DSeparation¶
Algorithm for testing dseparation in DAGs.
dseparation is a test for conditional independence in probability distributions that can be factorized using DAGs. It is a purely graphical test that uses the underlying graph and makes no reference to the actual distribution parameters. See 1 for a formal definition.
The implementation is based on the conceptually simple linear time algorithm presented in 2. Refer to 3, 4 for a couple of alternative algorithms.
Examples
>>>
>>> # HMM graph with five states and observation nodes
... g = nx.DiGraph()
>>> g.add_edges_from(
... [
... ("S1", "S2"),
... ("S2", "S3"),
... ("S3", "S4"),
... ("S4", "S5"),
... ("S1", "O1"),
... ("S2", "O2"),
... ("S3", "O3"),
... ("S4", "O4"),
... ("S5", "O5"),
... ]
... )
>>>
>>> # states/obs before 'S3' are dseparated from states/obs after 'S3'
... nx.d_separated(g, {"S1", "S2", "O1", "O2"}, {"S4", "S5", "O4", "O5"}, {"S3"})
True
References
 1
Pearl, J. (2009). Causality. Cambridge: Cambridge University Press.
 2
Darwiche, A. (2009). Modeling and reasoning with Bayesian networks. Cambridge: Cambridge University Press.
 3
Shachter, R. D. (1998). Bayesball: rational pastime (for determining irrelevance and requisite information in belief networks and influence diagrams). In , Proceedings of the Fourteenth Conference on Uncertainty in Artificial Intelligence (pp. 480–487). San Francisco, CA, USA: Morgan Kaufmann Publishers Inc.
 4
Koller, D., & Friedman, N. (2009). Probabilistic graphical models: principles and techniques. The MIT Press.

Return whether node sets 