Sidestepping the Triangulation Problem in Bayesian Net Computations

This paper presents a new approach for com­ puting posterior probabilities in Bayesian nets, which sidesteps the triangulation prob­ lem. The current state of art is the clique tree propagation approach. When the underlying graph of a Bayesian net is triangulated, this approach arranges its cliques into a tree and computes posterior probabilities by appropri­ ately passing around messages in that tree. The computation in each clique is simply di­ rect marginalization. When the underlying graph is not triangulated, one has to first tri­ angulated it by adding edges. Referred to as the triangulation problem, the problem of finding an optimal or even a "good" trian­ gulation proves to be difficult. In this pa­ per, we propose to first decompose a Bayesian net into smaller components by making use of Tarjan's algorithm for decomposing an undirected graph at all its minimal complete separators. Then, the components are ar­ ranged into a tree and posterior probabili­ ties are computed by appropriately passing around messages in that tree. The compu­ tation in each component is carried out by repeating the whole procedure from the be­ ginning. Thus the triangulation problem is sidestepped.