Bayesian Inference in Treewidth-Bounded Graphical Models Without Indegree Constraints

We present new polynomial time algorithms for inference problems in Bayesian networks (BNs) when restricted to instances that satisfy the following two conditions: they have bounded treewidth and the conditional probability table (CPT) at each node is specified concisely using an r-symmetric function for some constant r. Our polynomial time algorithms work directly on the unmoralized graph. Our results significantly extend known results regarding inference problems on treewidth bounded BNs to a larger class of problem instances. We also show that relaxing either of the conditions used by our algorithms leads to computational intractability.