643 |      "delete_cmd_prefix": "del ",
644 |      "library": "var_list.py",
645 |      "varRefreshCmd": "print(var_dic_list())"
646 |     },
647 |     "r": {
648 |      "delete_cmd_postfix": ") ",
649 |      "delete_cmd_prefix": "rm(",
650 |      "library": "var_list.r",
651 |      "varRefreshCmd": "cat(var_dic_list()) "
652 |     }
653 |    },
654 |    "types_to_exclude": [
655 |     "module",
656 |     "function",
657 |     "builtin_function_or_method",
658 |     "instance",
659 |     "_Feature"
660 |    ],
661 |    "window_display": false
662 |   }
663 |  },
664 |  "nbformat": 4,
665 |  "nbformat_minor": 2
666 | }
667 | 


--------------------------------------------------------------------------------
/3.6 - Inverse Probability Weighing.ipynb:
--------------------------------------------------------------------------------
   1 | {
   2 |  "cells": [
   3 |   {
   4 |    "cell_type": "markdown",
   5 |    "metadata": {},
   6 |    "source": [
   7 |     "<div style=\"width: 100%; overflow: hidden;\">\n",
   8 |     "    <div style=\"width: 150px; float: left;\"> <img src=\"https://raw.githubusercontent.com/DataForScience/Networks/master/data/D4Sci_logo_ball.png\" alt=\"Data For Science, Inc\" align=\"left\" border=\"0\" width=150px> </div>\n",
   9 |     "    <div style=\"float: left; margin-left: 10px;\"> <h1>Causal Inference In Statistics - A Primer</h1>\n",
  10 |     "        <h1>3.6 Inverse Probability Weighing</h1>\n",
  11 |     "        <p>Bruno Gonçalves<br/>\n",
  12 |     "        <a href=\"http://www.data4sci.com/\">www.data4sci.com</a><br/>\n",
  13 |     "            @bgoncalves, @data4sci</p></div>\n",
  14 |     "    <div style=\"float: right; margin-right:10px;\"> <p><a href=\"https://amzn.to/3gsFlkO\" target=_blank><img src='data/causality.jpeg' width='100px'>\n",
  15 |     "        <!--Amazon Affiliate Link--></a></p></div>\n",
  16 |     "</div>"
  17 |    ]
  18 |   },
  19 |   {
  20 |    "cell_type": "code",
  21 |    "execution_count": 1,
  22 |    "metadata": {},
  23 |    "outputs": [],
  24 |    "source": [
  25 |     "from collections import Counter\n",
  26 |     "from pprint import pprint\n",
  27 |     "\n",
  28 |     "import pandas as pd\n",
  29 |     "import numpy as np\n",
  30 |     "\n",
  31 |     "import matplotlib\n",
  32 |     "import matplotlib.pyplot as plt \n",
  33 |     "\n",
  34 |     "from CausalModel import CausalModel\n",
  35 |     "\n",
  36 |     "import watermark\n",
  37 |     "\n",
  38 |     "%load_ext watermark\n",
  39 |     "%matplotlib inline"
  40 |    ]
  41 |   },
  42 |   {
  43 |    "cell_type": "markdown",
  44 |    "metadata": {},
  45 |    "source": [
  46 |     "We start by print out the versions of the libraries we're using for future reference"
  47 |    ]
  48 |   },
  49 |   {
  50 |    "cell_type": "code",
  51 |    "execution_count": 2,
  52 |    "metadata": {},
  53 |    "outputs": [
  54 |     {
  55 |      "name": "stdout",
  56 |      "output_type": "stream",
  57 |      "text": [
  58 |       "Python implementation: CPython\n",
  59 |       "Python version       : 3.8.5\n",
  60 |       "IPython version      : 7.19.0\n",
  61 |       "\n",
  62 |       "Compiler    : Clang 10.0.0 \n",
  63 |       "OS          : Darwin\n",
  64 |       "Release     : 20.2.0\n",
  65 |       "Machine     : x86_64\n",
  66 |       "Processor   : i386\n",
  67 |       "CPU cores   : 16\n",
  68 |       "Architecture: 64bit\n",
  69 |       "\n",
  70 |       "Git hash: 6ba5a323994ecc2dbeee8be27219dbf5207f8dfb\n",
  71 |       "\n",
  72 |       "numpy     : 1.19.2\n",
  73 |       "matplotlib: 3.3.2\n",
  74 |       "watermark : 2.1.0\n",
  75 |       "pandas    : 1.1.3\n",
  76 |       "\n"
  77 |      ]
  78 |     }
  79 |    ],
  80 |    "source": [
  81 |     "%watermark -n -v -m -g -iv"
  82 |    ]
  83 |   },
  84 |   {
  85 |    "cell_type": "markdown",
  86 |    "metadata": {},
  87 |    "source": [
  88 |     "Load default figure style"
  89 |    ]
  90 |   },
  91 |   {
  92 |    "cell_type": "code",
  93 |    "execution_count": 3,
  94 |    "metadata": {},
  95 |    "outputs": [],
  96 |    "source": [
  97 |     "plt.style.use('./d4sci.mplstyle')\n",
  98 |     "colors = plt.rcParams['axes.prop_cycle'].by_key()['color']"
  99 |    ]
 100 |   },
 101 |   {
 102 |    "cell_type": "markdown",
 103 |    "metadata": {},
 104 |    "source": [
 105 |     "We load the DAG from Fig 1.10 for ease of reference"
 106 |    ]
 107 |   },
 108 |   {
 109 |    "cell_type": "code",
 110 |    "execution_count": 4,
 111 |    "metadata": {},
 112 |    "outputs": [],
 113 |    "source": [
 114 |     "G = CausalModel('dags/Primer.Fig.1.10.dot')"
 115 |    ]
 116 |   },
 117 |   {
 118 |    "cell_type": "code",
 119 |    "execution_count": 5,
 120 |    "metadata": {},
 121 |    "outputs": [
 122 |     {
 123 |      "data": {
 124 |       "image/png": 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\n",
 125 |       "text/plain": [
 126 |        "<Figure size 660x660 with 1 Axes>"
 127 |       ]
 128 |      },
 129 |      "metadata": {},
 130 |      "output_type": "display_data"
 131 |     }
 132 |    ],
 133 |    "source": [
 134 |     "fig, ax = plt.subplots(1, figsize=(2.2,2.2))\n",
 135 |     "G.plot(ax=ax)"
 136 |    ]
 137 |   },
 138 |   {
 139 |    "cell_type": "markdown",
 140 |    "metadata": {},
 141 |    "source": [
 142 |     "In our example, the data for the joint probability $P\\left(X, Y, Z\\right)$ is:"
 143 |    ]
 144 |   },
 145 |   {
 146 |    "cell_type": "code",
 147 |    "execution_count": 6,
 148 |    "metadata": {},
 149 |    "outputs": [],
 150 |    "source": [
 151 |     "PXYZ = pd.DataFrame({\n",
 152 |     "    'X':    ['Yes',  'Yes',    'Yes',  'Yes',    'No',   'No',     'No',   'No'],\n",
 153 |     "    'Y':    ['Yes',  'Yes',    'No',   'No',     'Yes',  'Yes',    'No',   'No'],\n",
 154 |     "    'Z':    ['Male', 'Female', 'Male', 'Female', 'Male', 'Female', 'Male', 'Female'],\n",
 155 |     "    'Prob': [0.116,   0.274,    0.009,   0.101,    0.334,  0.079,    0.051,  0.036]\n",
 156 |     "})"
 157 |    ]
 158 |   },
 159 |   {
 160 |    "cell_type": "code",
 161 |    "execution_count": 7,
 162 |    "metadata": {},
 163 |    "outputs": [
 164 |     {
 165 |      "data": {
 166 |       "text/html": [
 167 |        "<div>\n",
 168 |        "<style scoped>\n",
 169 |        "    .dataframe tbody tr th:only-of-type {\n",
 170 |        "        vertical-align: middle;\n",
 171 |        "    }\n",
 172 |        "\n",
 173 |        "    .dataframe tbody tr th {\n",
 174 |        "        vertical-align: top;\n",
 175 |        "    }\n",
 176 |        "\n",
 177 |        "    .dataframe thead th {\n",
 178 |        "        text-align: right;\n",
 179 |        "    }\n",
 180 |        "</style>\n",
 181 |        "<table border=\"1\" class=\"dataframe\">\n",
 182 |        "  <thead>\n",
 183 |        "    <tr style=\"text-align: right;\">\n",
 184 |        "      <th></th>\n",
 185 |        "      <th>X</th>\n",
 186 |        "      <th>Y</th>\n",
 187 |        "      <th>Z</th>\n",
 188 |        "      <th>Prob</th>\n",
 189 |        "    </tr>\n",
 190 |        "  </thead>\n",
 191 |        "  <tbody>\n",
 192 |        "    <tr>\n",
 193 |        "      <th>0</th>\n",
 194 |        "      <td>Yes</td>\n",
 195 |        "      <td>Yes</td>\n",
 196 |        "      <td>Male</td>\n",
 197 |        "      <td>0.116</td>\n",
 198 |        "    </tr>\n",
 199 |        "    <tr>\n",
 200 |        "      <th>1</th>\n",
 201 |        "      <td>Yes</td>\n",
 202 |        "      <td>Yes</td>\n",
 203 |        "      <td>Female</td>\n",
 204 |        "      <td>0.274</td>\n",
 205 |        "    </tr>\n",
 206 |        "    <tr>\n",
 207 |        "      <th>2</th>\n",
 208 |        "      <td>Yes</td>\n",
 209 |        "      <td>No</td>\n",
 210 |        "      <td>Male</td>\n",
 211 |        "      <td>0.009</td>\n",
 212 |        "    </tr>\n",
 213 |        "    <tr>\n",
 214 |        "      <th>3</th>\n",
 215 |        "      <td>Yes</td>\n",
 216 |        "      <td>No</td>\n",
 217 |        "      <td>Female</td>\n",
 218 |        "      <td>0.101</td>\n",
 219 |        "    </tr>\n",
 220 |        "    <tr>\n",
 221 |        "      <th>4</th>\n",
 222 |        "      <td>No</td>\n",
 223 |        "      <td>Yes</td>\n",
 224 |        "      <td>Male</td>\n",
 225 |        "      <td>0.334</td>\n",
 226 |        "    </tr>\n",
 227 |        "    <tr>\n",
 228 |        "      <th>5</th>\n",
 229 |        "      <td>No</td>\n",
 230 |        "      <td>Yes</td>\n",
 231 |        "      <td>Female</td>\n",
 232 |        "      <td>0.079</td>\n",
 233 |        "    </tr>\n",
 234 |        "    <tr>\n",
 235 |        "      <th>6</th>\n",
 236 |        "      <td>No</td>\n",
 237 |        "      <td>No</td>\n",
 238 |        "      <td>Male</td>\n",
 239 |        "      <td>0.051</td>\n",
 240 |        "    </tr>\n",
 241 |        "    <tr>\n",
 242 |        "      <th>7</th>\n",
 243 |        "      <td>No</td>\n",
 244 |        "      <td>No</td>\n",
 245 |        "      <td>Female</td>\n",
 246 |        "      <td>0.036</td>\n",
 247 |        "    </tr>\n",
 248 |        "  </tbody>\n",
 249 |        "</table>\n",
 250 |        "</div>"
 251 |       ],
 252 |       "text/plain": [
 253 |        "     X    Y       Z   Prob\n",
 254 |        "0  Yes  Yes    Male  0.116\n",
 255 |        "1  Yes  Yes  Female  0.274\n",
 256 |        "2  Yes   No    Male  0.009\n",
 257 |        "3  Yes   No  Female  0.101\n",
 258 |        "4   No  Yes    Male  0.334\n",
 259 |        "5   No  Yes  Female  0.079\n",
 260 |        "6   No   No    Male  0.051\n",
 261 |        "7   No   No  Female  0.036"
 262 |       ]
 263 |      },
 264 |      "execution_count": 7,
 265 |      "metadata": {},
 266 |      "output_type": "execute_result"
 267 |     }
 268 |    ],
 269 |    "source": [
 270 |     "PXYZ"
 271 |    ]
 272 |   },
 273 |   {
 274 |    "cell_type": "markdown",
 275 |    "metadata": {},
 276 |    "source": [
 277 |     "We check that it all sums up to one"
 278 |    ]
 279 |   },
 280 |   {
 281 |    "cell_type": "code",
 282 |    "execution_count": 8,
 283 |    "metadata": {},
 284 |    "outputs": [
 285 |     {
 286 |      "data": {
 287 |       "text/plain": [
 288 |        "1.0"
 289 |       ]
 290 |      },
 291 |      "execution_count": 8,
 292 |      "metadata": {},
 293 |      "output_type": "execute_result"
 294 |     }
 295 |    ],
 296 |    "source": [
 297 |     "PXYZ['Prob'].sum()"
 298 |    ]
 299 |   },
 300 |   {
 301 |    "cell_type": "markdown",
 302 |    "metadata": {},
 303 |    "source": [
 304 |     "The conditional probability $P\\left(Y, Z | X\\right)$ for X=Yes:"
 305 |    ]
 306 |   },
 307 |   {
 308 |    "cell_type": "code",
 309 |    "execution_count": 9,
 310 |    "metadata": {},
 311 |    "outputs": [],
 312 |    "source": [
 313 |     "PYZ_X = PXYZ[PXYZ['X'] == 'Yes'].copy()\n",
 314 |     "PYZ_X['Prob'] /= PYZ_X['Prob'].sum()"
 315 |    ]
 316 |   },
 317 |   {
 318 |    "cell_type": "code",
 319 |    "execution_count": 10,
 320 |    "metadata": {},
 321 |    "outputs": [
 322 |     {
 323 |      "data": {
 324 |       "text/html": [
 325 |        "<div>\n",
 326 |        "<style scoped>\n",
 327 |        "    .dataframe tbody tr th:only-of-type {\n",
 328 |        "        vertical-align: middle;\n",
 329 |        "    }\n",
 330 |        "\n",
 331 |        "    .dataframe tbody tr th {\n",
 332 |        "        vertical-align: top;\n",
 333 |        "    }\n",
 334 |        "\n",
 335 |        "    .dataframe thead th {\n",
 336 |        "        text-align: right;\n",
 337 |        "    }\n",
 338 |        "</style>\n",
 339 |        "<table border=\"1\" class=\"dataframe\">\n",
 340 |        "  <thead>\n",
 341 |        "    <tr style=\"text-align: right;\">\n",
 342 |        "      <th></th>\n",
 343 |        "      <th>X</th>\n",
 344 |        "      <th>Y</th>\n",
 345 |        "      <th>Z</th>\n",
 346 |        "      <th>Prob</th>\n",
 347 |        "    </tr>\n",
 348 |        "  </thead>\n",
 349 |        "  <tbody>\n",
 350 |        "    <tr>\n",
 351 |        "      <th>0</th>\n",
 352 |        "      <td>Yes</td>\n",
 353 |        "      <td>Yes</td>\n",
 354 |        "      <td>Male</td>\n",
 355 |        "      <td>0.232</td>\n",
 356 |        "    </tr>\n",
 357 |        "    <tr>\n",
 358 |        "      <th>1</th>\n",
 359 |        "      <td>Yes</td>\n",
 360 |        "      <td>Yes</td>\n",
 361 |        "      <td>Female</td>\n",
 362 |        "      <td>0.548</td>\n",
 363 |        "    </tr>\n",
 364 |        "    <tr>\n",
 365 |        "      <th>2</th>\n",
 366 |        "      <td>Yes</td>\n",
 367 |        "      <td>No</td>\n",
 368 |        "      <td>Male</td>\n",
 369 |        "      <td>0.018</td>\n",
 370 |        "    </tr>\n",
 371 |        "    <tr>\n",
 372 |        "      <th>3</th>\n",
 373 |        "      <td>Yes</td>\n",
 374 |        "      <td>No</td>\n",
 375 |        "      <td>Female</td>\n",
 376 |        "      <td>0.202</td>\n",
 377 |        "    </tr>\n",
 378 |        "  </tbody>\n",
 379 |        "</table>\n",
 380 |        "</div>"
 381 |       ],
 382 |       "text/plain": [
 383 |        "     X    Y       Z   Prob\n",
 384 |        "0  Yes  Yes    Male  0.232\n",
 385 |        "1  Yes  Yes  Female  0.548\n",
 386 |        "2  Yes   No    Male  0.018\n",
 387 |        "3  Yes   No  Female  0.202"
 388 |       ]
 389 |      },
 390 |      "execution_count": 10,
 391 |      "metadata": {},
 392 |      "output_type": "execute_result"
 393 |     }
 394 |    ],
 395 |    "source": [
 396 |     "PYZ_X.round(3)"
 397 |    ]
 398 |   },
 399 |   {
 400 |    "cell_type": "markdown",
 401 |    "metadata": {},
 402 |    "source": [
 403 |     "These numbers still differ slightly from the corrected in the [online Errata](http://bayes.cs.ucla.edu/PRIMER/pearl-etal-2016-primer-errata-pages-july2020.pdf)"
 404 |    ]
 405 |   },
 406 |   {
 407 |    "cell_type": "markdown",
 408 |    "metadata": {},
 409 |    "source": [
 410 |     "Here we note that these values are just the corresponding values of $P\\left(X, Y, Z\\right)$ divided by $P\\left(X=\\mathrm{Yes}\\right)$"
 411 |    ]
 412 |   },
 413 |   {
 414 |    "cell_type": "code",
 415 |    "execution_count": 11,
 416 |    "metadata": {},
 417 |    "outputs": [],
 418 |    "source": [
 419 |     "PX = PXYZ[['X', 'Prob']].groupby('X', as_index=False).sum()"
 420 |    ]
 421 |   },
 422 |   {
 423 |    "cell_type": "code",
 424 |    "execution_count": 12,
 425 |    "metadata": {},
 426 |    "outputs": [
 427 |     {
 428 |      "data": {
 429 |       "text/html": [
 430 |        "<div>\n",
 431 |        "<style scoped>\n",
 432 |        "    .dataframe tbody tr th:only-of-type {\n",
 433 |        "        vertical-align: middle;\n",
 434 |        "    }\n",
 435 |        "\n",
 436 |        "    .dataframe tbody tr th {\n",
 437 |        "        vertical-align: top;\n",
 438 |        "    }\n",
 439 |        "\n",
 440 |        "    .dataframe thead th {\n",
 441 |        "        text-align: right;\n",
 442 |        "    }\n",
 443 |        "</style>\n",
 444 |        "<table border=\"1\" class=\"dataframe\">\n",
 445 |        "  <thead>\n",
 446 |        "    <tr style=\"text-align: right;\">\n",
 447 |        "      <th></th>\n",
 448 |        "      <th>X</th>\n",
 449 |        "      <th>Prob</th>\n",
 450 |        "    </tr>\n",
 451 |        "  </thead>\n",
 452 |        "  <tbody>\n",
 453 |        "    <tr>\n",
 454 |        "      <th>0</th>\n",
 455 |        "      <td>No</td>\n",
 456 |        "      <td>0.5</td>\n",
 457 |        "    </tr>\n",
 458 |        "    <tr>\n",
 459 |        "      <th>1</th>\n",
 460 |        "      <td>Yes</td>\n",
 461 |        "      <td>0.5</td>\n",
 462 |        "    </tr>\n",
 463 |        "  </tbody>\n",
 464 |        "</table>\n",
 465 |        "</div>"
 466 |       ],
 467 |       "text/plain": [
 468 |        "     X  Prob\n",
 469 |        "0   No   0.5\n",
 470 |        "1  Yes   0.5"
 471 |       ]
 472 |      },
 473 |      "execution_count": 12,
 474 |      "metadata": {},
 475 |      "output_type": "execute_result"
 476 |     }
 477 |    ],
 478 |    "source": [
 479 |     "PX"
 480 |    ]
 481 |   },
 482 |   {
 483 |    "cell_type": "markdown",
 484 |    "metadata": {},
 485 |    "source": [
 486 |     "Please note that the calculations in earlier editions of the book are wrong. For instance, in Page 74 we have:"
 487 |    ]
 488 |   },
 489 |   {
 490 |    "cell_type": "code",
 491 |    "execution_count": 13,
 492 |    "metadata": {},
 493 |    "outputs": [
 494 |     {
 495 |      "data": {
 496 |       "text/plain": [
 497 |        "0.501"
 498 |       ]
 499 |      },
 500 |      "execution_count": 13,
 501 |      "metadata": {},
 502 |      "output_type": "execute_result"
 503 |     }
 504 |    ],
 505 |    "source": [
 506 |     "0.116+0.274+0.01+0.101"
 507 |    ]
 508 |   },
 509 |   {
 510 |    "cell_type": "markdown",
 511 |    "metadata": {},
 512 |    "source": [
 513 |     "since they didn't correct the 0.01 to 0.009."
 514 |    ]
 515 |   },
 516 |   {
 517 |    "cell_type": "markdown",
 518 |    "metadata": {},
 519 |    "source": [
 520 |     "The gender distribution is:"
 521 |    ]
 522 |   },
 523 |   {
 524 |    "cell_type": "code",
 525 |    "execution_count": 14,
 526 |    "metadata": {},
 527 |    "outputs": [],
 528 |    "source": [
 529 |     "PZ = PXYZ[['Z', 'Prob']].groupby('Z').sum()"
 530 |    ]
 531 |   },
 532 |   {
 533 |    "cell_type": "code",
 534 |    "execution_count": 15,
 535 |    "metadata": {},
 536 |    "outputs": [
 537 |     {
 538 |      "data": {
 539 |       "text/html": [
 540 |        "<div>\n",
 541 |        "<style scoped>\n",
 542 |        "    .dataframe tbody tr th:only-of-type {\n",
 543 |        "        vertical-align: middle;\n",
 544 |        "    }\n",
 545 |        "\n",
 546 |        "    .dataframe tbody tr th {\n",
 547 |        "        vertical-align: top;\n",
 548 |        "    }\n",
 549 |        "\n",
 550 |        "    .dataframe thead th {\n",
 551 |        "        text-align: right;\n",
 552 |        "    }\n",
 553 |        "</style>\n",
 554 |        "<table border=\"1\" class=\"dataframe\">\n",
 555 |        "  <thead>\n",
 556 |        "    <tr style=\"text-align: right;\">\n",
 557 |        "      <th></th>\n",
 558 |        "      <th>Prob</th>\n",
 559 |        "    </tr>\n",
 560 |        "    <tr>\n",
 561 |        "      <th>Z</th>\n",
 562 |        "      <th></th>\n",
 563 |        "    </tr>\n",
 564 |        "  </thead>\n",
 565 |        "  <tbody>\n",
 566 |        "    <tr>\n",
 567 |        "      <th>Female</th>\n",
 568 |        "      <td>0.49</td>\n",
 569 |        "    </tr>\n",
 570 |        "    <tr>\n",
 571 |        "      <th>Male</th>\n",
 572 |        "      <td>0.51</td>\n",
 573 |        "    </tr>\n",
 574 |        "  </tbody>\n",
 575 |        "</table>\n",
 576 |        "</div>"
 577 |       ],
 578 |       "text/plain": [
 579 |        "        Prob\n",
 580 |        "Z           \n",
 581 |        "Female  0.49\n",
 582 |        "Male    0.51"
 583 |       ]
 584 |      },
 585 |      "execution_count": 15,
 586 |      "metadata": {},
 587 |      "output_type": "execute_result"
 588 |     }
 589 |    ],
 590 |    "source": [
 591 |     "PZ"
 592 |    ]
 593 |   },
 594 |   {
 595 |    "cell_type": "markdown",
 596 |    "metadata": {},
 597 |    "source": [
 598 |     "And the conditional probability $P\\left(\\mathrm{Drug}|\\mathrm{Gender}\\right)$ is:"
 599 |    ]
 600 |   },
 601 |   {
 602 |    "cell_type": "code",
 603 |    "execution_count": 16,
 604 |    "metadata": {},
 605 |    "outputs": [],
 606 |    "source": [
 607 |     "PX_Z = PXYZ[['X', 'Z', 'Prob']].groupby(['X', 'Z'], as_index=False).sum()\n",
 608 |     "PX_Z['Prob'] = PX_Z.apply(lambda x: x['Prob']/PZ.loc[x.Z], axis=1) #Normalization"
 609 |    ]
 610 |   },
 611 |   {
 612 |    "cell_type": "code",
 613 |    "execution_count": 17,
 614 |    "metadata": {},
 615 |    "outputs": [],
 616 |    "source": [
 617 |     "PX_Z.set_index(['X', 'Z'], inplace=True)"
 618 |    ]
 619 |   },
 620 |   {
 621 |    "cell_type": "code",
 622 |    "execution_count": 18,
 623 |    "metadata": {},
 624 |    "outputs": [
 625 |     {
 626 |      "data": {
 627 |       "text/html": [
 628 |        "<div>\n",
 629 |        "<style scoped>\n",
 630 |        "    .dataframe tbody tr th:only-of-type {\n",
 631 |        "        vertical-align: middle;\n",
 632 |        "    }\n",
 633 |        "\n",
 634 |        "    .dataframe tbody tr th {\n",
 635 |        "        vertical-align: top;\n",
 636 |        "    }\n",
 637 |        "\n",
 638 |        "    .dataframe thead th {\n",
 639 |        "        text-align: right;\n",
 640 |        "    }\n",
 641 |        "</style>\n",
 642 |        "<table border=\"1\" class=\"dataframe\">\n",
 643 |        "  <thead>\n",
 644 |        "    <tr style=\"text-align: right;\">\n",
 645 |        "      <th></th>\n",
 646 |        "      <th></th>\n",
 647 |        "      <th>Prob</th>\n",
 648 |        "    </tr>\n",
 649 |        "    <tr>\n",
 650 |        "      <th>X</th>\n",
 651 |        "      <th>Z</th>\n",
 652 |        "      <th></th>\n",
 653 |        "    </tr>\n",
 654 |        "  </thead>\n",
 655 |        "  <tbody>\n",
 656 |        "    <tr>\n",
 657 |        "      <th rowspan=\"2\" valign=\"top\">No</th>\n",
 658 |        "      <th>Female</th>\n",
 659 |        "      <td>0.234694</td>\n",
 660 |        "    </tr>\n",
 661 |        "    <tr>\n",
 662 |        "      <th>Male</th>\n",
 663 |        "      <td>0.754902</td>\n",
 664 |        "    </tr>\n",
 665 |        "    <tr>\n",
 666 |        "      <th rowspan=\"2\" valign=\"top\">Yes</th>\n",
 667 |        "      <th>Female</th>\n",
 668 |        "      <td>0.765306</td>\n",
 669 |        "    </tr>\n",
 670 |        "    <tr>\n",
 671 |        "      <th>Male</th>\n",
 672 |        "      <td>0.245098</td>\n",
 673 |        "    </tr>\n",
 674 |        "  </tbody>\n",
 675 |        "</table>\n",
 676 |        "</div>"
 677 |       ],
 678 |       "text/plain": [
 679 |        "                Prob\n",
 680 |        "X   Z               \n",
 681 |        "No  Female  0.234694\n",
 682 |        "    Male    0.754902\n",
 683 |        "Yes Female  0.765306\n",
 684 |        "    Male    0.245098"
 685 |       ]
 686 |      },
 687 |      "execution_count": 18,
 688 |      "metadata": {},
 689 |      "output_type": "execute_result"
 690 |     }
 691 |    ],
 692 |    "source": [
 693 |     "PX_Z"
 694 |    ]
 695 |   },
 696 |   {
 697 |    "cell_type": "markdown",
 698 |    "metadata": {},
 699 |    "source": [
 700 |     "The lack of correction for 0.009 subsists even in $P\\left(Y|Male\\right)$ which is why we obtain 0.245 instead of 0.247"
 701 |    ]
 702 |   },
 703 |   {
 704 |    "cell_type": "markdown",
 705 |    "metadata": {},
 706 |    "source": [
 707 |     "The results of the intervention, as calculated the inverse probability weighing are then:"
 708 |    ]
 709 |   },
 710 |   {
 711 |    "cell_type": "code",
 712 |    "execution_count": 19,
 713 |    "metadata": {},
 714 |    "outputs": [],
 715 |    "source": [
 716 |     "PYdoXZ = PXYZ.copy()"
 717 |    ]
 718 |   },
 719 |   {
 720 |    "cell_type": "code",
 721 |    "execution_count": 20,
 722 |    "metadata": {},
 723 |    "outputs": [],
 724 |    "source": [
 725 |     "PYdoXZ['Prob'] = PYdoXZ.apply(lambda x: x.Prob/PX_Z.loc[x.X, x.Z], axis=1)"
 726 |    ]
 727 |   },
 728 |   {
 729 |    "cell_type": "code",
 730 |    "execution_count": 21,
 731 |    "metadata": {},
 732 |    "outputs": [
 733 |     {
 734 |      "data": {
 735 |       "text/html": [
 736 |        "<div>\n",
 737 |        "<style scoped>\n",
 738 |        "    .dataframe tbody tr th:only-of-type {\n",
 739 |        "        vertical-align: middle;\n",
 740 |        "    }\n",
 741 |        "\n",
 742 |        "    .dataframe tbody tr th {\n",
 743 |        "        vertical-align: top;\n",
 744 |        "    }\n",
 745 |        "\n",
 746 |        "    .dataframe thead th {\n",
 747 |        "        text-align: right;\n",
 748 |        "    }\n",
 749 |        "</style>\n",
 750 |        "<table border=\"1\" class=\"dataframe\">\n",
 751 |        "  <thead>\n",
 752 |        "    <tr style=\"text-align: right;\">\n",
 753 |        "      <th></th>\n",
 754 |        "      <th>X</th>\n",
 755 |        "      <th>Y</th>\n",
 756 |        "      <th>Z</th>\n",
 757 |        "      <th>Prob</th>\n",
 758 |        "    </tr>\n",
 759 |        "  </thead>\n",
 760 |        "  <tbody>\n",
 761 |        "    <tr>\n",
 762 |        "      <th>0</th>\n",
 763 |        "      <td>Yes</td>\n",
 764 |        "      <td>Yes</td>\n",
 765 |        "      <td>Male</td>\n",
 766 |        "      <td>0.473</td>\n",
 767 |        "    </tr>\n",
 768 |        "    <tr>\n",
 769 |        "      <th>1</th>\n",
 770 |        "      <td>Yes</td>\n",
 771 |        "      <td>Yes</td>\n",
 772 |        "      <td>Female</td>\n",
 773 |        "      <td>0.358</td>\n",
 774 |        "    </tr>\n",
 775 |        "    <tr>\n",
 776 |        "      <th>2</th>\n",
 777 |        "      <td>Yes</td>\n",
 778 |        "      <td>No</td>\n",
 779 |        "      <td>Male</td>\n",
 780 |        "      <td>0.037</td>\n",
 781 |        "    </tr>\n",
 782 |        "    <tr>\n",
 783 |        "      <th>3</th>\n",
 784 |        "      <td>Yes</td>\n",
 785 |        "      <td>No</td>\n",
 786 |        "      <td>Female</td>\n",
 787 |        "      <td>0.132</td>\n",
 788 |        "    </tr>\n",
 789 |        "    <tr>\n",
 790 |        "      <th>4</th>\n",
 791 |        "      <td>No</td>\n",
 792 |        "      <td>Yes</td>\n",
 793 |        "      <td>Male</td>\n",
 794 |        "      <td>0.442</td>\n",
 795 |        "    </tr>\n",
 796 |        "    <tr>\n",
 797 |        "      <th>5</th>\n",
 798 |        "      <td>No</td>\n",
 799 |        "      <td>Yes</td>\n",
 800 |        "      <td>Female</td>\n",
 801 |        "      <td>0.337</td>\n",
 802 |        "    </tr>\n",
 803 |        "    <tr>\n",
 804 |        "      <th>6</th>\n",
 805 |        "      <td>No</td>\n",
 806 |        "      <td>No</td>\n",
 807 |        "      <td>Male</td>\n",
 808 |        "      <td>0.068</td>\n",
 809 |        "    </tr>\n",
 810 |        "    <tr>\n",
 811 |        "      <th>7</th>\n",
 812 |        "      <td>No</td>\n",
 813 |        "      <td>No</td>\n",
 814 |        "      <td>Female</td>\n",
 815 |        "      <td>0.153</td>\n",
 816 |        "    </tr>\n",
 817 |        "  </tbody>\n",
 818 |        "</table>\n",
 819 |        "</div>"
 820 |       ],
 821 |       "text/plain": [
 822 |        "     X    Y       Z   Prob\n",
 823 |        "0  Yes  Yes    Male  0.473\n",
 824 |        "1  Yes  Yes  Female  0.358\n",
 825 |        "2  Yes   No    Male  0.037\n",
 826 |        "3  Yes   No  Female  0.132\n",
 827 |        "4   No  Yes    Male  0.442\n",
 828 |        "5   No  Yes  Female  0.337\n",
 829 |        "6   No   No    Male  0.068\n",
 830 |        "7   No   No  Female  0.153"
 831 |       ]
 832 |      },
 833 |      "execution_count": 21,
 834 |      "metadata": {},
 835 |      "output_type": "execute_result"
 836 |     }
 837 |    ],
 838 |    "source": [
 839 |     "PYdoXZ.round(3)"
 840 |    ]
 841 |   },
 842 |   {
 843 |    "cell_type": "markdown",
 844 |    "metadata": {},
 845 |    "source": [
 846 |     "The small differences we observe with respect to the corrected version in the [online Errata](http://bayes.cs.ucla.edu/PRIMER/pearl-etal-2016-primer-errata-pages-july2020.pdf) are due to the lack of correction from 0.01 to 0.009 as noted above."
 847 |    ]
 848 |   },
 849 |   {
 850 |    "cell_type": "markdown",
 851 |    "metadata": {},
 852 |    "source": [
 853 |     "And finally, the intervention values are:"
 854 |    ]
 855 |   },
 856 |   {
 857 |    "cell_type": "code",
 858 |    "execution_count": 22,
 859 |    "metadata": {},
 860 |    "outputs": [],
 861 |    "source": [
 862 |     "PYdoX = PYdoXZ[['X', 'Y', 'Prob']].groupby(['Y', 'X'], as_index=False).sum()"
 863 |    ]
 864 |   },
 865 |   {
 866 |    "cell_type": "code",
 867 |    "execution_count": 23,
 868 |    "metadata": {},
 869 |    "outputs": [
 870 |     {
 871 |      "data": {
 872 |       "text/html": [
 873 |        "<div>\n",
 874 |        "<style scoped>\n",
 875 |        "    .dataframe tbody tr th:only-of-type {\n",
 876 |        "        vertical-align: middle;\n",
 877 |        "    }\n",
 878 |        "\n",
 879 |        "    .dataframe tbody tr th {\n",
 880 |        "        vertical-align: top;\n",
 881 |        "    }\n",
 882 |        "\n",
 883 |        "    .dataframe thead th {\n",
 884 |        "        text-align: right;\n",
 885 |        "    }\n",
 886 |        "</style>\n",
 887 |        "<table border=\"1\" class=\"dataframe\">\n",
 888 |        "  <thead>\n",
 889 |        "    <tr style=\"text-align: right;\">\n",
 890 |        "      <th></th>\n",
 891 |        "      <th>Y</th>\n",
 892 |        "      <th>X</th>\n",
 893 |        "      <th>Prob</th>\n",
 894 |        "    </tr>\n",
 895 |        "  </thead>\n",
 896 |        "  <tbody>\n",
 897 |        "    <tr>\n",
 898 |        "      <th>0</th>\n",
 899 |        "      <td>No</td>\n",
 900 |        "      <td>No</td>\n",
 901 |        "      <td>0.221</td>\n",
 902 |        "    </tr>\n",
 903 |        "    <tr>\n",
 904 |        "      <th>1</th>\n",
 905 |        "      <td>No</td>\n",
 906 |        "      <td>Yes</td>\n",
 907 |        "      <td>0.169</td>\n",
 908 |        "    </tr>\n",
 909 |        "    <tr>\n",
 910 |        "      <th>2</th>\n",
 911 |        "      <td>Yes</td>\n",
 912 |        "      <td>No</td>\n",
 913 |        "      <td>0.779</td>\n",
 914 |        "    </tr>\n",
 915 |        "    <tr>\n",
 916 |        "      <th>3</th>\n",
 917 |        "      <td>Yes</td>\n",
 918 |        "      <td>Yes</td>\n",
 919 |        "      <td>0.831</td>\n",
 920 |        "    </tr>\n",
 921 |        "  </tbody>\n",
 922 |        "</table>\n",
 923 |        "</div>"
 924 |       ],
 925 |       "text/plain": [
 926 |        "     Y    X   Prob\n",
 927 |        "0   No   No  0.221\n",
 928 |        "1   No  Yes  0.169\n",
 929 |        "2  Yes   No  0.779\n",
 930 |        "3  Yes  Yes  0.831"
 931 |       ]
 932 |      },
 933 |      "execution_count": 23,
 934 |      "metadata": {},
 935 |      "output_type": "execute_result"
 936 |     }
 937 |    ],
 938 |    "source": [
 939 |     "PYdoX.round(3)"
 940 |    ]
 941 |   },
 942 |   {
 943 |    "cell_type": "markdown",
 944 |    "metadata": {},
 945 |    "source": [
 946 |     "<div style=\"width: 100%; overflow: hidden;\">\n",
 947 |     "     <img src=\"data/D4Sci_logo_full.png\" alt=\"Data For Science, Inc\" align=\"center\" border=\"0\" width=300px> \n",
 948 |     "</div>"
 949 |    ]
 950 |   }
 951 |  ],
 952 |  "metadata": {
 953 |   "kernelspec": {
 954 |    "display_name": "Python 3",
 955 |    "language": "python",
 956 |    "name": "python3"
 957 |   },
 958 |   "language_info": {
 959 |    "codemirror_mode": {
 960 |     "name": "ipython",
 961 |     "version": 3
 962 |    },
 963 |    "file_extension": ".py",
 964 |    "mimetype": "text/x-python",
 965 |    "name": "python",
 966 |    "nbconvert_exporter": "python",
 967 |    "pygments_lexer": "ipython3",
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 969 |   },
 970 |   "varInspector": {
 971 |    "cols": {
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 973 |     "lenType": 16,
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 975 |    },
 976 |    "kernels_config": {
 977 |     "python": {
 978 |      "delete_cmd_postfix": "",
 979 |      "delete_cmd_prefix": "del ",
 980 |      "library": "var_list.py",
 981 |      "varRefreshCmd": "print(var_dic_list())"
 982 |     },
 983 |     "r": {
 984 |      "delete_cmd_postfix": ") ",
 985 |      "delete_cmd_prefix": "rm(",
 986 |      "library": "var_list.r",
 987 |      "varRefreshCmd": "cat(var_dic_list()) "
 988 |     }
 989 |    },
 990 |    "types_to_exclude": [
 991 |     "module",
 992 |     "function",
 993 |     "builtin_function_or_method",
 994 |     "instance",
 995 |     "_Feature"
 996 |    ],
 997 |    "window_display": false
 998 |   }
 999 |  },
1000 |  "nbformat": 4,
1001 |  "nbformat_minor": 4
1002 | }
1003 | 


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/3.7 - Mediation.ipynb:
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  1 | {
  2 |  "cells": [
  3 |   {
  4 |    "cell_type": "markdown",
  5 |    "metadata": {},
  6 |    "source": [
  7 |     "<div style=\"width: 100%; overflow: hidden;\">\n",
  8 |     "    <div style=\"width: 150px; float: left;\"> <img src=\"https://raw.githubusercontent.com/DataForScience/Networks/master/data/D4Sci_logo_ball.png\" alt=\"Data For Science, Inc\" align=\"left\" border=\"0\" width=150px> </div>\n",
  9 |     "    <div style=\"float: left; margin-left: 10px;\"> <h1>Causal Inference In Statistics - A Primer</h1>\n",
 10 |     "        <h1>3.7 Mediation</h1>\n",
 11 |     "        <p>Bruno Gonçalves<br/>\n",
 12 |     "        <a href=\"http://www.data4sci.com/\">www.data4sci.com</a><br/>\n",
 13 |     "            @bgoncalves, @data4sci</p></div>\n",
 14 |     "    <div style=\"float: right; margin-right:10px;\"> <p><a href=\"https://amzn.to/3gsFlkO\" target=_blank><img src='data/causality.jpeg' width='100px'>\n",
 15 |     "        <!--Amazon Affiliate Link--></a></p></div>\n",
 16 |     "</div>"
 17 |    ]
 18 |   },
 19 |   {
 20 |    "cell_type": "code",
 21 |    "execution_count": 1,
 22 |    "metadata": {},
 23 |    "outputs": [],
 24 |    "source": [
 25 |     "from collections import Counter\n",
 26 |     "from pprint import pprint\n",
 27 |     "\n",
 28 |     "import pandas as pd\n",
 29 |     "import numpy as np\n",
 30 |     "\n",
 31 |     "import matplotlib\n",
 32 |     "import matplotlib.pyplot as plt \n",
 33 |     "\n",
 34 |     "from CausalModel import CausalModel\n",
 35 |     "\n",
 36 |     "import watermark\n",
 37 |     "\n",
 38 |     "%load_ext watermark\n",
 39 |     "%matplotlib inline"
 40 |    ]
 41 |   },
 42 |   {
 43 |    "cell_type": "markdown",
 44 |    "metadata": {},
 45 |    "source": [
 46 |     "We start by print out the versions of the libraries we're using for future reference"
 47 |    ]
 48 |   },
 49 |   {
 50 |    "cell_type": "code",
 51 |    "execution_count": 2,
 52 |    "metadata": {},
 53 |    "outputs": [
 54 |     {
 55 |      "name": "stdout",
 56 |      "output_type": "stream",
 57 |      "text": [
 58 |       "Python implementation: CPython\n",
 59 |       "Python version       : 3.8.5\n",
 60 |       "IPython version      : 7.19.0\n",
 61 |       "\n",
 62 |       "Compiler    : Clang 10.0.0 \n",
 63 |       "OS          : Darwin\n",
 64 |       "Release     : 20.3.0\n",
 65 |       "Machine     : x86_64\n",
 66 |       "Processor   : i386\n",
 67 |       "CPU cores   : 16\n",
 68 |       "Architecture: 64bit\n",
 69 |       "\n",
 70 |       "Git hash: c41ed8befecf49059999a81adcec3b026fe5d326\n",
 71 |       "\n",
 72 |       "json      : 2.0.9\n",
 73 |       "watermark : 2.1.0\n",
 74 |       "pandas    : 1.1.3\n",
 75 |       "numpy     : 1.19.2\n",
 76 |       "matplotlib: 3.3.2\n",
 77 |       "\n"
 78 |      ]
 79 |     }
 80 |    ],
 81 |    "source": [
 82 |     "%watermark -n -v -m -g -iv"
 83 |    ]
 84 |   },
 85 |   {
 86 |    "cell_type": "markdown",
 87 |    "metadata": {},
 88 |    "source": [
 89 |     "Load default figure style"
 90 |    ]
 91 |   },
 92 |   {
 93 |    "cell_type": "code",
 94 |    "execution_count": 3,
 95 |    "metadata": {},
 96 |    "outputs": [],
 97 |    "source": [
 98 |     "plt.style.use('./d4sci.mplstyle')\n",
 99 |     "colors = plt.rcParams['axes.prop_cycle'].by_key()['color']"
100 |    ]
101 |   },
102 |   {
103 |    "cell_type": "markdown",
104 |    "metadata": {},
105 |    "source": [
106 |     "We build the DAG from Fig 3.11"
107 |    ]
108 |   },
109 |   {
110 |    "cell_type": "code",
111 |    "execution_count": 4,
112 |    "metadata": {},
113 |    "outputs": [],
114 |    "source": [
115 |     "G = CausalModel()\n",
116 |     "G.add_causation('X', 'Y')\n",
117 |     "G.add_causation('X', 'Z')\n",
118 |     "G.add_causation('Z', 'Y')\n",
119 |     "\n",
120 |     "G.pos = {'X': (0, 0), 'Z': (1, 1), 'Y': (2, 0)}"
121 |    ]
122 |   },
123 |   {
124 |    "cell_type": "code",
125 |    "execution_count": 5,
126 |    "metadata": {},
127 |    "outputs": [
128 |     {
129 |      "data": {
130 |       "image/png": 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\n",
131 |       "text/plain": [
132 |        "<Figure size 660x660 with 1 Axes>"
133 |       ]
134 |      },
135 |      "metadata": {},
136 |      "output_type": "display_data"
137 |     }
138 |    ],
139 |    "source": [
140 |     "fig, ax = plt.subplots(1, figsize=(2.2,2.2))\n",
141 |     "G.plot(ax=ax)"
142 |    ]
143 |   },
144 |   {
145 |    "cell_type": "code",
146 |    "execution_count": 6,
147 |    "metadata": {},
148 |    "outputs": [],
149 |    "source": [
150 |     "G.save_model('dags/Primer.Fig.3.11.dot')"
151 |    ]
152 |   },
153 |   {
154 |    "cell_type": "markdown",
155 |    "metadata": {},
156 |    "source": [
157 |     "And the DAG from Fig 3.12"
158 |    ]
159 |   },
160 |   {
161 |    "cell_type": "code",
162 |    "execution_count": 7,
163 |    "metadata": {},
164 |    "outputs": [],
165 |    "source": [
166 |     "G = CausalModel()\n",
167 |     "G.add_causation('X', 'Y')\n",
168 |     "G.add_causation('X', 'Z')\n",
169 |     "G.add_causation('Z', 'Y')\n",
170 |     "G.add_causation('I', 'Y')\n",
171 |     "G.add_causation('I', 'Z')\n",
172 |     "\n",
173 |     "G.pos = {'X': (0, 0), 'Z': (1, 1), 'Y': (2, 0), 'I': (2, 1)}"
174 |    ]
175 |   },
176 |   {
177 |    "cell_type": "code",
178 |    "execution_count": 8,
179 |    "metadata": {},
180 |    "outputs": [
181 |     {
182 |      "data": {
183 |       "image/png": 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\n",
184 |       "text/plain": [
185 |        "<Figure size 660x660 with 1 Axes>"
186 |       ]
187 |      },
188 |      "metadata": {},
189 |      "output_type": "display_data"
190 |     }
191 |    ],
192 |    "source": [
193 |     "fig, ax = plt.subplots(1, figsize=(2.2,2.2))\n",
194 |     "G.plot(ax=ax)"
195 |    ]
196 |   },
197 |   {
198 |    "cell_type": "code",
199 |    "execution_count": 9,
200 |    "metadata": {},
201 |    "outputs": [],
202 |    "source": [
203 |     "G.save_model('dags/Primer.Fig.3.12.dot')"
204 |    ]
205 |   },
206 |   {
207 |    "cell_type": "markdown",
208 |    "metadata": {},
209 |    "source": [
210 |     "We can easily compute the modified graph resulting from intervening on X and Z:"
211 |    ]
212 |   },
213 |   {
214 |    "cell_type": "code",
215 |    "execution_count": 10,
216 |    "metadata": {},
217 |    "outputs": [
218 |     {
219 |      "data": {
220 |       "image/png": 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\n",
221 |       "text/plain": [
222 |        "<Figure size 660x660 with 1 Axes>"
223 |       ]
224 |      },
225 |      "metadata": {},
226 |      "output_type": "display_data"
227 |     }
228 |    ],
229 |    "source": [
230 |     "G2 = G.intervention_graph(['X', 'Z'])\n",
231 |     "fig, ax = plt.subplots(1, figsize=(2.2,2.2))\n",
232 |     "G2.plot(ax=ax)"
233 |    ]
234 |   },
235 |   {
236 |    "cell_type": "markdown",
237 |    "metadata": {},
238 |    "source": [
239 |     "<div style=\"width: 100%; overflow: hidden;\">\n",
240 |     "     <img src=\"data/D4Sci_logo_full.png\" alt=\"Data For Science, Inc\" align=\"center\" border=\"0\" width=300px> \n",
241 |     "</div>"
242 |    ]
243 |   }
244 |  ],
245 |  "metadata": {
246 |   "kernelspec": {
247 |    "display_name": "Python 3",
248 |    "language": "python",
249 |    "name": "python3"
250 |   },
251 |   "language_info": {
252 |    "codemirror_mode": {
253 |     "name": "ipython",
254 |     "version": 3
255 |    },
256 |    "file_extension": ".py",
257 |    "mimetype": "text/x-python",
258 |    "name": "python",
259 |    "nbconvert_exporter": "python",
260 |    "pygments_lexer": "ipython3",
261 |    "version": "3.8.5"
262 |   },
263 |   "varInspector": {
264 |    "cols": {
265 |     "lenName": 16,
266 |     "lenType": 16,
267 |     "lenVar": 40
268 |    },
269 |    "kernels_config": {
270 |     "python": {
271 |      "delete_cmd_postfix": "",
272 |      "delete_cmd_prefix": "del ",
273 |      "library": "var_list.py",
274 |      "varRefreshCmd": "print(var_dic_list())"
275 |     },
276 |     "r": {
277 |      "delete_cmd_postfix": ") ",
278 |      "delete_cmd_prefix": "rm(",
279 |      "library": "var_list.r",
280 |      "varRefreshCmd": "cat(var_dic_list()) "
281 |     }
282 |    },
283 |    "types_to_exclude": [
284 |     "module",
285 |     "function",
286 |     "builtin_function_or_method",
287 |     "instance",
288 |     "_Feature"
289 |    ],
290 |    "window_display": false
291 |   }
292 |  },
293 |  "nbformat": 4,
294 |  "nbformat_minor": 4
295 | }
296 | 


--------------------------------------------------------------------------------
/CausalModel.py:
--------------------------------------------------------------------------------
  1 | ### −∗− mode : python ; −∗−
  2 | # @file CausalModel.py
  3 | # @author Bruno Goncalves
  4 | ######################################################
  5 | 
  6 | import networkx as nx
  7 | from networkx.drawing.nx_pydot import graphviz_layout
  8 | from itertools import combinations
  9 | import numpy as np
 10 | import pandas as pd
 11 | import matplotlib as mpl
 12 | import matplotlib.pyplot as plt
 13 | import re
 14 | import base64
 15 | import requests
 16 | 
 17 | import warnings
 18 | warnings.filterwarnings("ignore")
 19 | 
 20 | from tqdm import tqdm
 21 | tqdm.pandas()
 22 | 
 23 | plt.style.use('./d4sci.mplstyle')
 24 | 
 25 | class CausalModel(object):
 26 |     """Simple Causal Model Implementation
 27 |     
 28 |         Provides a way to represent causal DAGs
 29 |     """
 30 | 
 31 |     def __init__(self, filename=None):
 32 |         self.pos = None
 33 | 
 34 |         if filename is not None:
 35 |             self.load_model(filename)
 36 |         else:
 37 |             self.dag = nx.DiGraph()
 38 | 
 39 |         self.colors = plt.rcParams['axes.prop_cycle'].by_key()['color']
 40 | 
 41 |     def copy(self):
 42 |         G = CausalModel()
 43 |         G.dag = self.dag.copy()
 44 |         G.pos = dict(self.pos)
 45 |         G.colors = [color for color in self.colors]
 46 | 
 47 |         return G
 48 | 
 49 | 
 50 |     def add_causation(self, source, target, label=None):
 51 |         """Add a causal link between source and target with an optional label.
 52 | 
 53 |         Parameters
 54 |         ----------
 55 |         source : node-like
 56 |             The source node
 57 | 
 58 |         target : node-like
 59 |             The target node
 60 | 
 61 |         label : string-like or None
 62 |             The label for the causal link
 63 | 
 64 |         Returns
 65 |         -------
 66 |         None
 67 | 
 68 |         Examples
 69 |         --------
 70 |         >>> G = CausalModel()
 71 |         >>> G.add_causation('X', 'Y')
 72 | 
 73 |         """
 74 |      
 75 |         if label is None:        
 76 |             self.dag.add_edge(source, target)
 77 |         else:
 78 |             self.dag.add_edge(source, target, label=label)        
 79 | 
 80 |     def load_model(self, path):
 81 |         """Initialize the CausalModel object by reading the information from the dot file with the passed path.
 82 | 
 83 |         The file should be a `dot` file and if it contains multiple graphs, only the first such graph is returned. All graphs _except_ the first are silently ignored.
 84 | 
 85 |         Parameters
 86 |         ----------
 87 |         path : str or file
 88 |             Filename or file handle.
 89 | 
 90 |         Returns
 91 |         -------
 92 |         None
 93 | 
 94 |         Examples
 95 |         --------
 96 |         >>> G = CausalModel()
 97 |         >>> G.load_model('temp.dot')
 98 | 
 99 |         Notes
100 |         -----
101 |         The heavy lifting is done by `networkx.drawing.nx_pydot.read_dot`
102 | 
103 |         """
104 | 
105 |         G = nx.drawing.nx_pydot.read_dot(path)
106 | 
107 |         pos = {}
108 | 
109 |         for key, values in G.nodes(data=True):
110 |             if 'x' not in values:
111 |                 pos = None
112 |                 break
113 | 
114 |             x = values['x']
115 |             y = values['y']
116 |             
117 |             if x[0] == '"':
118 |                 x = x[1:-1]
119 |             
120 |             if y[0] == '"':
121 |                 y = y[1:-1]
122 |                 
123 |             pos[key] = (float(x), float(y))
124 | 
125 |         self.dag = nx.DiGraph(G)
126 |         self.pos = pos
127 | 
128 | 
129 |     def save_model(self, path):
130 |         """Save the causal model as a `dot` file.
131 | 
132 |         Parameters
133 |         ----------
134 |         path : str or file
135 |             Filename or file handle.
136 | 
137 |         Returns
138 |         -------
139 |         None
140 | 
141 |         Examples
142 |         --------
143 |         >>> G = CausalModel()
144 |         >>> G.add_causation('X', 'Y')
145 |         >>> G.add_causation('Y', 'Z')
146 |         >>> G.pos = {'X':(-1, 0), 'Y': (0, 0), 'Z': (1, 0)}
147 |         >>> G.save_model('temp.dot')
148 | 
149 |         Notes
150 |         -----
151 |         The heavy lifting is done by `networkx.drawing.nx_pydot.write_dot`
152 | 
153 |         """
154 |         G = self.dag.copy()
155 | 
156 |         if self.pos is not None:
157 |             nodes = list(G.nodes())
158 | 
159 |             for node in nodes:
160 |                 G.nodes[node]['x'] = str(self.pos[node][0])
161 |                 G.nodes[node]['y'] = str(self.pos[node][1])
162 | 
163 |         nx.drawing.nx_pydot.write_dot(G, path)
164 | 
165 |     def layout(self):
166 |         """Initialize the CausalModel object by reading the information from the dot file with the passed path.
167 | 
168 |         The file should be a `dot` file and if it contains multiple graphs, only the first such graph is returned. All graphs _except_ the first are silently ignored.
169 | 
170 |         Parameters
171 |         ----------
172 |         path : str or file
173 |             Filename or file handle.
174 | 
175 |         Returns
176 |         -------
177 |         None
178 | 
179 |         Examples
180 |         --------
181 |         >>> G = CausalModel()
182 |         >>> G.load_model('temp.dot')
183 | 
184 |         Notes
185 |         -----
186 |         The heavy lifting is done by `networkx.drawing.nx_pydot.read_dot`
187 | 
188 |         """
189 |         pos = graphviz_layout(self.dag, 'dot')
190 | 
191 |         keys = list(pos.keys())
192 |         coords = np.array([pos[key] for key in keys])
193 |         coords = nx.rescale_layout(coords, 1)
194 |         pos = dict(zip(keys, coords))
195 | 
196 |         xs = []
197 |         ys = []
198 | 
199 |         for key, value in pos.items():
200 |             xs.append(value[0])
201 |             ys.append(value[1])
202 | 
203 |         # All xx coordinates are the same, switch x and y
204 |         # To make it horizontal instead of vertical
205 |         if len(set(xs)) == 1:
206 |             pos = {key: [-value[1], value[0]] for key, value in pos.items()}
207 | 
208 |         return pos
209 | 
210 |     def parents(self, node):
211 |         """Initialize the CausalModel object by reading the information from the dot file with the passed path.
212 | 
213 |         The file should be a `dot` file and if it contains multiple graphs, only the first such graph is returned. All graphs _except_ the first are silently ignored.
214 | 
215 |         Parameters
216 |         ----------
217 |         path : str or file
218 |             Filename or file handle.
219 | 
220 |         Returns
221 |         -------
222 |         None
223 | 
224 |         Examples
225 |         --------
226 |         >>> G = CausalModel()
227 |         >>> G.load_model('temp.dot')
228 | 
229 |         Notes
230 |         -----
231 |         The heavy lifting is done by `networkx.drawing.nx_pydot.read_dot`
232 | 
233 |         """
234 |         return list(self.dag.predecessors(node))
235 | 
236 |     def ancestors(self, node):
237 |         """Initialize the CausalModel object by reading the information from the dot file with the passed path.
238 | 
239 |         The file should be a `dot` file and if it contains multiple graphs, only the first such graph is returned. All graphs _except_ the first are silently ignored.
240 | 
241 |         Parameters
242 |         ----------
243 |         path : str or file
244 |             Filename or file handle.
245 | 
246 |         Returns
247 |         -------
248 |         None
249 | 
250 |         Examples
251 |         --------
252 |         >>> G = CausalModel()
253 |         >>> G.load_model('temp.dot')
254 | 
255 |         Notes
256 |         -----
257 |         The heavy lifting is done by `networkx.drawing.nx_pydot.read_dot`
258 | 
259 |         """
260 |         return list(nx.ancestors(self.dag, node))
261 | 
262 |     def children(self, source):
263 |         """Obtain the children of a node.
264 | 
265 |         Children are the nodes at the other end of outgoing edges.
266 | 
267 |         Parameters
268 |         ----------
269 |         source : node in `G`
270 |             The parent node
271 | 
272 |         Returns
273 |         -------
274 |         list()
275 |             List of the children of `source` in `G`
276 | 
277 |         Examples
278 |         --------
279 |         >>> G.children('X')
280 | 
281 |         Notes
282 |         -----
283 |         The heavy lifting is done by `networkx.successors`
284 | 
285 |         """
286 |         return list(self.dag.successors(source))
287 | 
288 |     def descendants(self, source):
289 |         """Obtain the descendants of a node.
290 | 
291 |         Descendants are all the nodes reacheable through outgoing edges.
292 | 
293 |         Parameters
294 |         ----------
295 |         path : str or file
296 |             Filename or file handle.
297 | 
298 |         Returns
299 |         -------
300 |         list()
301 |             List of the descendants of `source` in `G`
302 | 
303 |         Examples
304 |         --------
305 |         >>> G = CausalModel()
306 |         >>> G.load_model('temp.dot')
307 | 
308 |         Notes
309 |         -----
310 |         The heavy lifting is done by `networkx.descendants`
311 | 
312 |         """
313 |         return list(nx.descendants(self.dag, source))
314 | 
315 |     def backdoor_paths(self, source, target):
316 |         """Initialize the CausalModel object by reading the information from the dot file with the passed path.
317 | 
318 |         The file should be a `dot` file and if it contains multiple graphs, only the first such graph is returned. All graphs _except_ the first are silently ignored.
319 | 
320 |         Parameters
321 |         ----------
322 |         path : str or file
323 |             Filename or file handle.
324 | 
325 |         Returns
326 |         -------
327 |         None
328 | 
329 |         Examples
330 |         --------
331 |         >>> G = CausalModel()
332 |         >>> G.load_model('temp.dot')
333 | 
334 |         Notes
335 |         -----
336 |         The heavy lifting is done by `networkx.drawing.nx_pydot.read_dot`
337 | 
338 |         """
339 | 
340 |         allPaths = self.all_paths(source, target)
341 |         directed = self.directed_paths(source, target)
342 | 
343 |         return allPaths-directed
344 | 
345 | 
346 |     def directed_paths(self, source, target):
347 |         """Initialize the CausalModel object by reading the information from the dot file with the passed path.
348 | 
349 |         The file should be a `dot` file and if it contains multiple graphs, only the first such graph is returned. All graphs _except_ the first are silently ignored.
350 | 
351 |         Parameters
352 |         ----------
353 |         path : str or file
354 |             Filename or file handle.
355 | 
356 |         Returns
357 |         -------
358 |         None
359 | 
360 |         Examples
361 |         --------
362 |         >>> G = CausalModel()
363 |         >>> G.load_model('temp.dot')
364 | 
365 |         Notes
366 |         -----
367 |         The heavy lifting is done by `networkx.drawing.nx_pydot.read_dot`
368 | 
369 |         """
370 |         return {tuple(path) for path in nx.all_simple_paths(self.dag, source, target)}
371 | 
372 |     def all_paths(self, source, target):
373 |         """Initialize the CausalModel object by reading the information from the dot file with the passed path.
374 | 
375 |         The file should be a `dot` file and if it contains multiple graphs, only the first such graph is returned. All graphs _except_ the first are silently ignored.
376 | 
377 |         Parameters
378 |         ----------
379 |         path : str or file
380 |             Filename or file handle.
381 | 
382 |         Returns
383 |         -------
384 |         None
385 | 
386 |         Examples
387 |         --------
388 |         >>> G = CausalModel()
389 |         >>> G.load_model('temp.dot')
390 | 
391 |         Notes
392 |         -----
393 |         The heavy lifting is done by `networkx.drawing.nx_pydot.read_dot`
394 | 
395 |         """
396 |         return {tuple(path) for path in nx.all_simple_paths(self.dag.to_undirected(), source, target)}
397 | 
398 | 
399 |     def all_paths_conditional(self, source, target, remove):
400 |         """Initialize the CausalModel object by reading the information from the dot file with the passed path.
401 | 
402 |         The file should be a `dot` file and if it contains multiple graphs, only the first such graph is returned. All graphs _except_ the first are silently ignored.
403 | 
404 |         Parameters
405 |         ----------
406 |         path : str or file
407 |             Filename or file handle.
408 | 
409 |         Returns
410 |         -------
411 |         None
412 | 
413 |         Examples
414 |         --------
415 |         >>> G = CausalModel()
416 |         >>> G.load_model('temp.dot')
417 | 
418 |         Notes
419 |         -----
420 |         The heavy lifting is done by `networkx.drawing.nx_pydot.read_dot`
421 | 
422 |         """
423 | 
424 |         dag = self.dag.to_undirected()
425 |         dag.remove_nodes_from(remove)
426 | 
427 |         return {tuple(path) for path in nx.all_simple_paths(dag, source, target)}
428 | 
429 | 
430 |     def plot_path(self, path, edges=False, ax=None, conditional=False, lw=3):
431 |         """Initialize the CausalModel object by reading the information from the dot
432 |          file with the passed path.
433 | 
434 |         The file should be a `dot` file and if it contains multiple graphs, only the 
435 |         first such graph is returned. All graphs _except_ the first are silently ignored.
436 | 
437 |         Parameters
438 |         ----------
439 |         path : str or file
440 |             Filename or file handle.
441 | 
442 |         Returns
443 |         -------
444 |         None
445 | 
446 |         Examples
447 |         --------
448 |         >>> G = CausalModel()
449 |         >>> G.load_model('temp.dot')
450 | 
451 |         Notes
452 |         -----
453 |         The heavy lifting is done by `networkx.drawing.nx_pydot.read_dot`
454 | 
455 | 
456 |         """
457 |         fig = None
458 |         
459 |         if ax == None:
460 |             fig, ax = plt.subplots(1)
461 |         
462 |         if edges:
463 |             edgelist = path
464 |         else:
465 |             edgelist = {(path[i], path[i+1]) for i in range(len(path)-1)}
466 | 
467 |         edges = set(self.dag.edges()) - set(edgelist)
468 |         
469 |         nx.draw(self.dag, self.pos, node_color=self.colors[0], ax=ax, edgelist=[])
470 |         nx.draw_networkx_labels(self.dag, self.pos, ax=ax)
471 | 
472 |         if conditional:
473 |             nx.draw_networkx_edges(self.dag, self.pos,
474 |                                edgelist=edgelist,
475 |                                width=lw, edge_color=self.colors[1], ax=ax, style='dotted')
476 |         else:
477 |             nx.draw_networkx_edges(self.dag, self.pos,
478 |                                edgelist=edgelist,
479 |                                width=lw, edge_color=self.colors[1], ax=ax)
480 | 
481 |         nx.draw_networkx_edges(self.dag, self.pos,
482 |                            edgelist=edges,
483 |                            width=1, ax=ax)
484 | 
485 |         if fig is not None:
486 |             fig.tight_layout()
487 | 
488 | 
489 |     def inputs(self):
490 |         nodes = set()
491 | 
492 |         for node, deg in self.dag.in_degree():
493 |             if deg == 0:
494 |                 nodes.add(node)
495 | 
496 |         return nodes
497 | 
498 |     def outputs(self):
499 |         nodes = set()
500 | 
501 |         for node, deg in self.dag.out_degree():
502 |             if deg == 0:
503 |                 nodes.add(node)
504 | 
505 |         return nodes
506 | 
507 |     def plot(self, output=None, pos=None, legend=False, ax=None, colors=False):
508 |         if pos is None:
509 |             if self.pos is None:
510 |                 self.pos = self.layout()
511 |             
512 |             pos = self.pos
513 | 
514 |         nodes = list(pos.keys())
515 |         inputs = self.inputs()
516 |         outputs = self.outputs()
517 | 
518 |         node_colors = []
519 |         node_pos = []
520 | 
521 |         for node in nodes:
522 |             node_pos.append(pos[node])
523 | 
524 |             if colors:
525 |                 if node in inputs:
526 |                     node_colors.append(self.colors[2])
527 |                 elif node in outputs:
528 |                     node_colors.append(self.colors[1])
529 |                 else:
530 |                     node_colors.append(self.colors[0])
531 |             else:
532 |                 node_colors.append(self.colors[0])
533 | 
534 |         node_pos = np.array(node_pos)
535 | 
536 |         if ax is None:
537 |             ax = nx.draw(self.dag, pos, nodelist=nodes, node_color=node_colors)
538 |         else:
539 |             nx.draw(self.dag, pos, nodelist=nodes, node_color=node_colors, ax=ax)
540 | 
541 | 
542 |         labels = {(node_i, node_j) : label for node_i, node_j, label in self.dag.edges(data='label', default='')}
543 | 
544 |         nx.draw_networkx_labels(self.dag, pos, ax=ax)
545 |         nx.draw_networkx_edge_labels(self.dag, pos, labels, ax=ax)
546 | 
547 |         if legend:
548 |             node_types = ['Regular node', 'Input', 'Output']
549 |             node_colors = [self.colors[0], self.colors[2], self.colors[1]]
550 | 
551 |             patches = [mpl.patches.Patch(color=node_colors[i], label=label) for i, label in enumerate(node_types)]
552 | 
553 |             plt.legend(handles=patches, fontsize=10)
554 | 
555 |         plt.gcf().tight_layout()
556 | 
557 |         if output is None:
558 |             plt.show()
559 |         else:
560 |             plt.savefig(output, dpi=300)
561 |             plt.close()
562 |         
563 | 
564 |     def v_structures(self):
565 |         structs = set()
566 | 
567 |         degrees = dict(self.dag.in_degree())
568 | 
569 |         for node in degrees:
570 |             if degrees[node] >= 2:
571 |                 for edge_i, edge_j in combinations(self.dag.in_edges(node), 2):
572 |                     node_i = edge_i[0]
573 |                     node_j = edge_j[0]
574 |                     
575 |                     if not (node_i, node_j) in self.dag.edges and not (node_j, node_i) in self.dag.edges:
576 |                         structs.add(tuple(sorted([edge_i, edge_j])))
577 | 
578 |         return structs
579 | 
580 |     def equivalence_class(self):
581 |         edges = list(self.dag.edges(data=True))
582 | 
583 |         equivalent = [[self.copy(), []]]
584 | 
585 |         structs = self.v_structures()
586 | 
587 |         for i, edge in enumerate(edges):
588 |             new_edges = list(edges)
589 | 
590 |             new_edges[i] = (edge[1], edge[0], edge[2])
591 | 
592 |             G = CausalModel()
593 |             G.dag.add_edges_from(new_edges)
594 | 
595 |             new_structs = CausalModel.v_structures(G)
596 | 
597 |             if new_structs == structs and len(list(nx.simple_cycles(G.dag)))==0:
598 |                 G.pos = dict(self.pos)
599 |                 G.colors = [color for color in self.colors]
600 |                 equivalent.append([G, new_edges[i][:2]])
601 | 
602 |         return equivalent
603 | 
604 | 
605 |     def basis_set(self):
606 |         nodes = set(self.dag.nodes())
607 | 
608 |         eqn = []
609 | 
610 |         for node in nodes:
611 |             parents = set(self.parents(node))
612 |             descendants = set(self.descendants(node))
613 |             
614 |             others = {n for n in nodes if n != node}
615 |             others -= parents
616 |             others -= descendants
617 |             
618 |             others = sorted(others)
619 |             parents = sorted(parents)
620 | 
621 |             if len(others) > 0:
622 |                 if len(parents) > 0:
623 |                     eqn.append('%s _||_ %s | %s' % (node, ", ".join(others), ', '.join(parents)))
624 |                 else:
625 |                     eqn.append('%s _||_ %s' % (node, ", ".join(others)))
626 | 
627 |         return sorted(eqn)
628 |             
629 | 
630 |     def intervention_graph(self, nodes, drop_nodes=False):
631 |         G = self.copy()
632 | 
633 |         for node in nodes:
634 |             G.dag.remove_edges_from(list(self.dag.in_edges(nodes)))
635 | 
636 |         if drop_nodes:
637 |             degrees = dict(G.dag.degree())
638 | 
639 |             remove = []
640 | 
641 |             for node in degrees:
642 |                 if degrees[node] == 0:
643 |                     remove.append(node)
644 |                     del G.pos[node]
645 | 
646 |             G.dag.remove_nodes_from(remove)
647 | 
648 |         return G
649 | 
650 |     def conditional_intervention_graph(self, nodes, dependencies, drop_nodes=False):
651 |         G = self.copy()
652 | 
653 |         for node in nodes:
654 |             G.dag.remove_edges_from(list(self.dag.in_edges(nodes)))
655 | 
656 |         G.dag.add_edges_from(dependencies)
657 | 
658 |         if drop_nodes:
659 |             degrees = dict(G.dag.degree())
660 | 
661 |             remove = []
662 | 
663 |             for node in degrees:
664 |                 if degrees[node] == 0:
665 |                     remove.append(node)
666 |                     del G.pos[node]
667 | 
668 |             G.dag.remove_nodes_from(remove)
669 | 
670 |         return G
671 | 
672 | 
673 | 
674 | if __name__ == "__main__":
675 |     names = ['m331', 'moAh6a6', 'vcFQ']
676 | 
677 |     graph_id = 'temp'#names[2]
678 | 
679 |     G = CausalModel()#graph_id)
680 |     G.load_model('dags/Primer.Fig.2.9.dot')
681 | 
682 |     Gx = G.intervention_graph('X')
683 |     Gx2 = Gx.intervention_graph('Z3')
684 |     print("ok")


--------------------------------------------------------------------------------
/LICENSE:
--------------------------------------------------------------------------------
 1 | MIT License
 2 | 
 3 | Copyright (c) 2020 Data For Science
 4 | 
 5 | Permission is hereby granted, free of charge, to any person obtaining a copy
 6 | of this software and associated documentation files (the "Software"), to deal
 7 | in the Software without restriction, including without limitation the rights
 8 | to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
 9 | copies of the Software, and to permit persons to whom the Software is
10 | furnished to do so, subject to the following conditions:
11 | 
12 | The above copyright notice and this permission notice shall be included in all
13 | copies or substantial portions of the Software.
14 | 
15 | THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
16 | IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
17 | FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
18 | AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
19 | LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
20 | OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
21 | SOFTWARE.
22 | 


--------------------------------------------------------------------------------
/README.md:
--------------------------------------------------------------------------------
 1 | ![GitHub](https://img.shields.io/github/license/DataForScience/Causality)
 2 | [![Twitter @data4sci](https://img.shields.io/twitter/follow/data4sci)](https://twitter.com/intent/follow?screen_name=data4sci)
 3 | ![GitHub top language](https://img.shields.io/github/languages/top/DataForScience/Causality)
 4 | ![GitHub repo size](https://img.shields.io/github/repo-size/DataForScience/Causality)
 5 | ![GitHub last commit](https://img.shields.io/github/last-commit/DataForScience/Causality)
 6 | [![Binder](https://mybinder.org/badge_logo.svg)](https://mybinder.org/v2/gh/DataForScience/Causality/master)
 7 | 
 8 | [![Sunday Briefing](https://img.shields.io/badge/Sunday_Briefing-Subscribe-blue)](https://data4sci.ck.page/8a51c452bc)
 9 | 
10 | # Causality
11 | 
12 | How do causes lead to effects? Can you associate the cause leading to the observed effect? Big Data opens the doors for us to be able to answer questions such as this, but before we are able to do so, we must dive into the field of Causal Inference, a field championed by Judea Pearl.
13 | In this series of blog posts we will learn about the main ideas of Causality by working our way through “Causal Inference In Statistics” a nice Primer co-authored by Pearl himself.
14 | 
15 | <p align="center">
16 | <a href='https://amzn.to/3gsFlkO' alt='Judea Pearl — Causal Inference in Statistics: A Primer'><img src='data/causality.jpeg'></a>
17 |  <br/>
18 |   Amazon Affiliate Link: https://amzn.to/3gsFlkO
19 | </p>
20 | 
21 | 
22 | The book is divided into Four chapters. The first chapter covers background material in probability and statistics. The other three chapters are (roughly) organized to match the “Three steps” in the ladder of causality as defined by Pearl:
23 | 
24 | 1. — Association
25 | 2. — Intervention
26 | 3. — Counterfactuals
27 | 
28 | In this series of blog posts we will cover most of the content of the book, with a special emphasis on the parts that I believe are more interesting or relevant to practical applications. In addition to summarizing and explaining the content, we will also explore some of the ideas using simple (or as simple as possible) Python code you can run on Binder: [![Binder](https://mybinder.org/badge_logo.svg)](https://mybinder.org/v2/gh/DataForScience/Causality/master)
29 | 
30 | 
31 | 
32 | ## Chapter 1
33 | 1.2 - [Simpson's Paradox](https://data4sci.substack.com/p/simpsons-paradox) -- [1.2 - Simpson's Paradox.ipynb](https://github.com/DataForScience/Causality/blob/master/1.2%20-%20Simpsons%20Paradox.ipynb)
34 | 
35 | 1.3 - [Probability Theory](https://data4sci.substack.com/p/probability-theory) -- [1.3 - Probability and Statistics.ipynb](https://github.com/DataForScience/Causality/blob/master/1.3%20-%20Probability%20and%20Statistics.ipynb)
36 | 
37 | 1.4 - [Graphs](https://data4sci.substack.com/p/graphs) -- [1.4 - Graphs.ipynb](https://github.com/DataForScience/Causality/blob/master/1.4%20-%20Graphs.ipynb)
38 | 
39 | 1.5 - [Structural Causal Models](https://data4sci.substack.com/p/structural-causal-models-e4d) -- [1.5 - Structural Causal Models.ipynb](https://github.com/DataForScience/Causality/blob/master/1.5%20-%20Structural%20Causal%20Models.ipynb)
40 | 
41 | ## Chapter 2
42 | 2.2 - [Chains and Forks](https://data4sci.substack.com/p/chains-and-forks) -- [2.2 - Chains and Forks.ipynb](https://github.com/DataForScience/Causality/blob/master/2.2%20-%20Chains%20and%20Forks.ipynb)
43 | 
44 | 2.3 - [Colliders](https://data4sci.substack.com/p/colliders) -- [2.3 - Colliders.ipynb](https://github.com/DataForScience/Causality/blob/master/2.3%20-%20Colliders.ipynb)
45 | 
46 | 2.4 - [d-separation](https://data4sci.substack.com/p/d-separation) -- [2.4 - d-separation.ipynb](https://github.com/DataForScience/Causality/blob/master/2.4%20-%20d-separation.ipynb)
47 | 
48 | 2.5 - [Model Testing and Causal Search](https://data4sci.substack.com/p/model-testing-and-causal-search) -- [2.5 - Model Testing and Causal Search.ipynb](https://github.com/DataForScience/Causality/blob/master/2.5%20-%20Model%20Testing%20and%20Causal%20Search.ipynb)
49 | 
50 | ## Chapter 3
51 | 
52 | 3.1 - [Interventions](https://data4sci.substack.com/p/interventions) -- [3.1 - Interventions.ipynb](https://github.com/DataForScience/Causality/blob/master/3.1%20-%20Interventions.ipynb)
53 | 
54 | 3.2 - [Adjustment Formula](https://data4sci.substack.com/p/the-adjustment-formula) -- [3.2 - The Adjustment Formula.ipynb](https://github.com/DataForScience/Causality/blob/master/3.2%20-%20The%20Adjustment%20Formula.ipynb)
55 | 
56 | 3.3 - [Backdoor Criterion](https://data4sci.substack.com/p/backdoor-criterion) -- [3.3 - Backdoor Criterion.ipynb](https://github.com/DataForScience/Causality/blob/master/3.3%20-%20Backdoor%20Criterion.ipynb)
57 | 
58 | 3.4 - [Front-Door Criterion](https://data4sci.substack.com/p/front-door-criterion) -- [3.4 - Front-Door Criterion.ipynb](https://github.com/DataForScience/Causality/blob/master/3.4%20-%20Front-Door%20Criterion.ipynb)
59 | 
60 | 3.5 - [Conditional Interventions and Covariate-Specific Effects](https://data4sci.substack.com/p/conditional-interventions-and-covariate) -- [3.5 - Conditional Interventions and Covariate-Specific Effects.ipynb](https://github.com/DataForScience/Causality/blob/master/3.5%20-%20Conditional%20Interventions%20and%20Covariate-Specific%20Effects.ipynb)
61 | 
62 | 3.6 - [Inverse Probability Weighing](https://data4sci.substack.com/p/inverse-probability-weighing) -- [3.6 - Inverse Probability Weighing.ipynb](https://github.com/DataForScience/Causality/blob/master/3.6%20-%20Inverse%20Probability%20Weighing.ipynb)
63 | 
64 | 3.7 - [Mediation](https://data4sci.substack.com/p/mediation) -- [3.7 - Mediation.ipynb](https://github.com/DataForScience/Causality/blob/master/3.7%20-%20Mediation.ipynb)
65 | 
66 | ---
67 | 
68 | For a more in-depth analysis, checkout Pearl's more technical book:
69 | 
70 | <p align="center">
71 | <a href='https://amzn.to/2OSBP6u' alt='Judea Pearl — Causality'><img src='data/book2.jpeg' height=250></a>
72 |  <br/>
73 |   Amazon Affiliate Link: https://amzn.to/2OSBP6u
74 | </p>
75 | 
76 | ---
77 | 
78 | Sign up to the [Data Science Briefing](http://data4sci.com/newsletter) newsletter to be the first to know when we publish new posts:
79 | 
80 | <p align="center">
81 | <a href='https://data4sci.ck.page/8a51c452bc' alt='Data Science Briefing Newsletter'><img src='data/newsletter.png' width=500></a>
82 | </p>
83 | 


--------------------------------------------------------------------------------
/d4sci.mplstyle:
--------------------------------------------------------------------------------
 1 | # Data For Science style
 2 | # Author: Bruno Goncalves <bgoncalves@data4sci.com>
 3 | # Modified from the matplotlib FiveThirtyEight style by
 4 | # Author: Cameron Davidson-Pilon, replicated styles from FiveThirtyEight.com
 5 | # See https://www.dataorigami.net/blogs/fivethirtyeight-mpl
 6 | 
 7 | lines.linewidth: 4
 8 | lines.solid_capstyle: butt
 9 | 
10 | legend.fancybox: true
11 | 
12 | axes.prop_cycle: cycler('color', ['51a7f9', 'cf51f9', '70bf41', 'f39019', 'f9e351', 'f9517b', '6d904f', '8b8b8b','810f7c']) 
13 | 
14 | axes.labelsize: large
15 | axes.axisbelow: true
16 | axes.grid: true
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  1 | sepal_length,sepal_width,petal_length,petal_width,species
  2 | 5.1,3.5,1.4,0.2,setosa
  3 | 4.9,3.0,1.4,0.2,setosa
  4 | 4.7,3.2,1.3,0.2,setosa
  5 | 4.6,3.1,1.5,0.2,setosa
  6 | 5.0,3.6,1.4,0.2,setosa
  7 | 5.4,3.9,1.7,0.4,setosa
  8 | 4.6,3.4,1.4,0.3,setosa
  9 | 5.0,3.4,1.5,0.2,setosa
 10 | 4.4,2.9,1.4,0.2,setosa
 11 | 4.9,3.1,1.5,0.1,setosa
 12 | 5.4,3.7,1.5,0.2,setosa
 13 | 4.8,3.4,1.6,0.2,setosa
 14 | 4.8,3.0,1.4,0.1,setosa
 15 | 4.3,3.0,1.1,0.1,setosa
 16 | 5.8,4.0,1.2,0.2,setosa
 17 | 5.7,4.4,1.5,0.4,setosa
 18 | 5.4,3.9,1.3,0.4,setosa
 19 | 5.1,3.5,1.4,0.3,setosa
 20 | 5.7,3.8,1.7,0.3,setosa
 21 | 5.1,3.8,1.5,0.3,setosa
 22 | 5.4,3.4,1.7,0.2,setosa
 23 | 5.1,3.7,1.5,0.4,setosa
 24 | 4.6,3.6,1.0,0.2,setosa
 25 | 5.1,3.3,1.7,0.5,setosa
 26 | 4.8,3.4,1.9,0.2,setosa
 27 | 5.0,3.0,1.6,0.2,setosa
 28 | 5.0,3.4,1.6,0.4,setosa
 29 | 5.2,3.5,1.5,0.2,setosa
 30 | 5.2,3.4,1.4,0.2,setosa
 31 | 4.7,3.2,1.6,0.2,setosa
 32 | 4.8,3.1,1.6,0.2,setosa
 33 | 5.4,3.4,1.5,0.4,setosa
 34 | 5.2,4.1,1.5,0.1,setosa
 35 | 5.5,4.2,1.4,0.2,setosa
 36 | 4.9,3.1,1.5,0.2,setosa
 37 | 5.0,3.2,1.2,0.2,setosa
 38 | 5.5,3.5,1.3,0.2,setosa
 39 | 4.9,3.6,1.4,0.1,setosa
 40 | 4.4,3.0,1.3,0.2,setosa
 41 | 5.1,3.4,1.5,0.2,setosa
 42 | 5.0,3.5,1.3,0.3,setosa
 43 | 4.5,2.3,1.3,0.3,setosa
 44 | 4.4,3.2,1.3,0.2,setosa
 45 | 5.0,3.5,1.6,0.6,setosa
 46 | 5.1,3.8,1.9,0.4,setosa
 47 | 4.8,3.0,1.4,0.3,setosa
 48 | 5.1,3.8,1.6,0.2,setosa
 49 | 4.6,3.2,1.4,0.2,setosa
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 51 | 5.0,3.3,1.4,0.2,setosa
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 53 | 6.4,3.2,4.5,1.5,versicolor
 54 | 6.9,3.1,4.9,1.5,versicolor
 55 | 5.5,2.3,4.0,1.3,versicolor
 56 | 6.5,2.8,4.6,1.5,versicolor
 57 | 5.7,2.8,4.5,1.3,versicolor
 58 | 6.3,3.3,4.7,1.6,versicolor
 59 | 4.9,2.4,3.3,1.0,versicolor
 60 | 6.6,2.9,4.6,1.3,versicolor
 61 | 5.2,2.7,3.9,1.4,versicolor
 62 | 5.0,2.0,3.5,1.0,versicolor
 63 | 5.9,3.0,4.2,1.5,versicolor
 64 | 6.0,2.2,4.0,1.0,versicolor
 65 | 6.1,2.9,4.7,1.4,versicolor
 66 | 5.6,2.9,3.6,1.3,versicolor
 67 | 6.7,3.1,4.4,1.4,versicolor
 68 | 5.6,3.0,4.5,1.5,versicolor
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 80 | 6.0,2.9,4.5,1.5,versicolor
 81 | 5.7,2.6,3.5,1.0,versicolor
 82 | 5.5,2.4,3.8,1.1,versicolor
 83 | 5.5,2.4,3.7,1.0,versicolor
 84 | 5.8,2.7,3.9,1.2,versicolor
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 86 | 5.4,3.0,4.5,1.5,versicolor
 87 | 6.0,3.4,4.5,1.6,versicolor
 88 | 6.7,3.1,4.7,1.5,versicolor
 89 | 6.3,2.3,4.4,1.3,versicolor
 90 | 5.6,3.0,4.1,1.3,versicolor
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 92 | 5.5,2.6,4.4,1.2,versicolor
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 97 | 5.7,3.0,4.2,1.2,versicolor
 98 | 5.7,2.9,4.2,1.3,versicolor
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100 | 5.1,2.5,3.0,1.1,versicolor
101 | 5.7,2.8,4.1,1.3,versicolor
102 | 6.3,3.3,6.0,2.5,virginica
103 | 5.8,2.7,5.1,1.9,virginica
104 | 7.1,3.0,5.9,2.1,virginica
105 | 6.3,2.9,5.6,1.8,virginica
106 | 6.5,3.0,5.8,2.2,virginica
107 | 7.6,3.0,6.6,2.1,virginica
108 | 4.9,2.5,4.5,1.7,virginica
109 | 7.3,2.9,6.3,1.8,virginica
110 | 6.7,2.5,5.8,1.8,virginica
111 | 7.2,3.6,6.1,2.5,virginica
112 | 6.5,3.2,5.1,2.0,virginica
113 | 6.4,2.7,5.3,1.9,virginica
114 | 6.8,3.0,5.5,2.1,virginica
115 | 5.7,2.5,5.0,2.0,virginica
116 | 5.8,2.8,5.1,2.4,virginica
117 | 6.4,3.2,5.3,2.3,virginica
118 | 6.5,3.0,5.5,1.8,virginica
119 | 7.7,3.8,6.7,2.2,virginica
120 | 7.7,2.6,6.9,2.3,virginica
121 | 6.0,2.2,5.0,1.5,virginica
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127 | 7.2,3.2,6.0,1.8,virginica
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133 | 7.9,3.8,6.4,2.0,virginica
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139 | 6.4,3.1,5.5,1.8,virginica
140 | 6.0,3.0,4.8,1.8,virginica
141 | 6.9,3.1,5.4,2.1,virginica
142 | 6.7,3.1,5.6,2.4,virginica
143 | 6.9,3.1,5.1,2.3,virginica
144 | 5.8,2.7,5.1,1.9,virginica
145 | 6.8,3.2,5.9,2.3,virginica
146 | 6.7,3.3,5.7,2.5,virginica
147 | 6.7,3.0,5.2,2.3,virginica
148 | 6.3,2.5,5.0,1.9,virginica
149 | 6.5,3.0,5.2,2.0,virginica
150 | 6.2,3.4,5.4,2.3,virginica
151 | 5.9,3.0,5.1,1.8,virginica
152 | 


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/data/newsletter.png:
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https://raw.githubusercontent.com/DataForScience/Causality/f7b1abb57541776dc786174deb102ca4ab864df6/data/newsletter.png


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/environment.yml:
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 1 | dependencies:
 2 |   - matplotlib==3.1.3
 3 |   - networkx==2.4
 4 |   - numpy==1.18.1
 5 |   - pandas==1.0.1
 6 |   - requests=2.21.0
 7 |   - scikit-learn==0.22.1
 8 |   - statsmodels==0.11.1
 9 |   - tqdm==4.46.0
10 |   - watermark==2.0.2
11 |   - pygraphviz==1.5
12 |   - pydot==1.4.1


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