A BGe score for tied-covariance mixtures of Gaussian Bayesian networks

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.