Node Level Primitives for Parallel Exact Inference

Abstract

We present node level primitives for parallel exact inference on an arbitrary Bayesian network. We explore the probability representation on each node of Bayesian networks and each clique of junction trees. We study the operations with respect to these probability representations and categorize the operations into four node level primitives: table extension, table multiplication, table division, and table marginalization. Exact inference on Bayesian networks can be implemented based on these node level primitives. We develop parallel algorithms for the above and achieve parallel computational complexity of O(omega2r(omega+1)N/p), O(Nromega) space complexity and scalability up to O(romega), where N is the number of cliques in the junction tree, r is the number of states of a random variable, w is the maximal size of the cliques, and p is the number of processors. Experimental results illustrate the scalability of our parallel algorithms for each of these primitives.