A simple method for testing independencies in Bayesian networks

Abstract

Testing independencies is a fundamental task in reasoning with Bayesian networks (BNs). In practice, d-separation is often utilized for this task, since it has linear-time complexity. However, many have had difficulties in understanding d-separation in BNs. An equivalent method that is easier to understand, called m-separation, transforms the problem from directed separation in BNs into classical separation in undirected graphs. Two main steps of this transformation are pruning the BN and adding undirected edges. In this paper, we propose u-separation as an even simpler method for testing independencies in a BN. Our approach also converts the problem into classical separation in an undirected graph. However, our method is based upon the novel concepts of inaugural variables and rationalization. Thereby, the primary advantage of u-separation over m-separation is that m-separation can prune unnecessarily and add superfluous edges. Hence, u-separation is a simpler method in this respect.