Hierarchically Coupled Gaussian Bayesian Networks

Chang Ma, Marco Grzegorczyk
Proceedings of the 13th International Conference on Probabilistic Graphical Models, PMLR 343:523-544, 2026.

Abstract

Gaussian Bayesian networks are probabilistic graphical models for learning network structures from continuous data. Standard approaches typically assume that all observations arise from a homogeneous population. In many applications, however, the data originate from multiple related but heterogeneous groups that share a common network structure while having group-specific network parameters. Pooling all observations and inferring a single set of parameters ignores between-group heterogeneity and may lead to biased inference. Conversely, estimating group-specific parameters independently substantially increases model complexity and inferential uncertainty. We introduce a hierarchical prior that enables information sharing across groups. The proposed prior preserves group-specific parameters while introducing shrinkage by coupling the group-specific mean vectors and covariance structures through shared global hyperparameters. The corresponding coupling strengths are inferred from the data, allowing the degree of information sharing to adapt automatically to the observed heterogeneity across groups. We develop a Markov chain Monte Carlo (MCMC) algorithm for posterior inference and demonstrate empirically that the proposed approach improves both network structure learning and predictive performance.

Cite this Paper

BibTeX
@InProceedings{pmlr-v343-ma26a, title = {Hierarchically Coupled {Gaussian} {Bayesian} Networks}, author = {Ma, Chang and Grzegorczyk, Marco}, booktitle = {Proceedings of the 13th International Conference on Probabilistic Graphical Models}, pages = {523--544}, year = {2026}, editor = {Camps-Valls, Gustau and Leonelli, Manuele and Varando, Gherardo}, volume = {343}, series = {Proceedings of Machine Learning Research}, month = {09--11 Sep}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v343/main/assets/ma26a/ma26a.pdf}, url = {https://proceedings.mlr.press/v343/ma26a.html}, abstract = {Gaussian Bayesian networks are probabilistic graphical models for learning network structures from continuous data. Standard approaches typically assume that all observations arise from a homogeneous population. In many applications, however, the data originate from multiple related but heterogeneous groups that share a common network structure while having group-specific network parameters. Pooling all observations and inferring a single set of parameters ignores between-group heterogeneity and may lead to biased inference. Conversely, estimating group-specific parameters independently substantially increases model complexity and inferential uncertainty. We introduce a hierarchical prior that enables information sharing across groups. The proposed prior preserves group-specific parameters while introducing shrinkage by coupling the group-specific mean vectors and covariance structures through shared global hyperparameters. The corresponding coupling strengths are inferred from the data, allowing the degree of information sharing to adapt automatically to the observed heterogeneity across groups. We develop a Markov chain Monte Carlo (MCMC) algorithm for posterior inference and demonstrate empirically that the proposed approach improves both network structure learning and predictive performance.} }
Endnote
%0 Conference Paper %T Hierarchically Coupled Gaussian Bayesian Networks %A Chang Ma %A Marco Grzegorczyk %B Proceedings of the 13th International Conference on Probabilistic Graphical Models %C Proceedings of Machine Learning Research %D 2026 %E Gustau Camps-Valls %E Manuele Leonelli %E Gherardo Varando %F pmlr-v343-ma26a %I PMLR %P 523--544 %U https://proceedings.mlr.press/v343/ma26a.html %V 343 %X Gaussian Bayesian networks are probabilistic graphical models for learning network structures from continuous data. Standard approaches typically assume that all observations arise from a homogeneous population. In many applications, however, the data originate from multiple related but heterogeneous groups that share a common network structure while having group-specific network parameters. Pooling all observations and inferring a single set of parameters ignores between-group heterogeneity and may lead to biased inference. Conversely, estimating group-specific parameters independently substantially increases model complexity and inferential uncertainty. We introduce a hierarchical prior that enables information sharing across groups. The proposed prior preserves group-specific parameters while introducing shrinkage by coupling the group-specific mean vectors and covariance structures through shared global hyperparameters. The corresponding coupling strengths are inferred from the data, allowing the degree of information sharing to adapt automatically to the observed heterogeneity across groups. We develop a Markov chain Monte Carlo (MCMC) algorithm for posterior inference and demonstrate empirically that the proposed approach improves both network structure learning and predictive performance.
APA
Ma, C. & Grzegorczyk, M.. (2026). Hierarchically Coupled Gaussian Bayesian Networks. Proceedings of the 13th International Conference on Probabilistic Graphical Models, in Proceedings of Machine Learning Research 343:523-544 Available from https://proceedings.mlr.press/v343/ma26a.html.

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