# Advances in Learning Bayesian Networks of Bounded Treewidth

arXiv: https://arxiv.org/abs/1406.1411 · HTML: https://mlsanity.com/paper/1406.1411/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Jun 2014.

## Built on by (most cited first, 10 of 10)

- [DAGs with No Curl: An Efficient DAG Structure Learning Approach](https://mlsanity.com/paper/2106.07197/) (2021)
- [Differentiable DAG Sampling](https://mlsanity.com/paper/2203.08509/) (2022)
- [CoLiDE: Concomitant Linear DAG Estimation](https://mlsanity.com/paper/2310.02895/) (2023)
- [Learning Bayesian Networks in the Presence of Structural Side Information](https://mlsanity.com/paper/2112.10884/) (2021)
- [Recursive Causal Discovery](https://mlsanity.com/paper/2403.09300/) (2024)
- [Differentiable Invariant Causal Discovery](https://mlsanity.com/paper/2205.15638/) (2022)
- [Optimal estimation of Gaussian (poly)trees](https://mlsanity.com/paper/2402.06380/) (2024)
- [DAG-WGAN: Causal Structure Learning With Wasserstein Generative Adversarial Networks](https://mlsanity.com/paper/2204.00387/) (2022)
- [The Parameterized Complexity of Computing the VC-Dimension](https://mlsanity.com/paper/2510.17451/) (2025)
- [Causality Learning With Wasserstein Generative Adversarial Networks](https://mlsanity.com/paper/2206.01496/) (2022)

## Abstract (arXiv)

This work presents novel algorithms for learning Bayesian network structures with bounded treewidth. Both exact and approximate methods are developed. The exact method combines mixed-integer linear programming formulations for structure learning and treewidth computation. The approximate method consists in uniformly sampling k-trees (maximal graphs of treewidth k), and subsequently selecting, exactly or approximately, the best structure whose moral graph is a subgraph of that k-tree. Some properties of these methods are discussed and proven. The approaches are empirically compared to each other and to a state-of-the-art method for learning bounded treewidth structures on a collection of public data sets with up to 100 variables. The experiments show that our exact algorithm outperforms the state of the art, and that the approximate approach is fairly accurate.