Parallel Exact Inference

In this paper, we present complete message-passing implementation that shows scalable performance while performing exact inference on arbitrary Bayesian networks. Our work is based on a parallel version of the classical technique of converting a Bayesian network to a junction tree before computing inference. We propose a parallel algorithm for constructing potential tables for a junction tree and explore the parallelism of rerooting technique for multiple evidence propagation. Our implementation also uses pointer jumping for parallel inference over the junction tree. For an arbitrary Bayesian network with n vertices using p processors, we show an execution time of O(nk m + nw + (nw + wN log n + rwwN + rwN log N)/p), where w is the clique width, r is the number of states of the random variables, k is the maximum node degree in the Bayesian network, km is the maximum node degree in the moralized graph and N is the number of cliques in the junction tree. Our implementation is shown to be scalable for 1 ≤ p ≤ n for moralization and clique identification, and 1 ≤ p ≤ N for junction tree construction, potential table construction, rerooting and evidence propagation. We have implemented the parallel algorithm using MPI on state-of-the-art clusters and our experiments show scalable performance.