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Markov Networks

a)
[2 P]For the given joint probability draw an appropriate Markov network and write down the formula for the given conditional probability. Simplify the formula for the conditional probability as far as possible.

(i)
$ P(A,B,C,D,E) = \frac{1}{Z}\phi(A,C)\phi(B,C)\phi(C,D)\phi(C,E)$ ,
$ P(A\vert C) = ?$
(ii)
$ P(A,B,C,D,E) = \frac{1}{Z}\phi(A,B,C)\phi(C,D)\phi(D,E)$ ,
$ P(A\vert D) = ?$

b)
[3 P]In this example you have to write down the joint distribution for the given Markov network and proof that a given independence assumption holds.

(i)
$ B \perp C \vert A$

Image markovNetwork1
(ii)
$ A \perp E \vert D$

Image markovNetwork2



2015 Gernot Griesbacher, Anand Subramoney