A Joint Convex Penalty for Inverse Covariance Matrix Estimation

• Activity Number: 508
• Type: Contributed
• Date/Time: Wednesday, August 6, 2014 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistical Computing
• Author(s): Ashwini Maurya*+
• Companies: Michigan State University
• Keywords: Joint Penalty ; Convex Optimization ; Sparsity ; Proximal Gradient

Abstract

The paper proposes a joint convex penalty for estimating the Gaussian inverse covariance matrix. A proximal gradient method is developed to solve the resulting optimization problem with more than one penalty constraints. Under mild conditions the algorithm achieves sublinear rate of convergence which makes it attractive choice for many optimization problems. The simulation shows that imposing a single constraint is not enough and estimator can be improved by a trade-off between two convex penalties. The proposed method has better performance than other two methods for at least three of the four underlying inverse covariance matrix settings. Also the performance of a particular method depends upon the evaluation criteria and the underlying structure of the inverse covariance matrix.