# Attributing Distributional Changes

When attributing distribution changes, we answer the question:

What mechanism in my system changed between two sets of data?

For example, in a distributed computing system, we want to know why an important system metric changed in a negative way.

## How to use it

To see how the method works, let’s take the example from above and assume we have a system of three services X, Y, Z, producing latency numbers. The first dataset data_old is before the deployment, data_new is after the deployment:

>>> import networkx as nx, numpy as np, pandas as pd
>>> from dowhy import gcm
>>> from scipy.stats import halfnorm

>>> X = halfnorm.rvs(size=1000, loc=0.5, scale=0.2)
>>> Y = halfnorm.rvs(size=1000, loc=1.0, scale=0.2)
>>> Z = np.maximum(X, Y) + np.random.normal(loc=0, scale=1, size=1000)
>>> data_old = pd.DataFrame(data=dict(X=X, Y=Y, Z=Z))

>>> X = halfnorm.rvs(size=1000, loc=0.5, scale=0.2)
>>> Y = halfnorm.rvs(size=1000, loc=1.0, scale=0.2)
>>> Z = X + Y + np.random.normal(loc=0, scale=1, size=1000)
>>> data_new = pd.DataFrame(data=dict(X=X, Y=Y, Z=Z))


The change here simulates an accidental conversion of multi-threaded code into sequential one (waiting for X and Y in parallel vs. waiting for them sequentially).

Next, we’ll model cause-effect relationships as a probabilistic causal model:

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

>>> attributions = gcm.distribution_change(causal_model, data_old, data_new, 'Z')

As we can see, $$Z$$ got the highest attribution score here, which matches what we would expect, given that we changed the mechanism for variable $$Z$$ in our data generation.
As the reader may have noticed, there is no fitting step involved when using this method. The reason is, that this function will call fit internally. To be precise, this function will make two copies of the causal graph and fit one graph to the first dataset and the second graph to the second dataset.