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# Markov Blanket [4 P]

Let be a random variable corresponding to some node in a Bayesian Network. Recall that a Markov Blanket of is a set of variables consisting of 's parents, children and children's parents in the Network. Thus

Denote by the set of all variables in the system (i.e. variables that correspond to some node in the Network) except for .

a)
[2 P]

Show that , i.e. a variable is conditionally independent of all other variables given its Markov Blanket. Use the fact that is conditionally independent of all its non-descendants given its parents (this is true by construction of the Bayesian Network). Be sure to specify what a "non-descendant" node is.

b)
[2 P]

Show (e.g. by counter example) that cannot be left out of the definition of a Markov Blanket. So you need to show that there is a network in which some is not conditionally independent of all other nodes given .

Next: d-separation [4* P] Up: MLA_Exercises_2007 Previous: Bayes' Decision Theory [5+2*
Haeusler Stefan 2007-12-03