Title: A principle of Robustification for Big Data

Abstract: Heavy-tailed distributions are ubiquitous in modern statistical analysis and machine learning problems. This talk gives a simple principle for robust high-dimensional statistical inference via an appropriate shrinkage on the data.  This widens the scope of high-dimensional techniques, reducing the moment conditions from sub-exponential or sub-Gaussian distributions to merely bounded second moment. As an illustration of this principle, we focus on robust estimation of the low-rank matrix from the trace regression model.  It encompasses four popular problems: sparse linear models, compressed sensing, matrix completion, and multi-task regression.  Under only bounded $2+\delta$ moment condition, the proposed robust methodology yields an estimator that possesses the same statistical error rates as previous literature with sub-Gaussian errors. We also illustrate the idea for estimation of large covariance matrix. The benefits of shrinkage are also demonstrated by financial, economic, and simulated data. Joint work with Weichen Wang and Zhiwei Zhu.

Bio: Jianqing Fan is Frederick L. Moore Professor at Princeton University.  After receiving his Ph.D. from the University of California at Berkeley, he has been appointed as assistant, associate, and full professor at the University of North Carolina at Chapel Hill (1989-2003), professor at the University of California at Los Angeles (1997-2000), and professor at the Princeton University (2003--).  He was the past president of the Institute of Mathematical Statistics and International Chinese Statistical Association. He is co-editing  Journal of Econometrics and was the co-editor of The Annals of Statistics,  Probability Theory and Related Fields and Econometrics Journal.    His published work on statistics, economics, finance, and computational biology has been recognized by The 2000 COPSS Presidents' Award, The 2007 Morningside Gold Medal of Applied Mathematics, Guggenheim Fellow, P.L. Hsu Prize, Royal Statistical Society Guy medal in silver, and election to Academician of Academia Sinica and follow of American Associations for Advancement of Science.