Probabilistic Graphical Models
Probabilistic Graphical Models
Probabilistic Graphical Models
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Active trailsAn undirected path in BN structure G is calledactive trail for observed variables O ⊆ {X 1 ,…,X n }, if forevery consecutive triple of vars X,Y,Z on the pathX Y Z and Y is unobserved (Y ∉ O)X Y Z and Y is unobserved (Y ∉ O)X Y Z and Y is unobserved (Y ∉ O)X Y Z and Y or any of Y’s descendants is observedAny variables X i and X j for which ∄ active trail forobservations O are called d-separated by OWe write d-sep(X i ;X j | O)Sets A and B are d-separated given O if d-sep(X,Y |O)for all X∈A, Y∈B. Write d-sep(A; B | O)7
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