Convex Banding of the Covariance Matrix

• Activity Number: 275
• Type: Topic Contributed
• Date/Time: Tuesday, August 5, 2014 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistical Learning and Data Mining
• Author(s): Jacob Bien*+ and Florentina Bunea and Luo Xiao
• Companies: Cornell University and Cornell University and Johns Hopkins University
• Keywords: covariance ; high-dimensional ; group lasso

Abstract

We introduce a sparse and positive definite estimator of the covariance matrix designed for high-dimensional situations in which the variables have a known ordering. Our estimator is the solution to a convex optimization problem that involves a hierarchical group lasso penalty. We show how it can be efficiently computed, compare it to other methods such as tapering by a fixed matrix, and develop several theoretical results that demonstrate its strong statistical properties. Finally, we show how using convex banding can improve the performance of high-dimensional procedures such as linear and quadratic discriminant analysis.