科学研究

Dr. Yiyuan She obtained his PhD from Stanford University in 2008. He is currently a professor in the Statistics Department at Florida State University. Dr. She is a fellow of ASA, a fellow of IMS and an elected member of ISI. His research interests include high dimensional statistics, machine learning, optimization, robust statistics and others. Dr. She is currently an associate editor of Statistica Sinica, JASA, and IEEE Transactions on Network Science and Technology.

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.