Learning Bayesian Network Parameters from Small Data Sets by Using Ranked Nodes Method

Abstract

Bayesian Networks (BNs) are graphical probabilistic models that offer a suitable modeling approach for decision support problems under uncertainty. Both the graphical structure and conditional probability tables of BNs can be learned from data. This study focuses on learning conditional probability of BNs in cases where data are in limited amounts. The ranked nodes method has been proposed to reduce the number of parameters required to define conditional probability tables of variables with ordinal states. This method assigns an underlying Truncated Normal distribution to ordinal BN variables, and it defines the conditional probability distribution with equations with fewer parameters than those required by tables. Despite this advantage, in the previous studies, the method of ranked nodes was used only to elicit BNs from expert knowledge, and methods for learning ranked nodes from data were not examined. This study proposes an approach to learn ranked nodes from data. This approach uses Truncated Normal regression, Beta regression and linear regression to learn the relations between the underlying continuous distributions of ranked nodes, and then it transforms these to conditional probability tables for BNs. The performance of the proposed method has been evaluated using experiments with different data sizes and BN structures.