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Bayes Regularized Graphical Model Estimation in High Dimensions

There has been an intense development of Bayes graphical model estimation approaches over the past decade - however, most of the existing methods are restricted to moderate dimensions. We propose a novel approach suitable for high dimensional settings, by decoupling model fitting and covariance selection. First, a full model based on a complete graph is fit under novel class of continuous shrinkage priors on the precision matrix elements, which induces shrinkage under an equivalence with Cholesky-based regularization while enabling conjugate updates of entire precision matrices. Subsequently, we propose a post-fitting graphical model estimation step which proceeds using penalized joint credible regions to perform neighborhood selection sequentially for each node. The posterior computation proceeds using straightforward fully Gibbs sampling, and the approach is scalable to high dimensions. The proposed approach is shown to be asymptotically consistent in estimating the graph structure for fixed $p$ when the truth is a Gaussian graphical model. Simulations show that our approach compares favorably with Bayesian competitors both in terms of graphical model estimation and computational efficiency. We apply our methods to high dimensional gene expression and microRNA datasets in cancer genomics.