# Partitioned hybrid learning of Bayesian network structures

arXiv: https://arxiv.org/abs/2103.12188 · HTML: https://mlsanity.com/paper/2103.12188/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 54 references that are in the map.
- First posted on arXiv 22 Mar 2021.

## Builds on (most cited first, 15 of 15)

- [Learning Bayesian Networks: The Combination of Knowledge and Statistical Data](https://mlsanity.com/paper/1302.6815/) (2013)
- [Causal Inference and Causal Explanation with Background Knowledge](https://mlsanity.com/paper/1302.4972/) (2013)
- [Learning Equivalence Classes of Bayesian Networks Structures](https://mlsanity.com/paper/1302.3566/) (2013)
- [High-dimensional consistency in score-based and hybrid structure learning](https://mlsanity.com/paper/1507.02608/) (2015)
- [A fast PC algorithm for high dimensional causal discovery with multi-core PCs](https://mlsanity.com/paper/1502.02454/) (2015)
- [Theory Refinement on Bayesian Networks](https://mlsanity.com/paper/1303.5709/) (2013)
- [Learning Bayesian Network Structure from Massive Datasets: The "Sparse Candidate" Algorithm](https://mlsanity.com/paper/1301.6696/) (2013)
- [Bayesian Network Constraint-Based Structure Learning Algorithms: Parallel and Optimised Implementations in the bnlearn R Package](https://mlsanity.com/paper/1406.7648/) (2014)
- [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)
- [cuPC: CUDA-based Parallel PC Algorithm for Causal Structure Learning on GPU](https://mlsanity.com/paper/1812.08491/) (2018)
- [Penalized Estimation of Directed Acyclic Graphs From Discrete Data](https://mlsanity.com/paper/1403.2310/) (2014)
- [Learning Large-Scale Bayesian Networks with the sparsebn Package](https://mlsanity.com/paper/1703.04025/) (2017)
- [A Bayesian Method for Constructing Bayesian Belief Networks from Databases](https://mlsanity.com/paper/1303.5714/) (2013)
- [Scaling up Greedy Causal Search for Continuous Variables](https://mlsanity.com/paper/1507.07749/) (2015)

## Built on by (most cited first, 4 of 4)

- [Causal Discovery over High-Dimensional Structured Hypothesis Spaces with Causal Graph Partitioning](https://mlsanity.com/paper/2406.06348/) (2024)
- [A Fast Kernel-based Conditional Independence test with Application to Causal Discovery](https://mlsanity.com/paper/2505.11085/) (2025)
- [Optimal Clustering with Dependent Costs in Bayesian Networks](https://mlsanity.com/paper/2308.03970/) (2023)
- [Causal Discovery for Cross-Sectional Data Based on Super-Structure and Divide-and-Conquer](https://mlsanity.com/paper/2602.03914/) (2026)

## Abstract (arXiv)

We develop a novel hybrid method for Bayesian network structure learning called partitioned hybrid greedy search (pHGS), composed of three distinct yet compatible new algorithms: Partitioned PC (pPC) accelerates skeleton learning via a divide-and-conquer strategy, p-value adjacency thresholding (PATH) effectively accomplishes parameter tuning with a single execution, and hybrid greedy initialization (HGI) maximally utilizes constraint-based information to obtain a high-scoring and well-performing initial graph for greedy search. We establish structure learning consistency of our algorithms in the large-sample limit, and empirically validate our methods individually and collectively through extensive numerical comparisons. The combined merits of pPC and PATH achieve significant computational reductions compared to the PC algorithm without sacrificing the accuracy of estimated structures, and our generally applicable HGI strategy reliably improves the estimation structural accuracy of popular hybrid algorithms with negligible additional computational expense. Our empirical results demonstrate the superior empirical performance of pHGS against many state-of-the-art structure learning algorithms.