Some Recent Progress on Non-Convex Regularization Methods for Sparse Estimation

Friday, February 27, 2015 - 10:15am - 11:05am
Keller 3-180
Tong Zhang (Rutgers, The State University of New Jersey)
Non-convex regularization methods provide natural procedures for sparse recovery but are difficult to analyze. In this talk I will review some progress we have made in recent years. I will first show improved sparse recovery performance for local solutions of nonconvex formulations obtained via specialized numerical procedures. I will then present a unified framework describing the relationship of these local minima to the global minimizer of the underlying nonconvex formulation. In particular, we show that under suitable conditions, the global solution of nonconvex regularization leads to desirable recovery performance and it corresponds to the unique sparse local solution, which can be obtained via different numerical procedures. This unified view leads to a more satisfactory treatment of non-convex high dimensional sparse estimation procedures, and has led to additional numerical procedures for handling non-convex sparse regularization.

Collaborators: Cunhui Zhang, Han Liu, Zhaoran Wang, Tuo Zhao, Qiang Sun