A BGe score for tied-covariance mixture Gaussian Bayesian networks

2025/11/10 by Marco Grzegorczyk, Grzegorczyk, Marco · 1 voice
#Bayesian Modeling and Causal Inference #Gaussian Processes and Bayesian Inference #Bayesian Methods and Mixture Models

paper · pdf · doi:10.1016/j.ijar.2026.109771

Abstract

Mixtures of Gaussian Bayesian networks have previously been studied under full-covariance assumptions, where each mixture component has its own covariance matrix. We propose a mixture model with tied-covariance, in which all components share a common covariance matrix. Our main contribution is the derivation of its marginal likelihood, which remains analytic. Unlike in the full-covariance case, however, the marginal likelihood no longer factorizes into component-specific terms. We refer to the new likelihood as the BGe scoring metric for tied-covariance mixtures of Gaussian Bayesian networks. For model inference, we implement MCMC schemes combining structure MCMC with a fast Gibbs sampler for mixtures, and we empirically compare the tied- and full-covariance mixtures of Gaussian Bayesian networks on simulated and benchmark data.

Discussions

• Marco Grzegorczyk: A BGe score for tied-covariance mixtures of Gaussian Bayesian networks https://arxiv.org/abs/2511.07050 https://arxiv.org/pdf/2511.07050 https://arxiv.org/html/2511.07050 [bsky, 0 points, 0 comments]

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