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M-Separation
M-Separation
This is a property of graphs, in particular of directed graphs (possibly cyclic),
and by extension to other graphs that represent equivalence classes over
directed graphs or directed acyclic graphs. The definition for directed acyclic
graphs is given in Pearl (1988); its extension to cyclic graphs is given in
Spirtes (??). Under the assumption of faithfulness, X is d-separated from conditional
in a set Z just in case X is independent of Y conditional on Z in the population,
so running an algorithm using m-separation facts alone produces the output graph
that would obtain under faithfulness if all conditional independence judgments
were correct.