# Learning big Gaussian Bayesian networks: partition, estimation, and fusion

arXiv: https://arxiv.org/abs/1904.10900 · HTML: https://mlsanity.com/paper/1904.10900/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Apr 2019.

## Built on by (most cited first, 13 of 13)

- [Reliable Causal Discovery with Improved Exact Search and Weaker Assumptions](https://mlsanity.com/paper/2201.05666/) (2022)
- [DCILP: A Distributed Approach for Large-Scale Causal Structure Learning](https://mlsanity.com/paper/2406.10481/) (2024)
- [Partitioned hybrid learning of Bayesian network structures](https://mlsanity.com/paper/2103.12188/) (2021)
- [Causal Discovery over High-Dimensional Structured Hypothesis Spaces with Causal Graph Partitioning](https://mlsanity.com/paper/2406.06348/) (2024)
- [Coarsening Causal DAG Models](https://mlsanity.com/paper/2601.10531/) (2026)
- [Learning Sparse Fixed-Structure Gaussian Bayesian Networks](https://mlsanity.com/paper/2107.10450/) (2021)
- [Extracting the Multiscale Causal Backbone of Brain Dynamics](https://mlsanity.com/paper/2311.00118/) (2023)
- [Coordinated Multi-Neighborhood Learning on a Directed Acyclic Graph](https://mlsanity.com/paper/2405.15358/) (2024)
- [Optimal Clustering with Dependent Costs in Bayesian Networks](https://mlsanity.com/paper/2308.03970/) (2023)
- [Learning Bayesian Networks with Heterogeneous Agronomic Data Sets via Mixed-Effect Models and Hierarchical Clustering](https://mlsanity.com/paper/2308.06399/) (2023)
- [Divide-and-Conquer Strategy for Large-Scale Dynamic Bayesian Network Structure Learning](https://mlsanity.com/paper/2312.01739/) (2023)
- [Scalable Structure Learning of Bayesian Networks by Learning Algorithm Ensembles](https://mlsanity.com/paper/2506.22848/) (2025)
- [Efficient Causal Structure Learning via Modular Subgraph Integration](https://mlsanity.com/paper/2601.21014/) (2026)

## Abstract (arXiv)

Structure learning of Bayesian networks has always been a challenging problem. Nowadays, massive-size networks with thousands or more of nodes but fewer samples frequently appear in many areas. We develop a divide-and-conquer framework, called partition-estimation-fusion (PEF), for structure learning of such big networks. The proposed method first partitions nodes into clusters, then learns a subgraph on each cluster of nodes, and finally fuses all learned subgraphs into one Bayesian network. The PEF method is designed in a flexible way so that any structure learning method may be used in the second step to learn a subgraph structure as either a DAG or a CPDAG. In the clustering step, we adapt the hierarchical clustering method to automatically choose a proper number of clusters. In the fusion step, we propose a novel hybrid method that sequentially add edges between subgraphs. Extensive numerical experiments demonstrate the competitive performance of our PEF method, in terms of both speed and accuracy compared to existing methods. Our method can improve the accuracy of structure learning by 20% or more, while reducing running time up to two orders-of-magnitude.