A Hybrid Method: Resolving the Impact of Variable Ordering in Bayesian Network Structure Learning

Abstract

In recent years, the development of machine learning has introduced new analytical methods to theoretical research, one of which is Bayesian network—a probabilistic graphical model well-suited for modelling complex non-deterministic systems. A recent study has revealed that the order in which variables are read from data can impact the structure of a Bayesian network (Kitson and Constantinou in The impact of variable ordering on Bayesian Network Structure Learning, 2022. arXiv preprint arXiv:2206.08952). However, in empirical studies, the variable order in a dataset is often arbitrary, leading to unreliable results. To address this issue, this study proposed a hybrid method that combined theory-driven and data-driven approaches to mitigate the impact of variable ordering on the learning of Bayesian network structures. The proposed method was illustrated using an empirical study predicting depression and aggressive behavior in high school students. The results demonstrated that the obtained Bayesian network structure is robust to variable orders and theoretically interpretable. The commonalities and specificities in the network structure of depression and aggressive behavior are both in line with theorical expectations, providing empirical evidence for the validity of the hybrid method.