A Bayesian Hierarchical Score for Structure Learning from Related Data Sets

TL;DR

This paper introduces a Bayesian Hierarchical Dirichlet score for structure learning in Bayesian networks that effectively leverages related data sets, outperforming traditional scores in accuracy and interpretability when data are heterogeneous.

Contribution

The paper proposes a novel Bayesian Hierarchical Dirichlet score that pools information across related data sets, accounting for their differences, and provides a closed-form approximation for efficient computation.

Findings

BHD outperforms BDeu in reconstruction accuracy with multiple data sets.

BHD produces sparser, more interpretable networks.

BHD performs as well as BDeu on homogeneous data.

Abstract

Score functions for learning the structure of Bayesian networks in the literature assume that data are a homogeneous set of observations; whereas it is often the case that they comprise different related, but not homogeneous, data sets collected in different ways. In this paper we propose a new Bayesian Dirichlet score, which we call Bayesian Hierarchical Dirichlet (BHD). The proposed score is based on a hierarchical model that pools information across data sets to learn a single encompassing network structure, while taking into account the differences in their probabilistic structures. We derive a closed-form expression for BHD using a variational approximation of the marginal likelihood, we study the associated computational cost and we evaluate its performance using simulated data. We find that, when data comprise multiple related data sets, BHD outperforms the Bayesian Dirichlet equivalent uniform (BDeu) score in terms of reconstruction accuracy as measured by the Structural Hamming distance, and that it is as accurate as BDeu when data are homogeneous. This improvement is particularly clear when either the number of variables in the network or the number of observations is large. Moreover, the estimated networks are sparser and therefore more interpretable than those obtained with BDeu thanks to a lower number of false positive arcs.