# Feature Selection for Efficient Local-to-Global Bayesian Network Structure Learning

arXiv: https://arxiv.org/abs/2112.10369 · HTML: https://mlsanity.com/paper/2112.10369/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 50 references that are in the map.
- First posted on arXiv 20 Dec 2021.

## Builds on (most cited first, 6 of 6)

- [DAGs with NO TEARS: Continuous Optimization for Structure Learning](https://mlsanity.com/paper/1803.01422/) (2018)
- [DAG-GNN: DAG Structure Learning with Graph Neural Networks](https://mlsanity.com/paper/1904.10098/) (2019)
- [D-VAE: A Variational Autoencoder for Directed Acyclic Graphs](https://mlsanity.com/paper/1904.11088/) (2019)
- [A Tutorial on Learning With Bayesian Networks](https://mlsanity.com/paper/2002.00269/) (2020)
- [Distinguishing cause from effect using observational data: methods and benchmarks](https://mlsanity.com/paper/1412.3773/) (2014)
- [Entropy-based Pruning for Learning Bayesian Networks using BIC](https://mlsanity.com/paper/1707.06194/) (2017)

## Built on by (most cited first, 2 of 2)

- [Local Causal Discovery with Linear non-Gaussian Cyclic Models](https://mlsanity.com/paper/2403.14843/) (2024)
- [Hybrid Local Causal Discovery](https://mlsanity.com/paper/2412.19507/) (2024)

## Abstract (arXiv)

Local-to-global learning approach plays an essential role in Bayesian network (BN) structure learning. Existing local-to-global learning algorithms first construct the skeleton of a DAG (directed acyclic graph) by learning the MB (Markov blanket) or PC (parents and children) of each variable in a data set, then orient edges in the skeleton. However, existing MB or PC learning methods are often computationally expensive especially with a large-sized BN, resulting in inefficient local-to-global learning algorithms. To tackle the problem, in this paper, we develop an efficient local-to-global learning approach using feature selection. Specifically, we first analyze the rationale of the well-known Minimum-Redundancy and Maximum-Relevance (MRMR) feature selection approach for learning a PC set of a variable. Based on the analysis, we propose an efficient F2SL (feature selection-based structure learning) approach to local-to-global BN structure learning. The F2SL approach first employs the MRMR approach to learn a DAG skeleton, then orients edges in the skeleton. Employing independence tests or score functions for orienting edges, we instantiate the F2SL approach into two new algorithms, F2SL-c (using independence tests) and F2SL-s (using score functions). Compared to the state-of-the-art local-to-global BN learning algorithms, the experiments validated that the proposed algorithms in this paper are more efficient and provide competitive structure learning quality than the compared algorithms.