Matrix factorization based Bayesian network embedding for efficient probabilistic inferences

Abstract

Bayesian network (BN) is a well adopted framework for representing and inferring uncertain knowledge. By the existing methods, multiple probabilistic inferences on the same BN are often fulfilled one by one via repeated searches and calculations of probabilities. However, lots of intermediate results of probability calculations cannot be shared and reused among different probabilistic inferences. It is necessary to improve the overall efficiency of multiple probabilistic inferences on the same BN by incorporating an easy-to-calculate representation of BN and an easy-to-reuse technique for common calculations in multiple inferences. In this paper, we first propose the method of Bayesian network embedding to generate the easy-to-reuse node embeddings. Specifically, we transform BN into the point mutual information (PMI) matrix to simultaneously preserve the directed acyclic graph (DAG) and conditional probability tables (CPTs). Then, we give the singular value decomposition (SVD) based method to factorize the PMI matrix for generating node embeddings. Secondly, we propose a novel method of random sampling to make multiple probabilistic inferences via similarity calculation between node embeddings. Experimental results show that the runtime of our proposed BNERS performing 10 times of inferences is 30% faster than Gibbs sampling (GS) and 50% faster than forward sampling (FS) on LINK BN (very large network), while maintaining almost the same results as GS and FS.