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Junction Trees

[3 P] Consider the following distribution 4

$\displaystyle P(A,B$ $\displaystyle ,C,D,E,F,G,H,I) =$    
  $\displaystyle P(A)P(B\vert A)P(C\vert A)P(D\vert A)P(E\vert B)P(F\vert C)P(G\vert D)P(H\vert E,F)P(I\vert F,G)$    

a)
Draw the Bayesian network for this distribution.
b)
Draw the moralised graph.
c)
Draw the triangulated graph. Your triangulated should contain cliques of the smallest size possible.
d)
Draw a junction tree for the above graph and verify that it satisfies the running intersection property.
e)
Write down a suitable initialization of clique potentials.
f)
Find an appropriate message updating schedule.



2015 Gernot Griesbacher, Anand Subramoney