High-Dimensional Posterior Convergence Rates for Decomposable Graphical Models

• Activity Number: 313
• Type: Contributed
• Date/Time: Tuesday, August 11, 2015 : 8:30 AM to 10:20 AM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Ruoxuan Xiang* and Kshitij Khare and Malay Ghosh
• Companies: University of Florida and University of Florida and University of Florida
• Keywords: Graphical models ; Decomposable graph ; Posterior consistency ; High-dimensional data

Abstract

Gaussian concentration graphical models are one of the most popular models for sparse covariance estimation with high-dimensional data. In recent years, a lot of work has been done to develop methods which facilitate Bayesian inference for these models under the standard G-Wishart prior. However, convergence properties of the resulting posterior are not completely understood, particularly in high-dimensional settings. Existing results in the literature provide high-dimensional posterior convergence rates for the class of banded concentration graphical models. In this paper, we derive high-dimensional posterior convergence rates for the much larger class of decomposable concentration graphical models. A key initial step in our analysis which facilitates this substantial generalization is transformation to the Cholesky factor of the inverse covariance matrix. As a by-product of our analysis, we also obtain convergence rates for the corresponding maximum likelihood estimator.