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Activity Number: 613 - Robust Learning and Posterior Summary
Type: Contributed
Date/Time: Thursday, August 1, 2019 : 8:30 AM to 10:20 AM
Sponsor: Section on Bayesian Statistical Science
Abstract #304696 Presentation
Title: An Empirical G-Wishart Prior for Sparse High-Dimensional Gaussian Graphical Models
Author(s): Chang Liu* and Ryan Martin
Companies: North Carolina State University and North Carolina State University
Keywords: Gaussian graphical model; sparse precision matrix; empirical Bayes; G-Wishart ; posterior convergence; Laplace approximation

In Gaussian graphical models, the zero entries in the precision matrix determine the dependence structure, so estimating that sparse precision matrix and, thereby, learning this underlying structure, is an important and challenging problem. We propose an empirical version of the G-Wishart prior for sparse precision matrices, where the prior mode is informed by the data in a suitable way. Paired with a prior on the structure, a marginal posterior distribution for the structure is obtained that takes the form of a ratio of two G-Wishart normalizing constants. We show that this ratio can be readily evaluated using an accurate Laplace approximation, which leads to fast and efficient posterior sampling even in high-dimensions. Numerical results demonstrate the proposed method's superior performance, in terms of speed and accuracy, across a variety of settings, and theoretical support is provided in the form of a posterior concentration rate theorem.

Authors who are presenting talks have a * after their name.

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