Bilinear Regression with Matrix Covariates in High Dimensions

• Activity Number: 406
• Type: Invited
• Date/Time: Tuesday, August 2, 2016 : 2:00 PM to 3:50 PM
• Sponsor: Section on Statistical Learning and Data Science
• Author(s): Dan Yang* and Dong Wang and Hongtu Zhu and Haipeng Shen
• Companies: Rutgers University and and The University of North Carolina at Chapel Hill and The University of Hong Kong
• Keywords: functional data analysis ; RKHS ; reproducing kernel Hilbert space ; tensor ; neuroimaging

Abstract

Traditional functional linear regression usually takes a one dimensional functional predictor as input and estimates the continuous coefficient function. Modern applications often generate two dimensional covariates, which when observed at grid points are matrices. To avoid inefficiency of the classical method involving estimation of a two dimensional coefficient function, we propose a bilinear regression model and obtain estimates via a smoothness regularization method. The proposed estimator exhibits minimax optimal property for prediction under the framework of Reproducing Kernel Hilbert Space. The merits of the method are further demonstrated by numerical experiments and an application on real imaging data.