# Learning discrete Bayesian networks with hierarchical Dirichlet shrinkage

arXiv: https://arxiv.org/abs/2509.13267 · HTML: https://mlsanity.com/paper/2509.13267/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 57 references that are in the map.
- First posted on arXiv 16 Sep 2025.

## Builds on (most cited first, 13 of 13)

- [Learning Bayesian Networks: The Combination of Knowledge and Statistical Data](https://mlsanity.com/paper/1302.6815/) (2013)
- [Log-concave sampling: Metropolis-Hastings algorithms are fast](https://mlsanity.com/paper/1801.02309/) (2018)
- [A survey of Bayesian Network structure learning](https://mlsanity.com/paper/2109.11415/) (2021)
- [The Bayesian Structural EM Algorithm](https://mlsanity.com/paper/1301.7373/) (2013)
- [Learning Discrete Concepts in Latent Hierarchical Models](https://mlsanity.com/paper/2406.00519/) (2024)
- [Bayesian Pyramids: Identifiable Multilayer Discrete Latent Structure Models for Discrete Data](https://mlsanity.com/paper/2101.10373/) (2021)
- [Structure Learning with Adaptive Random Neighborhood Informed MCMC](https://mlsanity.com/paper/2311.00599/) (2023)
- [Hierarchical Multinomial-Dirichlet model for the estimation of conditional probability tables](https://mlsanity.com/paper/1708.06935/) (2017)
- [Accurate parameter estimation for Bayesian Network Classifiers using Hierarchical Dirichlet Processes](https://mlsanity.com/paper/1708.07581/) (2017)
- [A Bayesian Hierarchical Score for Structure Learning from Related Data Sets](https://mlsanity.com/paper/2008.01683/) (2020)
- [Graphical Dirichlet Process for Clustering Non-Exchangeable Grouped Data](https://mlsanity.com/paper/2302.09111/) (2023)
- [Equivalence class selection of categorical graphical models](https://mlsanity.com/paper/2102.06437/) (2021)
- [Hierarchical Random Measures without Tables](https://mlsanity.com/paper/2505.02653/) (2025)

## Abstract (arXiv)

A discrete Bayesian network is a directed acyclic graph (DAG) consisting of categorical variables. Two popular approaches for DBN modeling include classification and nonparametric methods. However, both methods often require a large number of parameters, such as high-order interactions in the former and cell probabilities in the latter. In this article, we propose a hierarchical model for node-parent conditional probabilities, inducing shrinkage to low-dimensional latent parameters aposteriori. We generate samples from the posterior distribution of these latent variables using the Metropolis-adjusted Langevin algorithm within a Gibbs sampler. Moreover, we verify that the full conditional distribution is log-concave under mild conditions, facilitating efficient sampling. We then detail several algorithms for structure learning that incorporate our hierarchical prior and preserve the DAG property. Through simulations, we evaluate the performance of our method for sparse counts, discovering graph structure, and selecting between competing DAGs. We conclude with an application to uncovering prognostic network structure from a breast cancer dataset.