统计数科学术讲座

Supervised and Unsupervised Learning for Tensor Data in High Dimensions

演讲者:Dr. Qing Mai, Florida State University

时间:2019-12-11 15:00-16:00

地点:慧园3栋415报告厅

报告简介  Abstract

In contemporary scientific research, it is often of great interest to predict a categorical response based on a high-dimensional tensor (i.e. multi-dimensional array) and additional covariates. Motivated by applications in science and engineering, we propose a comprehensive and interpretable discriminant analysis model, called the CATCH model (in short for Covariate-Adjusted Tensor Classification in High-dimensions). The CATCH model efficiently integrates the covariates and the tensor to predict the categorical outcome. The tensor structure is utilized to achieve easy interpretation and accurate prediction. To tackle the new computational and statistical challenges arising from the intimidating tensor dimensions, we propose a penalized approach to select a subset of the tensor predictor entries that affect classification after adjustment for the covariates. An efficient algorithm is developed to take advantage of the tensor structure in the penalized estimation. Theoretical results confirm that the proposed method achieves variable selection and prediction consistency, even when the tensor dimension is much larger than the sample size. The superior performance of our method over existing methods is demonstrated in extensive simulated and real data examples. We further investigate unsupervised learning for tensor data where no categorical response is available. A doubly-enhanced EM algorithm is proposed that aggressively exploit tensor structure to improve efficiency. Numerical studies and theoretical studies strongly support the application of our proposal.


嘉宾简介  About the Speaker

Qing Mai is Associate Professor (with tenure), Department of Statistics, Florida State University. She received B.S. in Statistics from Nankai University, and Ph.D. in Statistics from University of Minnesota. Her current research interests include machine learning, high-dimensional statistics, tensor data analysis, discriminant analysis. She has published in both statistics and machine learning journals (such as Annals of Statistics, Journal of American Statistical Association, Biometrika, Journal of Machine Learning Research). She is a member of the American Statistical Association, the Institute of Mathematical Statistics, and the International Chinese Statistical Association.


讲座海报 Poster

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