Scalable Structure Learning of Bayesian Networks by Learning Algorithm Ensembles

2025-06-28

AI Summary

Large-scale Bayesian network (BN) structure learning suffers from low accuracy and poor stability. Method: This paper proposes Auto-SLE, a scalable ensemble learning framework integrating divide-and-conquer, multi-algorithm structure learning ensemble (SLE), and automated hyperparameter/weight optimization—enabling, for the first time, adaptive ensemble control over subproblem solving. Contributions/Results: (1) A lightweight SLE mechanism enhances robustness in local subnetwork learning; (2) An Auto-SLE meta-learner automatically discovers optimal algorithm combinations and fusion weights. On benchmark datasets with up to 10,000 variables, Auto-SLE improves structural accuracy by 30%–225% over single-algorithm baselines. It scales stably to over 30,000 variables and demonstrates strong generalization across heterogeneous BN topologies—including sparse, dense, and chain-like structures.

Technology Category

• Machine Learning: Structured Learning
• Search and Optimization: Learning to Search
• Constraint Satisfaction and Optimization: Constraint Learning and Acquisition

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Semantics and Knowledge: Scalable techniques for the creation, curation, publication, maintenance, and consumption of large, Web-based, structured, reusable, knowledge graphs and ontologies

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.

Problem

• Improving unstable accuracy in large Bayesian Networks learning
• Automating design of high-quality structure learning ensembles
• Scaling BN structure learning to datasets with 30000 variables

Innovation

• Ensemble of BN structure learning algorithms
• Automatic learning of near-optimal SLEs
• Integration with divide-and-conquer method