Simulating the Impact of Interventions

By simulating the impact of interventions, we answer the questions such as:

What will happen to the variable Z if I intervene on Y?

How to use it

To see how the method works, let’s generate some data:

>>> import numpy as np, pandas as pd

>>> X = np.random.normal(loc=0, scale=1, size=1000)
>>> Y = 2*X + np.random.normal(loc=0, scale=1, size=1000)
>>> Z = 3*Y + np.random.normal(loc=0, scale=1, size=1000)
>>> training_data = pd.DataFrame(data=dict(X=X, Y=Y, Z=Z))


Next, we’ll model cause-effect relationships as a probabilistic causal model and fit it to the data:

>>> import networkx as nx
>>> from dowhy import gcm

>>> causal_model = gcm.ProbabilisticCausalModel(nx.DiGraph([('X', 'Y'), ('Y', 'Z')])) # X -> Y -> Z
>>> causal_model.set_causal_mechanism('X', gcm.EmpiricalDistribution())

>>> gcm.fit(causal_model, training_data)


Finally, let’s perform an intervention on X. Here, we explicitly perform the intervention $$do(X:=1)$$:

>>> samples = gcm.interventional_samples(causal_model,
>>>                                      {'X': lambda x: 1},
>>>                                      num_samples_to_draw=1000)
X         Y          Z
0  1  3.481467  12.475105
1  1  1.282945   3.279435
2  1  2.508717   7.907412
3  1  2.077061   5.506252
4  1  1.400568   6.097633


As we can see, X is now fixed at a constant value of 1. This is known as an atomic intervention. We can also perform shift interventions where we shift the random variable X by some value:

>>> samples = gcm.interventional_samples(causal_model,
>>>                                      {'X': lambda x: x + 0.5},
>>>                                      num_samples_to_draw=1000)