Bayesian Learning of Sparse Gaussian Graphical Models

Sparse inverse covariance matrix modeling is an important tool for learning relationships among different variables in a Gaussian graph. Most existing algorithms are based on `1 regularization, with the regularization parameters tuned via cross-validation. In this paper, a Bayesian formulation of the problem is proposed, where the regularization parameters are inferred adaptively and cross-validation is avoided. Variational Bayes (VB) is used for the model inference. Results on simulated and real datasets validate the proposed approach. In addition, a graph extension algorithm is proposed to include a new variable in an existing graph, which can be used when separate testing data are available.