題  目：Taming Nonconvexity in Information Science

内容簡介：In various information science applications of interest, parameter estimation is naturally posed as a nonconvex optimization problem, especially in the high-dimensional scenario. In order to reduce the degrees of freedom and to combat the curse of dimensionality, it is often necessary to exploit low-dimensional geometric structures of the information embedded in the data, including sparsity, low-rank structure, and other structural priors. Notably, many important low-dimensional structures are best described using nonconvex constraints. This poses significant challenges --- both statistically and computationally --- for developing globally convergent algorithms with near-optimal statistical guarantees. In recent years, statistical procedures have been developed to promote low-dimensional structures using convex relaxation, which typically lift the problem into higher dimensions and convexify the problem. However such approaches are often computationally expensive.

Motivated by the computational consideration, there is a recent surge in designing nonconvex procedures, in which one attempts to solve the original nonconvex formulation directly. Fortunately, despite the nonconvexity, the loss surface of many information processing tasks exhibits benign geometric structures under natural statistical models, thus enabling provably efficient algorithmic solutions without resorting to convex relaxation. In this talk, I will introduce these recent findings and discuss how to design provably fast algorithms that properly exploit such geometric properties.

報告人：美國普林斯頓大學  Yuxin Chen（陳昱鑫）  助理教授

報告人簡介：Yuxin Chen is currently an assistant professor in the Department of Electrical Engineering at Princeton University. Prior to joining Princeton, he was a postdoctoral scholar in the Department of Statistics at Stanford University, and he completed his Ph.D. in Electrical Engineering at Stanford University. His research interests include high-dimensional statistics, convex and nonconvex optimization, statistical learning, and information theory. He received the AFOSR Young Investigator Award and Princeton SEAS Innovation Award.

時  間：2018年11月26日（周一）上午9：00始

地  點：南海樓124室

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