Bayesian Covariance Lasso

• Activity Number: 653
• Type: Topic Contributed
• Date/Time: Thursday, August 5, 2010 : 10:30 AM to 12:20 PM
• Sponsor: Biometrics Section
• Author(s): Zakaria Khondker*+ and Hongtu Zhu and Joseph G. Ibrahim and Haitao Chu
• Companies: The University of North Carolina at Chapel Hill and The University of North Carolina at Chapel Hill and The University of North Carolina at Chapel Hill and The University of North Carolina at Chapel Hill
• Keywords: precision matrix ; covariance matrix ; Bayesian ; efficient updating scheme ; high dimensional ; covariance lasso

Abstract

Estimation of sparse covariance and its inverse subject to positive definite constraints has drawn a lot of attention in recent years. The abundance of high-dimensional data, where sample size (n) is less than the dimension (d), calls for shrinkage estimators since the maximum likelihood estimator is not positive definite; when n is larger than d but n/d is fairly small shrinkage estimators are more stable. Frequentist methods have used penalized likelihoods; Bayesian approaches rely on decomposition or Wishart distribution for shrinkage. We propose a Bayesian estimator under the lasso penalty, discuss priors for some frequentist penalties, and propose an efficient sampling scheme that does not precalculate boundaries for positive definiteness. Simulation shows that Bayesian covariance lasso performs similarly as the frequentist methods for high-dimensional cases.