Variational Bayes learning of multiscale graphical models

Multiscale (multiresolution) graphical models have gained widespread popularity in recent years, since they enjoy rich modeling power as well as efficient inference procedures. Existing approaches to learning multiscale graphical models often leverage the framework of penalized likelihood, and therefore suffer from the issue of regularization selection. In this paper, we propose a novel method to learn multiscale graphical models from the Bayesian perspective. More specifically, the regularization parameters are treated as random variables that follow Gamma distributions. We then derive an efficient variational Bayes algorithm to learn the model, and further demonstrate the advantages of the proposed method through numerical experiments.