Abstract: High dimensional estimation problems, such as phase retrieval, low rank matrix estimation, and blind deconvolution, attracted intensive attention recently due to their wide applications in medical image, signal processing, social networks, etc. Traditional approaches to solving these problems are either empirical, which work well but lack theoretic guarantee; or via convex formulations, which come with performance guarantee but are computationally costly in large dimensions. Nonconvex approaches are recently emerging as a powerful framework to solve such problems, which come with provable performance guarantee and are computationally efficient.
In this talk, I will first introduce general ideas of using nonconvex methods for solving high dimensional estimation problems. I will then focus on the phase retrieval problem to present our recent advancements of nonconvex method. In particular, I will describe our design of a nonconvex objective that yields first-order algorithm outperforming all existing algorithms in both statistical and computational efficiency. I will then present our further design of stochastic algorithms for large-scale phase retrieval with provable convergence guarantee. I will finally conclude my talk with discussion of insights learned from our studies.
Biography: Dr. Yingbin Liang received the Ph.D. degree in Electrical Engineering from the University of Illinois at Urbana-Champaign in 2005. In 2005-2007, she was working as a postdoctoral research associate at Princeton University. In 2008-2009, she was an assistant professor at the University of Hawaii. Since December 2009, she has been on the faculty at Syracuse University, where she is an associate professor. Dr. Liang's research interests include machine learning, statistical signal processing, optimization, information theory, and wireless communication and networks.
Dr. Liang was a Vodafone Fellow at the University of Illinois at Urbana-Champaign during 2003-2005, and received the Vodafone-U.S. Foundation Fellows Initiative Research Merit Award in 2005. She also received the M. E. Van Valkenburg Graduate Research Award from the ECE department, University of Illinois at Urbana-Champaign, in 2005. In 2009, she received the National Science Foundation CAREER Award, and the State of Hawaii Governor Innovation Award. In 2014, she received EURASIP Best Paper Award for the EURASIP Journal on Wireless Communications and Networking. She served as an Associate Editor for the Shannon Theory of the IEEE Transactions on Information Theory during 2013-2015