# Entropy-based Pruning for Learning Bayesian Networks using BIC

arXiv: https://arxiv.org/abs/1707.06194 · HTML: https://mlsanity.com/paper/1707.06194/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Jul 2017.

## Built on by (most cited first, 6 of 6)

- [A survey of Bayesian Network structure learning](https://mlsanity.com/paper/2109.11415/) (2021)
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- [Improved Acyclicity Reasoning for Bayesian Network Structure Learning with Constraint Programming](https://mlsanity.com/paper/2106.12269/) (2021)
- [Feature Selection for Efficient Local-to-Global Bayesian Network Structure Learning](https://mlsanity.com/paper/2112.10369/) (2021)
- [Can LLMs Assist Expert Elicitation for Probabilistic Causal Modeling?](https://mlsanity.com/paper/2504.10397/) (2025)
- [Probabilistic Multi-Dimensional Classification](https://mlsanity.com/paper/2306.06517/) (2023)

## Abstract (arXiv)

For decomposable score-based structure learning of Bayesian networks, existing approaches first compute a collection of candidate parent sets for each variable and then optimize over this collection by choosing one parent set for each variable without creating directed cycles while maximizing the total score. We target the task of constructing the collection of candidate parent sets when the score of choice is the Bayesian Information Criterion (BIC). We provide new non-trivial results that can be used to prune the search space of candidate parent sets of each node. We analyze how these new results relate to previous ideas in the literature both theoretically and empirically. We show in experiments with UCI data sets that gains can be significant. Since the new pruning rules are easy to implement and have low computational costs, they can be promptly integrated into all state-of-the-art methods for structure learning of Bayesian networks.