Model-based clustering via Bayesian estimation of Gaussian graphical models and precision matrices

Oregon Convention Center 

Finite Gaussian mixture models are ubiquitous for model-based clustering of continuous data. These models' parameters scale quadratically with the number of variables. A rich literature exists on parsimonious models via covariance matrix decompositions or other structural assumptions. However, these models do not allow for direct estimation of conditional independencies via sparse precision matrices. Here, we introduce mixtures of Gaussian graphical models for model-based clustering with sparse precision matrices. We employ recent developments in Bayesian estimation of Gaussian graphical models to circumvent the doubly intractable partition function of the G-Wishart distribution and use conditional Bayes factors for model comparison in a Metropolis-Hastings framework. We extend this to mixtures of Gaussian graphical models and apply this to estimate conditional independence structures in the different mixture components via fast joint estimation of the graphs and precision matrices. Our framework results in a parsimonious model-based clustering of the data and provides conditional independence interpretations of the mixture components.

Model-based clustering

Finite Gaussian mixture models

Precision matrix

Gaussian graphical model

Markov chain Monte Carlo (MCMC)

G-Wishart Distribution 

Section on Bayesian Statistical Science