Learning NAT-Modeled Bayesian Networks from Data with Extended BD Scores

Abstract

Bayesian networks (BNs) are widely used for concise knowledge representation and probabilistic inference in uncertain environments. Non-impeding noisy-AND tree (NAT) models are local structures that can be applied to BNs to significantly improve the efficiency from exponential to linear on the number of parents per variable.

To take advantage of representation and inference efficiency by NAT-modeled BNs, this work studies a Bayesian approach for learning NAT-modeled BN structures from data. We extend meta-networks to encode NAT local structures and parameters. We develop a Bayesian Dirichlet (BD) scoring function to evaluate candidate structures. We present a heuristic search to reduce search complexity due to huge space of alternative combinations of global and local structures. An experiment is conducted to evaluate the extended BD score and heuristic search algorithms for learning NAT-modeled BN structures. It demonstrates that inference with learned NAT-modeled BNs is sufficiently accurate and significantly more efficient than equivalent tabular BNs.