Parameter Learning of Bayesian Network with Multiplicative Synergistic Constraints

Abstract

Learning the conditional probability table (CPT) parameters of Bayesian networks (BNs) is a key challenge in real-world decision support applications, especially when there are limited data available. The traditional approach to this challenge is introducing domain knowledge/expert judgments that are encoded as qualitative parameter constraints. In this paper, we focus on multiplicative synergistic constraints. The negative multiplicative synergy constraint and positive multiplicative synergy constraint in this paper are symmetric. In order to integrate multiplicative synergistic constraints into the learning process of Bayesian Network parameters, we propose four methods to deal with the multiplicative synergistic constraints based on the idea of classical isotonic regression algorithm. The four methods are simulated by using the lawn moist model and Asia network, and we compared them with the maximum likelihood estimation (MLE) algorithm. Simulation results show that the proposed methods are superior to the MLE algorithm in the accuracy of parameter learning, which can improve the results of the MLE algorithm to obtain more accurate estimators of the parameters. The proposed methods can reduce the dependence of parameter learning on expert experiences. Combining these constraint methods with Bayesian estimation can improve the accuracy of parameter learning under small sample conditions.