A BGe score for tied-covariance mixtures of Gaussian Bayesian networks
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866917070869889024 |
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| author | Grzegorczyk, Marco |
| author_facet | Grzegorczyk, Marco |
| 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_07050 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A BGe score for tied-covariance mixtures of Gaussian Bayesian networks Grzegorczyk, Marco Computation 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. |
| title | A BGe score for tied-covariance mixtures of Gaussian Bayesian networks |
| topic | Computation |
| url | https://arxiv.org/abs/2511.07050 |