Using Mixed-Effects Models to Learn Bayesian Networks from Related Data Sets
This work addresses the challenge of handling heterogeneous data in Bayesian network learning for continuous data, offering an incremental improvement over prior methods.
The authors tackled the problem of learning Bayesian networks from related but heterogeneous continuous data sets by proposing a method using mixed-effects models to pool information across them. They demonstrated that their approach outperforms existing methods, particularly for low sample sizes and unbalanced data sets.
We commonly assume that data are a homogeneous set of observations when learning the structure of Bayesian networks. However, they often comprise different data sets that are related but not homogeneous because they have been collected in different ways or from different populations. In our previous work (Azzimonti, Corani and Scutari, 2021), we proposed a closed-form Bayesian Hierarchical Dirichlet score for discrete data that pools information across related data sets to learn a single encompassing network structure, while taking into account the differences in their probabilistic structures. In this paper, we provide an analogous solution for learning a Bayesian network from continuous data using mixed-effects models to pool information across the related data sets. We study its structural, parametric, predictive and classification accuracy and we show that it outperforms both conditional Gaussian Bayesian networks (that do not perform any pooling) and classical Gaussian Bayesian networks (that disregard the heterogeneous nature of the data). The improvement is marked for low sample sizes and for unbalanced data sets.