# Scalable Structure Learning of Bayesian Networks by Learning Algorithm Ensembles

arXiv: https://arxiv.org/abs/2506.22848 · HTML: https://mlsanity.com/paper/2506.22848/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 16 of its 49 references that are in the map.
- First posted on arXiv 28 Jun 2025.

## Builds on (most cited first, 16 of 16)

- [Reliable evaluation of adversarial robustness with an ensemble of diverse parameter-free attacks](https://mlsanity.com/paper/2003.01690/) (2020)
- [DAGs with NO TEARS: Continuous Optimization for Structure Learning](https://mlsanity.com/paper/1803.01422/) (2018)
- [SMAC3: A Versatile Bayesian Optimization Package for Hyperparameter Optimization](https://mlsanity.com/paper/2109.09831/) (2021)
- [A survey of Bayesian Network structure learning](https://mlsanity.com/paper/2109.11415/) (2021)
- [Exact Recovery in the Stochastic Block Model](https://mlsanity.com/paper/1405.3267/) (2014)
- [Learning Equivalence Classes of Bayesian Networks Structures](https://mlsanity.com/paper/1302.3566/) (2013)
- [A Survey of Community Detection Approaches: From Statistical Modeling to Deep Learning](https://mlsanity.com/paper/2101.01669/) (2021)
- [Concave Penalized Estimation of Sparse Gaussian Bayesian Networks](https://mlsanity.com/paper/1401.0852/) (2014)
- [How Good Is Neural Combinatorial Optimization? A Systematic Evaluation on the Traveling Salesman Problem](https://mlsanity.com/paper/2209.10913/) (2022)
- [Learning Bayesian Network Structure from Massive Datasets: The "Sparse Candidate" Algorithm](https://mlsanity.com/paper/1301.6696/) (2013)
- [THP: Topological Hawkes Processes for Learning Causal Structure on Event Sequences](https://mlsanity.com/paper/2105.10884/) (2021)
- [Learning big Gaussian Bayesian networks: partition, estimation, and fusion](https://mlsanity.com/paper/1904.10900/) (2019)
- [A hybrid algorithm for Bayesian network structure learning with application to multi-label learning](https://mlsanity.com/paper/1506.05692/) (2015)
- [Automatic Construction of Parallel Portfolios via Explicit Instance Grouping](https://mlsanity.com/paper/1804.06088/) (2018)
- [Efficient and Scalable Structure Learning for Bayesian Networks: Algorithms and Applications](https://mlsanity.com/paper/2012.03540/) (2020)
- [On Performance Estimation in Automatic Algorithm Configuration](https://mlsanity.com/paper/1911.08200/) (2019)

## Abstract (arXiv)

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%~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.