时间：2018年10月29（星期一）14：00-15：00

地点：学院南路校区，学术会堂603

报告题目：Non-convexoptimization and statistical properties

报告人：Xiaoming Huo, Georgia Institute of Technology

报告摘要：Non-convexoptimization has been introduced into statistics with a range of applications.One application is in the model selection under the sparse regressionframework, with the celebrated methods such as the smoothly clipped absolutedeviation (SCAD), the minimax concave penalty (MCP), and many more. The newlyemerged deep-learning-related techniques often involve non-convex objectivefunctions as well. A non-convex optimization problem is generally NP-hard;therefore there is no guaranteed polynomial-time numerical solution. One can onlyhope to identify a local optimum. A difference-of-convex (DC) function can beexpressed as a difference of two convex functions, though the original functionitself may be non-convex. There is a large existing literature on theoptimization problems when their objectives and/or constraints involve the DCfunctions; they are commonly referred to as difference-of-convex algorithms(DCA). Efficient numerical solutions have been proposed. Under the DCframework, directional-stationary (d-stationary) solutions are considered, andthey are in general not unique. We show that under some mild conditions, acertain subset of d-stationary solutions in an optimization problem (with a DCobjective) has some ideal statistical properties: namely, asymptotic estimationconsistency, asymptotic model selection consistency, asymptotic efficiency. Theaforementioned properties are the ones that have been proven by manyresearchers for a range of proposed non-convex penalties in the sparseregression. Our analysis indicates that even with non-convex optimization, somestatistical theoretical guarantee can still be established, in some generalsenses. Our work potentially bridges the communities of optimization andstatistics. A joint work with Shanshan Cao.

报告人简介：Xiaoming Huo is a professor at theStewart School of Industrial & Systems Engineering at Georgia Tech. Dr. Huo’sresearch interests include statistical theory, statistical computing, andissues related to data analytics. He has made numerous contributions on topicssuch as sparse representation, wavelets, and statistical problems indetectability. His papers appeared in top journals, and some of them are highlycited. He is a senior member of IEEE since May 2004. He was a Fellow of IPAM inSeptember 2004. Dr. Huo received the B.S. degree in mathematics from theUniversity of Science and Technology, China, in 1993, and the M.S. degree inelectrical engineering and the Ph.D. degree in statistics from StanfordUniversity, Stanford, CA, in 1997 and 1999, respectively. Since August 1999, hehas been an Assistant/Associate/Full Professor with the School of Industrialand Systems Engineering, Georgia Institute of Technology, Atlanta. Herepresented China in the 30th International Mathematical Olympiad (IMO), whichwas held in Braunschweig, Germany, in 1989, and received a golden prize.

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