Bayesian Structure Learning in Graphical Models using Shrinkage priors

2019/07/26 by Banerjee, Sayantan
#FOS: Computer and information sciences #FOS: Mathematics #Methodology (stat.ME) #Statistics Theory (math.ST)

paper · doi:10.48550/arxiv.1908.02684

Abstract

We consider the problem of learning the structure of a high dimensional precision matrix under sparsity assumptions. We propose to use a shrinkage prior, called the DL-graphical prior based on the Dirichlet-Laplace prior used for the Gaussian mean problem. A posterior sampling scheme based on Gibbs sampling is also provided along with theoretical guarantees of the method by obtaining the posterior convergence rate of the precision matrix.

Related

• Contraction of a quasi-Bayesian model with shrinkage priors in precision matrix estimation
• Bayesian estimation of a sparse precision matrix
• Accelerating Bayesian Structure Learning in Sparse Gaussian Graphical Models
• Bayesian Regularization for Graphical Models with Unequal Shrinkage
• Bayesian computation for high-dimensional Gaussian Graphical Models with spike-and-slab priors