# A Branch-and-Bound Algorithm for MDL Learning Bayesian Networks

arXiv: https://arxiv.org/abs/1301.3897 · HTML: https://mlsanity.com/paper/1301.3897/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Jan 2013.

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

- [Fast Parallel Bayesian Network Structure Learning](https://mlsanity.com/paper/2212.04259/) (2022)
- [Factor Graph Optimization of Error-Correcting Codes for Belief Propagation Decoding](https://mlsanity.com/paper/2406.12900/) (2024)
- [Parallel Sampling for Efficient High-dimensional Bayesian Network Structure Learning](https://mlsanity.com/paper/2202.09691/) (2022)
- [Preserving Data Privacy in Learning Causal Structure with Fully Homomorphic Encryption](https://mlsanity.com/paper/2606.05129/) (2026)

## Abstract (arXiv)

This paper extends the work in [Suzuki, 1996] and presents an efficient depth-first branch-and-bound algorithm for learning Bayesian network structures, based on the minimum description length (MDL) principle, for a given (consistent) variable ordering. The algorithm exhaustively searches through all network structures and guarantees to find the network with the best MDL score. Preliminary experiments show that the algorithm is efficient, and that the time complexity grows slowly with the sample size. The algorithm is useful for empirically studying both the performance of suboptimal heuristic search algorithms and the adequacy of the MDL principle in learning Bayesian networks.