Factorization of ZDDs for representing Bayesian networks based on d-separations

Abstract

Multi-Linear Functions (MLFs) is a well known way of probability calculation based on Bayesian Networks (BNs). For a given BN, we can calculate the probability in a linear time to the size of MLF. However, the size of MLF grows exponentially with the size of BN, so the computation requires exponential time and space. Minato et al. have shown an efficient method of calculating the probability by using Zero-Suppressed BDDs (ZDDs). This method is more effective than the conventional approach of Darwiche et al. which encodes BNs into Conjunctive Normal Forms (CNFs) and then translates CNFs into factored MLFs. In this article, we present an improvement of Minato’s method by factoring ZDDs of MLFs into more factored form utilizing weak divison operation based on d-separation structure of BNs.