*Compilation of a MSBN into a Linked Junction Forest
Major steps in compiling a LJF
- Convert each DAG (hypernode) into a chordal graph such that all dependence relations are preserved.
- Express the chordal graph as a junction tree (JT) of cliques.
- Convert each hyperlink (d-sepset) into linkages, each of which is a subset of the d-sepest.
- Convert conditional probability distributions in each subnet to belief tables of the corresponding JT and d-sepset.
- Let B(Ni) be the belief table on a hypernode and B(Ij) be the belief table on a hyperlink. The joint system belief (JSB) of a LJF is ? i B(Ni) / ? j B(Ij).
Theorem: JSB of a LJF is equivalent to jpd of its MSBN.
Since each subnet is organized as a tree, a LJF is an equivalent but more effective data structure for inference computation.