Topic: Statistics meets optimization: algorithm analysis and statistical guarantees

Time & Date: 16:00 - 17:00, Friday, April 13, 2018

Venue: Room 110, Teaching Building D

Speaker: Prof. Yiyuan She, Florida State University

Abstract: Modern statistical problems often involve minimizing objective functions that are not necessarily convex or smooth. This paper investigates a broad surrogate framework defined by generalized Bregman divergence functions for developing scalable algorithms. Local linear approximation, mirror descent, iterative thresholding, and DC programming can all be viewed as particular instances. The Bergman re-characterization enables us to choose suitable measures of computational error to establish global convergence rate results even for nonconvex problems in high-dimensional settings. Moreover, under some regularity conditions, the sequence of iterates in Bregman surrogate optimization can be shown to approach the statistical truth within the desired accuracy geometrically fast. The algorithms can be accelerated with a careful control of relaxation and stepsize parameters. Furthermore, a novel scheme is proposed to obtain sharp error rates for jointly regularized sparse estimators which have multiple sparsity promoting penalties (possibly nonconvex) imposed on the same set of parameters. Various examples in structured parsimony pursuit are given to demonstrate the effectiveness of incorporating optimization analysis into statistical analysis.

Biography: Prof. Yiyuan She is currently a professor in the Department of Statistics at Florida State University. Yiyuan obtained his Ph.D. at Stanford in 2008. He received the NSF CAREER award and is currently an associate editor of Metrika and IEEE Transactions on Network Science and Engineering. His current research interests lie in the fields of high dimensional statistics, statistical machine learning, optimization, signal processing, robust statistics, and network science.