Topic：Statistical Inference over Time-Varying High-Dimensional Models

Time：2014年08月12日（周二）上午10:00-11:30

Venue：信电大楼-215学术会议室

Speaker：Lifeng Lai, Assistant Professor,

         Department of Electrical and Computer

         Engineering, Worcester Polytechnic

         Institute, USA

Biography

Lifeng Lai received the B.E. and M. E. degrees from Zhejiang University, Hangzhou, China in 2001 and 2004 respectively, and the PhD degree from The Ohio State University at Columbus, OH, in 2007. He was a postdoctoral research associate at Princeton University from 2007 to 2009. He is now an assistant professor at Worcester Polytechnic Institute. Dr. Lai’s research interests include information theory, stochastic signal processing and their applications in wireless communications, security and other related areas.Dr. Lai was a Distinguished University Fellow of the Ohio State University from 2004 to 2007. He is a co-recipient of the Best Paper Award from IEEE Global Communications Conference (Globecom) in 2008, the Best Paper Award from IEEE Conference on Communications (ICC) in 2011 and the Best Paper Award from IEEE Smart Grid Communications (SmartGridComm) in 2012. He received the National Science Foundation CAREER Award in 2011, and Northrop Young Researcher Award in 2012. He served as a Guest Editor for IEEE Journal on Selected Areas in Communications, Special Issue on Signal Processing Techniques for Wireless Physical Layer Security. He is currently serving as an Editor for IEEE Transactions on Wireless

Communications.

Abstract

Motivated by big data applications, there have been many recent work on understanding the performance of regularized estimators for estimating parameters in high-dimensional data. Most of existing work assume that the training data come from the same underlying model. In practice, however, the data may come from time-varying models. For example, data from gene regulatory network or complex networks evolves over time. In this talk, we discuss our recent work on sparse linear regression problems for which the underlying model undergoes multiple changes. Our goal is to estimate the number and locations of change-points that segment available data into different regions, and further produce sparse and interpretable models for each region. To address challenges of the existing approaches and to produce interpretable models, we propose a sparse group Lasso based approach for linear regression problems with change-points. Under certain mild assumptions and a properly chosen regularization term, we prove that the solution of the proposed approach is asymptotically consistent. In particular, we show that the estimation error of linear coefficients diminishes, and the locations of the estimated change-points are close to those of true change-points. We further propose a method to choose the regularization term so that the results mentioned above hold. In addition, we show that the complexity of the proposed algorithm is much smaller than those of existing approaches. Numerical examples are provided to validate

the analytic results.