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data & R code

Comparing causal networks

Other examples have showcased how to compare Bayesian networks as probabilitistic models, focusing on graphical differences and equivalence classes. None of these approaches is useful in determining how different two networks are when interpreted as causal models.

bnlearn implements the sid() measure of causal divergence, the causal analogue of shd(). Similarly to shd(), it takes two networks learned and true and evaluates the former taking the latter as ground truth.

> learned = model2network("[A][C][F][B|A][D|A:C][E|B:F]")
> true = model2network("[A][C][F][B|A][D|A:C][E|F]")
> sid(learned, true)

[1] 0
attr(,"bounds")
[1] 0 0

When both learned and true are DAGs, sid() returns a single value (their divergence). When either network is a CPDAG, the SID value is computed for each DAG in the equivalence class it represents using cextend.all(). When both networks are CPDAGs, sid() computes the divergence for all combinations of DAGs from the respective equivalence classes.

> sid(cpdag(learned), true)

[1] 0 3
attr(,"bounds")
[1] 0 3

> sid(learned, cpdag(true))

[1] 2 0 4 2
attr(,"bounds")
[1] 0 4

> sid(cpdag(learned), cpdag(true))

[1] 2 5 0 3 4 2 2 0
attr(,"bounds")
[1] 0 5

In addition, sid() will always attach to its return value the lower and upper bound of the computed SID values, for compatibility with the reference implementation provided by package sid.