title: Theoretical and Experimental Analyses of Tensor-Based Regression and Classification.
abstract: We theoretically and experimentally investigate tensor-based regression and classification. Our focus is regularization with various tensor norms, including the overlapped trace norm, the latent trace norm, and the scaled latent trace norm. We first give dual optimization methods using the alternating direction method of multipliers, which is computationally efficient when the number of training samples is moderate. We then theoretically derive an excess risk bound for each tensor norm and clarify their behavior. Finally, we perform extensive experiments using simulated and real data and demonstrate the superiority of tensor-based learning methods over vector- and matrix-based learning methods.
authors.affiliation: Department of Computer Science, Tokyo Institute of Technology, Meguro-ku, Tokyo 152-8552, Japan kishanwn@gmail.com.
authors.forename: Kishan
authors.initials: K
authors.lastname: Wimalawarne
authors.affiliation: Toyota Technological Institute at Chicago, Chicago, IL 60637, U.S.A. tomioka@ttic.edu.
authors.forename: Ryota
authors.initials: R
authors.lastname: Tomioka
authors.affiliation: Department of Complexity Science and Engineering, University of Tokyo, Bunkyo-ku, Tokyo 113-0033, Japan sugi@k.u-tokyo.ac.jp.
authors.forename: Masashi
authors.initials: M
authors.lastname: Sugiyama