next up previous
Next: Junction Trees Up: MLA_Exercises_2013 Previous: Factor graphs: HMM

Markov Networks

[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.

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

[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.

$ B \perp C \vert A$

Image markovNetwork1
$ A \perp E \vert D$

Image markovNetwork2

Hubner Florian 2014-01-21