Unformatted text preview: Z . Provide a transformation G of G such that we can test whether P B 1 ( X  Y ) = P B 2 ( X  Y ) using a single dseparation query on G . Note that Z may be the same as X , and that Z may also belong to Y . Your criterion should always be sound, but only be complete in the same sense that dseparation is complete, i.e., for “generic” CPDs. Hint: Although it is possible to do this problem using laborious case analysis, it is signi±cantly easier to think of how a dseparation query on a transformed graph G can be used to detect whether a perturbation on the CPD P ( Z  Pa Z ) makes a diFerence to P ( X  Y )....
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 Fall '07
 EranSegal
 Graph Theory

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