This week's Statistics Seminar speaker is Tong Zhang from Rutgers University.
Talk Title: Some Recent Progress on High Dimensional Sparse Estimation with Concave Regularization
Concave regularization methods provide natural procedures for sparse recovery. However, they are difficult to analyze in the high dimensional setting. In this talk I will review some progress we made on this topic 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 concave high dimensional sparse estimation procedures, and can serve as the guideline for developing additional numerical procedures for concave regularization.
This talk is based on joint work with Cunhui Zhang
Refreshments will be served after the seminar in 1181 Comstock Hall.