Distributed Evidence Propagation in Junction Trees on Clusters

Evidence propagation is a major step in exact inference, a key problem in exploring probabilistic graphical models. In this paper, we propose a novel approach for parallelizing evidence propagation in junction trees on clusters. Our proposed method explores structural parallelism in a given junction tree. We decompose a junction tree into a set of subtrees, each consisting of one or multiple leaf-root paths in the junction tree. In evidence propagation, we first perform evidence collection in these subtrees concurrently. Then, the partially updated subtrees exchange data for junction tree merging, so that all the cliques in the junction tree can be fully updated for evidence collection. Finally, evidence distribution is performed in all the subtrees to complete evidence propagation. Since merging subtrees requires communication across processors, we propose a technique called bitmap partitioning to explore the tradeoff between bandwidth utilization efficiency and the overhead due to the startup latency of message passing. We implemented the proposed method using Message Passing Interface (MPI) on a state-of-the-art Myrinet cluster consisting of 128 processors. Compared with a baseline method, our technique results in improved scalability.