(A) process of combining Bayesian networks

Abstract

Suppose that we are interested in modeling for a random vector $\bf{X}$ and that we are given a set of Bayesian network models, $\cal{G}_1, \cdots, \cal{G}_m$, for subvectors of $\bf{X}$ each of which share some variables with at least one of the other models. Under the assumption that the model of $\bf{X}$ is a Bayesian network (BN) model, we propose an approach of searching for model structures of $\bf{X}$ based on the given Bayesian network models. We first examined the relationship between a BN model and its marginal model and then applied the result to combining BN models. Suppose we combine two BN models A main route of the process consists of three operations; uniting, checking node-separateness, and checking marginalization. Uniting puts the two BNs into one BN by connecting nodes that are not separated in any one of the two BNs, and in the remaining two operations, we check if there exist any edges that are in conflict with the inter-relationships of the variables that lie in each of the two BNs. This process is illustrated through examples.