Block Regularized Lasso for Multivariate Multi-Response Linear Regression
Dr. Yingbin Liang
Department of EECS, Syracuse University
4-206 Center for Science and Technology
Syracuse, NY 13244, USA
Abstract:
Linear regression, as a basic statistical problem, has found its applications in almost all science and engineering fields. A challenging regime of this problem is when the number of samples is much smaller than the dimension of the regression vector. Excitingly, a powerful technique Lasso has recently been introduced to solve the problem in such high dimensional regime with theoretic guarantee if the regression vector is sparse enough.
In this talk, I will first give an overview of the existing results on applying Lasso for solving high dimensional linear regression problems, following which I will introduce the multivariate multi-response (MVMR) linear regression model that we study. One major advantage of our model lies in jointly studying multiple regression problems (i.e., tasks) together, which can reduce sample complexity significantly. I will then present our main results. Namely, we characterize sufficient and necessary conditions under which 1_1\1_2 regularized Lasso successfully recovers the support union of the MVMR model. These conditions admit a sharp threshold transition on the sample size. In particular, we analytically characterize the impact of sparsity of regression vectors and the number of tasks on the sample complexity, which quantitatively demonstrates the advantage of multi-task learning. I will finally talk about the implications of our results, its comparison to existing results, and our numerical results.
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 Department of Electrical Engineering at the University of Hawaii. Since December 2009, she has been an assistant professor at the Department of Electrical Engineering and Computer Science at the Syracuse University. Dr. Liang's research interests include machine learning, information theory, wireless communications 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.