# Using Mixed-Effects Models to Learn Bayesian Networks from Related Data Sets

arXiv: https://arxiv.org/abs/2206.03743 · HTML: https://mlsanity.com/paper/2206.03743/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 17 references that are in the map.
- First posted on arXiv 8 Jun 2022.

## Builds on (most cited first, 3 of 3)

- [Learning Bayesian Networks: The Combination of Knowledge and Statistical Data](https://mlsanity.com/paper/1302.6815/) (2013)
- [Learning Gaussian Networks](https://mlsanity.com/paper/1302.6808/) (2013)
- [A Bayesian Hierarchical Score for Structure Learning from Related Data Sets](https://mlsanity.com/paper/2008.01683/) (2020)

## Built on by (most cited first, 1 of 1)

- [Learning Bayesian Networks with Heterogeneous Agronomic Data Sets via Mixed-Effect Models and Hierarchical Clustering](https://mlsanity.com/paper/2308.06399/) (2023)

## Abstract (arXiv)

We commonly assume that data are a homogeneous set of observations when learning the structure of Bayesian networks. However, they often comprise different data sets that are related but not homogeneous because they have been collected in different ways or from different populations. In our previous work (Azzimonti, Corani and Scutari, 2021), we proposed a closed-form Bayesian Hierarchical Dirichlet score for discrete data that pools information across related data sets to learn a single encompassing network structure, while taking into account the differences in their probabilistic structures. In this paper, we provide an analogous solution for learning a Bayesian network from continuous data using mixed-effects models to pool information across the related data sets. We study its structural, parametric, predictive and classification accuracy and we show that it outperforms both conditional Gaussian Bayesian networks (that do not perform any pooling) and classical Gaussian Bayesian networks (that disregard the heterogeneous nature of the data). The improvement is marked for low sample sizes and for unbalanced data sets.