Scalable Structure Learning of Bayesian Networks by Learning Algorithm Ensembles

TL;DR

This paper introduces Auto-SLE, an automatic ensemble approach for structure learning of Bayesian networks that significantly improves accuracy and scalability on large datasets with thousands of variables.

Contribution

It proposes Auto-SLE, an automatic method to learn high-quality structure learning ensembles, enhancing divide-and-conquer strategies for large Bayesian network structure learning.

Findings

Achieves 30-225% accuracy improvement over single-algorithm D&D methods.

Successfully scales to datasets with up to 30,000 variables.

Generalizes well to different network characteristics and larger datasets.

Abstract

Learning the structure of Bayesian networks (BNs) from data is challenging, especially for datasets involving a large number of variables. The recently proposed divide-and-conquer (D\&D) strategies present a promising approach for learning large BNs. However, they still face a main issue of unstable learning accuracy across subproblems. In this work, we introduce the idea of employing structure learning ensemble (SLE), which combines multiple BN structure learning algorithms, to consistently achieve high learning accuracy. We further propose an automatic approach called Auto-SLE for learning near-optimal SLEs, addressing the challenge of manually designing high-quality SLEs. The learned SLE is then integrated into a D\&D method. Extensive experiments firmly show the superiority of our method over D\&D methods with single BN structure learning algorithm in learning large BNs, achieving accuracy improvement usually by 30\%$\sim$225\% on datasets involving 10,000 variables. Furthermore, our method generalizes well to datasets with many more (e.g., 30000) variables and different network characteristics than those present in the training data for learning the SLE. These results indicate the significant potential of employing (automatic learning of) SLEs for scalable BN structure learning.