Title: Bayesian Regularization for Gaussian Graphical Models
Abstract: In this talk, I will present a Bayesian framework for estimating a high-dimensional sparse precision matrix, in which adaptive shrinkage and sparsity are induced by a mixture of Laplace priors. Along with devising our model from a Bayesian standpoint, we study the MAP (maximum a posteriori) estimator from a penalized likelihood perspective. Optimal error rates for estimation consistency in terms of various matrix norms along with selection consistency for sparse structure recovery are shown for the unique MAP estimator under mild conditions. For fast and efficient computation, an EM algorithm is proposed to compute the MAP estimator of the precision matrix and (approximate) posterior probabilities on the edges of the underlying sparse structure. I will present some empirical results demonstrating the fine performance of our method compared with existing alternatives. (This is joint work with Lingrui Gan and Feng Liang).