Adding local constraints to Bayesian networks

Abstract

When using Bayesian networks, practitioners often express constraints among variables by conditioning a common child node to induce the desired distribution. For example, an 'or' constraint can be easily expressed by a node modelling a logical 'or' of its parents' values being conditioned to true. This has the desired effect that at least one parent must be true. However, conditioning also alters the distributions of further ancestors in the network. In this paper we argue that these side effects are undesirable when constraints are added during model design. We describe a method called shielding to remove these side effects while remaining within the directed language of Bayesian networks. This method is then compared to chain graphs which allow undirected and directed edges and which model equivalent distributions. Thus, in addition to solving this common modelling problem, shielded Bayesian networks provide a novel method for implementing chain graphs with existing Bayesian network tools. © Springer-Verlag Berlin Heidelberg 2007.