Sidestepping the Triangulation Problem in Bayesian Net Computations
  This paper presents a new approach for computing posterior probabilities in
Bayesian nets, which sidesteps the triangulation problem. 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 appropriately passing around messages
in that tree. The computation in each clique is simply direct marginalization.
When the underlying graph is not triangulated, one has to first triangulated it
by adding edges. Referred to as the triangulation problem, the problem of
finding an optimal or even a ?good? triangulation proves to be difficult. In
this paper, 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 arranged
into a tree and posterior probabilities are computed by appropriately passing
around messages in that tree. The computation in each component is carried out
by repeating the whole procedure from the beginning. Thus the triangulation
problem is sidestepped.
