# A Bayesian Approach to Learning Bayesian Networks with Local Structure

arXiv: https://arxiv.org/abs/1302.1528 · HTML: https://mlsanity.com/paper/1302.1528/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Feb 2013.

## Built on by (most cited first, 15 of 15)

- [Context-Specific Causal Discovery for Categorical Data Using Staged Trees](https://mlsanity.com/paper/2106.04416/) (2021)
- [Staged trees and asymmetry-labeled DAGs](https://mlsanity.com/paper/2108.01994/) (2021)
- [Causal Effect Identification with Context-specific Independence Relations of Control Variables](https://mlsanity.com/paper/2110.12064/) (2021)
- [Structural Learning of Simple Staged Trees](https://mlsanity.com/paper/2203.04390/) (2022)
- [Highly Efficient Structural Learning of Sparse Staged Trees](https://mlsanity.com/paper/2206.06970/) (2022)
- [Challenges and Considerations in the Evaluation of Bayesian Causal Discovery](https://mlsanity.com/paper/2406.03209/) (2024)
- [Structure Learning of Contextual Markov Networks using Marginal Pseudo-likelihood](https://mlsanity.com/paper/2103.15540/) (2021)
- [Scalable Bayesian Network Structure Learning with Splines](https://mlsanity.com/paper/2110.14626/) (2021)
- [Learning and interpreting asymmetry-labeled DAGs: a case study on COVID-19 fear](https://mlsanity.com/paper/2301.00629/) (2023)
- [Context-Specific Likelihood Weighting](https://mlsanity.com/paper/2101.09791/) (2021)
- [Reconsidering Dependency Networks from an Information Geometry Perspective](https://mlsanity.com/paper/2107.00871/) (2021)
- [DiscoVars: A New Data Analysis Perspective -- Application in Variable Selection for Clustering](https://mlsanity.com/paper/2304.03983/) (2023)
- [Bayesian Approach to Linear Bayesian Networks](https://mlsanity.com/paper/2311.15610/) (2023)
- [Sample Complexity of Nonparametric Closeness Testing for Continuous Distributions and Its Application to Causal Discovery with Hidden Confounding](https://mlsanity.com/paper/2503.07475/) (2025)
- [Reconsidering Dependency Networks from an Information Geometry Perspective](https://mlsanity.com/paper/2604.01117/) (2026)

## Abstract (arXiv)

Recently several researchers have investigated techniques for using data to learn Bayesian networks containing compact representations for the conditional probability distributions (CPDs) stored at each node. The majority of this work has concentrated on using decision-tree representations for the CPDs. In addition, researchers typically apply non-Bayesian (or asymptotically Bayesian) scoring functions such as MDL to evaluate the goodness-of-fit of networks to the data. In this paper we investigate a Bayesian approach to learning Bayesian networks that contain the more general decision-graph representations of the CPDs. First, we describe how to evaluate the posterior probability that is, the Bayesian score of such a network, given a database of observed cases. Second, we describe various search spaces that can be used, in conjunction with a scoring function and a search procedure, to identify one or more high-scoring networks. Finally, we present an experimental evaluation of the search spaces, using a greedy algorithm and a Bayesian scoring function.