Statistics and Data Science Seminar: Supervised Multivariate Learning with Simultaneous Feature Auto-grouping and Dimension Reduction

Co-sponsored by TRIADS

Abstract: Modern  high-dimensional methods often  adopt the "bet on sparsity'' principle, while in supervised multivariate learning statisticians  may face "dense'' problems with a large number of nonzero coefficients. This paper proposes a novel clustered reduced-rank learning (CRL) framework  that imposes two joint matrix regularizations to automatically group the features in constructing   predictive factors. CRL is more interpretable than  low-rank modeling and relaxes  the stringent sparsity  assumption in variable selection.  In this paper, new  information-theoretical limits are presented to  reveal the intrinsic cost of seeking for clusters, as well as   the blessing from dimensionality in multivariate learning. Moreover, an efficient optimization  algorithm is developed, which  performs subspace learning and clustering  with guaranteed convergence. The obtained  fixed-point estimators,  though not necessarily globally optimal, enjoy the desired statistical accuracy beyond the standard likelihood setup under some regularity conditions.  Moreover, a new kind of information criterion, as well as its scale-free form, is proposed  for cluster and rank   selection,  and has a rigorous theoretical support  without assuming an infinite sample size.  Extensive simulations and real-data experiments demonstrate the statistical accuracy and interpretability  of the proposed method.

Bio: Yiyuan She received Ph.D. in Statistics from Stanford University and is currently a professor at the Department of Statistics, Florida State University.  His research interests are in the areas of high dimensional statistics, statistical machine learning, optimization, signal processing, robust statistics, multivariate statistics, and network science. Yiyuan received the NSF CAREER award and currently serves as an Associate Editor for Journal of the American Statistical Association and Statistica Sinika. Yiyuan is a Fellow of ASA, Fellow of IMS, and an Elected Member of ISI.

Host: Xuming He