Efficient probabilistic inference in Bayesian networks with multi-valued NIN-AND tree local models

A multi-valued Non-Impeding Noisy-AND (NIN-AND) tree model has linear complexity and is more expressive than several Causal Independence Models (CIMs) for expressing Conditional Probability Tables (CPTs) in Bayesian Networks (BNs). We show that it is also more general than the well-known noisy-MAX. To exploit NIN-AND tree models in inference, we develop a sound Multiplicative Factorization (MF) of multi-valued NIN-AND tree models. We show how to apply the MF to NIN-AND tree modeled BNs, and how to compile such BNs for exact lazy inference. For BNs with sparse structures, we demonstrate experimentally significant gain of inference efficiency in both space and time.