CPT Approximation with NIN-AND Tree Causal Models
A Bayesian network (BN) is a probabilistic graphical model widely used in artificial intelligence (AI) to support uncertain knowledge representation and uncertain reasoning. In BNs, conditional probability tables (CPTs) are used to store quantitative knowledge. The size of a discrete variable’s CPT increases exponentially on the number of related causes. Causal models are proposed to specify a CPT with fewer parameters. Non-Impeding Noisy-AND tree (NIN-AND tree) causal modeling is an expressive causal model which can encode two types of causal interactions. Replacing a CPT with a NIN-AND tree causal model can save storage space, and speed up inference. Being motivated by the advantages of using NIN-AND tree causal modeling, we develop the techniques to approximate a given CPT with NIN-AND tree causal modeling in this research. In particular, we develop a suite of algorithms to approximate an arbitrary CPT of binary variables with a NIN-AND tree model. Based on the experimental results, the methods proposed in this research can result in reasonably good approximation accuracy.