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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2511.07050 |
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Table of Contents:
- 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.