# Bayesian Structure Learning in Graphical Models using Shrinkage priors

## TL;DR

This paper introduces a Bayesian method for high-dimensional graphical model structure learning using a novel shrinkage prior, with theoretical guarantees and a Gibbs sampling scheme.

## Contribution

It proposes the DL-graphical prior for precision matrix estimation and provides posterior convergence guarantees with a Gibbs sampling algorithm.

## Key findings

- Effective structure learning in high-dimensional settings
- Theoretical posterior convergence guarantees
- Gibbs sampling scheme for practical implementation

## 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.