Moralization and triangulization on belief networks

Question

Assume that I have a belief network with a set of nodes.

In order to create a valid junction tree I have to moralize the graph. Assume now that I have nodes with more than 2 parents (e.g 3 parents) then I have to link each of the parents. After doing that, the graphical models contain some unnecessary cliques. Can I use only a part of the cliques for the Junction Tree Creation? Or I must use every clique in the junction tree (e.g., a case with 8 nodes and 8 cliques)?

Answer 1

I'm trying to implement the junction tree algorithm in Ruby.

I found that after moralizing, triangulating, and creating the final cliques by variable elimination, the final cliques contained all of the cliques from triangulated graph, but the maximally connected cliques in the triangulated graph were combined into one clique in the junction tree.

I'm new at this, but I don't think you can drop cliques along the way.