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https://github.com/eschmidt42/bcg
First steps using Bayesian causal graphical models.
https://github.com/eschmidt42/bcg
Last synced: 6 days ago
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First steps using Bayesian causal graphical models.
- Host: GitHub
- URL: https://github.com/eschmidt42/bcg
- Owner: eschmidt42
- License: apache-2.0
- Created: 2020-04-15T13:50:27.000Z (over 4 years ago)
- Default Branch: master
- Last Pushed: 2022-07-22T06:00:10.000Z (over 2 years ago)
- Last Synced: 2023-03-09T08:56:22.727Z (over 1 year ago)
- Language: Jupyter Notebook
- Homepage: https://eschmidt42.github.io/bcg/
- Size: 21.4 MB
- Stars: 2
- Watchers: 2
- Forks: 1
- Open Issues: 2
-
Metadata Files:
- Readme: README.md
- Contributing: CONTRIBUTING.md
- License: LICENSE
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README
# Bayesian Causal Graphs - BCG
> Playing with Bayesian Causal Graphs.
The main references have so far been the following:
**References**
References for the dowhy package:
* Documentation: [here](https://microsoft.github.io/dowhy/)
* GitHub: [here](https://github.com/microsoft/dowhy)
Material which helped my introductory reading so far by :
* degeneratestate.org: [Pt I - potential outcomes](http://www.degeneratestate.org/posts/2018/Mar/24/causal-inference-with-python-part-1-potential-outcomes/) (contains definitions of ATE, ATT and ATC, among other things)
* degeneratestate.org: [Pt II - causal graphs & the backdoor criterion](http://www.degeneratestate.org/posts/2018/Jul/10/causal-inference-with-python-part-2-causal-graphical-models/)
* this youtube video [on backdoor paths](https://www.youtube.com/watch?v=F8vcki-uWJc)
* Rubin et al. 2005 on [causal inference and potential outcomes](http://www.stat.unipg.it/stanghellini/rubinjasa2005.pdf)
* wiki article on the [average treatment effect (ATE)](https://en.wikipedia.org/wiki/Average_treatment_effect)
* this wiki article [on propensity score matching](https://en.wikipedia.org/wiki/Propensity_score_matching)
**Brief list of concepts I found useful**:
* at the center of interest is the calculation of *potential outcomes* / *counterfactuals* $\rightarrow$ what Y would have been if X would have been different (so everything after all observations are done) $\rightarrow$ so we may want to know if a certain drug was taken or a placebo and measure the difference in effect
* potential outcomes and counterfactuals can be seen as being the same thing, see [Rubin et al. 2005](http://www.stat.unipg.it/stanghellini/rubinjasa2005.pdf) (really more of a useful thing know when reading the literature - man was I confused before knowing this)
* potential outcomes can be calculated without using a graphical model but graphical models help by guiding which variables should be conditioned on legally
* graphical models themselves require justification
**Technical note**:
In order to run this notebook, you'll need a symbolic link from `/notebooks/bcg` to `./bcg`.
## Small example using $ Y = a \cdot X_0 ^ b + c + X_1 $ to generate observations
```python
n = 1000
a,b,c = 1.5, 1., 0
target = 'Y'
obs = pd.DataFrame(columns=['X0', 'X1', target])
obs['X0'] = stats.uniform.rvs(loc=-1, scale=2, size=n)
# obs['X1'] = stats.norm.rvs(loc=0, scale=.1, size=n)
obs['X1'] = stats.uniform.rvs(loc=-.5, scale=1, size=n)
obs[target] = a * obs.X0 ** b + c + obs.X1
obs.head()
```
.dataframe tbody tr th:only-of-type {
vertical-align: middle;
}
.dataframe tbody tr th {
vertical-align: top;
}
.dataframe thead th {
text-align: right;
}
X0
X1
Y
0
-0.806061
0.370908
-0.838184
1
0.667759
0.228029
1.229667
2
0.158370
0.352362
0.589917
3
0.103955
-0.018955
0.136977
4
-0.755793
-0.387319
-1.521008
### Inspecting the observed data
```python
plot_target_vs_rest(obs)
```
```python
plot_var_hists(obs)
```
```python
show_correlations(obs)
```
## Generating the probably simplest possible causal graphical model
```python
gg = GraphGenerator(obs)
print(f'target var: {gg.target}, not target vars: {", ".join(gg.not_targets)}')
```
target var: Y, not target vars: X0, X1
```python
g = gg.get_only_Xi_to_Y()
gml = gg.get_gml(g)
```
```python
gg.vis_g(g)
```
```python
treatment = ['X0', ] # 'X1'
causal_model = dw.CausalModel(data=obs, treatment=treatment,
outcome=target, graph=gml)
```
INFO:dowhy.causal_graph:If this is observed data (not from a randomized experiment), there might always be missing confounders. Adding a node named "Unobserved Confounders" to reflect this.
INFO:dowhy.causal_model:Model to find the causal effect of treatment ['X0'] on outcome ['Y']
Note how `CausalModel` added an unobserved confounder variable `U`
```python
causal_model.view_model()
```
WARNING:dowhy.causal_graph:Warning: Pygraphviz cannot be loaded. Check that graphviz and pygraphviz are installed.
INFO:dowhy.causal_graph:Using Matplotlib for plotting
### Identifying the estimant
```python
identified_estimand = causal_model.identify_effect(proceed_when_unidentifiable=True)
print(identified_estimand)
```
INFO:dowhy.causal_identifier:Common causes of treatment and outcome:['U']
WARNING:dowhy.causal_identifier:If this is observed data (not from a randomized experiment), there might always be missing confounders. Causal effect cannot be identified perfectly.
INFO:dowhy.causal_identifier:Continuing by ignoring these unobserved confounders because proceed_when_unidentifiable flag is True.
INFO:dowhy.causal_identifier:Instrumental variables for treatment and outcome:[]
Estimand type: nonparametric-ate
### Estimand : 1
Estimand name: backdoor
Estimand expression:
d
─────(Expectation(Y))
d[X₀]
Estimand assumption 1, Unconfoundedness: If U→{X0} and U→Y then P(Y|X0,,U) = P(Y|X0,)
### Estimand : 2
Estimand name: iv
No such variable found!
### Computing the causal treatment estimate
```python
method_name = 'backdoor.linear_regression'
effect_kwargs = dict(
method_name=method_name,
control_value = 0,
treatment_value = 1,
target_units = 'ate',
test_significance = True
)
causal_estimate = causal_model.estimate_effect(identified_estimand,
**effect_kwargs)
```
INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator
INFO:dowhy.causal_estimator:b: Y~X0+X0*X1
```python
print(causal_estimate)
```
*** Causal Estimate ***
## Target estimand
Estimand type: nonparametric-ate
### Estimand : 1
Estimand name: backdoor
Estimand expression:
d
─────(Expectation(Y))
d[X₀]
Estimand assumption 1, Unconfoundedness: If U→{X0} and U→Y then P(Y|X0,,U) = P(Y|X0,)
### Estimand : 2
Estimand name: iv
No such variable found!
## Realized estimand
b: Y~X0+X0*X1
## Estimate
Value: 1.4816271269256485
## Statistical Significance
p-value: <0.001
### Trying to poke holes into the causal treatment effect
```python
method_name = 'placebo_treatment_refuter'
refute_kwargs = dict(
method_name=method_name,
placebo_type = "permute", # relevant for placebo refutation
)
refute_res = causal_model.refute_estimate(identified_estimand,
causal_estimate,
**refute_kwargs)
```
INFO:dowhy.causal_estimator:INFO: Using Linear Regression Estimator
INFO:dowhy.causal_estimator:b: Y~placebo+placebo*X1
```python
print(refute_res)
```
Refute: Use a Placebo Treatment
Estimated effect:(1.4816271269256485,)
New effect:(0.10464178347001926,)