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A, B, C, D are four variables. Why $A \perp C | \{ B , D \}$ and $B \perp D | \{ A , C \}$ could not be represented by a Bayesian network?

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  • $\begingroup$ This is an example discussed in the book "Probabilistic Graphical Models" by Koller and Friedman. The reason why these conditional independence assumptions cannot simultaneously be encoded in a Bayesian network can be proven by simply drawing all possible Bayesian Networks over four random variables, and concluding that none of them encodes both assumptions correctly. $\endgroup$ – Maurits M Jul 24 at 13:56

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