Lecture Series in Pattern Recognition
题 目（TITLE）： A General Theory of Concave Regularization for High Dimensional Sparse Estimation Problems
讲 座 人（SPEAKER）: Prof. Tong Zhang (Rutgers University)
主 持 人 (CHAIR)：Prof. Baogang Hu
时 间 (TIME)： 3:00 PM Aug. 9 (Tuesday), 2012
地 点 (VENUE)： The Second Meeting Room, 13th floor
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 first explain the advantage of non-convex regularization over Lasso, and review some recent results showing improved 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.
Joint work with Cunhui Zhang
Tong Zhang received a B.A. in mathematics and computer science from Cornell University in 1994 and a Ph.D. in Computer Science from Stanford University in 1998. After graduation, he worked at IBM T.J. Watson Research Center in Yorktown Heights, New York, and Yahoo Research in New York city. He is currently a professor of statistics at Rutgers University. His research interests include machine learning, algorithms for statistical computation, their mathematical analysis and applications.