The Difference between Single-Valued and Multi-Valued Cases in the Compact Representation of CPD in Bayesian Networks

This paper addresses an important issue about the compact representation of the conditional probability distribution (CPD) applied in the well known Bayesian Networks in uncertain causality representation and probabilistic inference. That is, there is an essential difference between the single-valued cases and the multi-valued cases, while this difference does not exist when the CPD is represented in the conditional probability table (CPT). In other words, the present compact representation and inference methods applicable in the single-valued cases may not be applicable in the multi-valued cases as people usually think. A detailed example is provided to illustrate this problem. The solution is provided in the references by the author.