Design patterns for modeling first-order expressive Bayesian networks

Abstract

Abstract First-order expressive capabilities allow Bayesian networks (BNs) to model problem domains where the number of entities, their attributes, and their relationships can vary significantly between model instantiations. First-order BNs are well-suited for capturing knowledge representation dependencies, but literature on design patterns specific to first-order BNs is few and scattered. To identify useful patterns, we investigated the range of dependency models between combinations of random variables (RVs) that represent unary attributes, functional relationships, and binary predicate relationships. We found eight major patterns, grouped into three categories, that cover a significant number of first-order BN situations. Selection behavior occurs in six patterns, where a relationship/attribute identifies which entities in a second relationship/attribute are applicable. In other cases, certain kinds of embedded dependencies based on semantic meaning are exploited. A significant contribution of our patterns is that they describe various behaviors used to establish the RV’s local probability distribution. Taken together, the patterns form a modeling framework that provides significant insight into first-order expressive BNs and can reduce efforts in developing such models. To the best of our knowledge, there are no comprehensive published accounts of such patterns.