Broadcasted nonparametric tensor regression

• 成果类型: Article
• 署名作者: Zhou, Ya; Wong, Raymond K. W.; He, Kejun
• 署名单位: Renmin University of China; Texas A&M University System; Texas A&M University College Station; Renmin University of China
• 刊物名称: JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
• ISSN/ISSBN: 1369-7412
• DOI: 10.1093/jrsssb/qkae027
• 发表日期: 2024
• 页码: 1197-1220
• 关键词: GENERALIZED LINEAR-MODELS; on-image regression; variable selection; local asymptotics; regularization; rates

摘要

We propose a novel use of a broadcasting operation, which distributes univariate functions to all entries of the tensor covariate, to model the nonlinearity in tensor regression nonparametrically. A penalized estimation and the corresponding algorithm are proposed. Our theoretical investigation, which allows the dimensions of the tensor covariate to diverge, indicates that the proposed estimation yields a desirable convergence rate. We also provide a minimax lower bound, which characterizes the optimality of the proposed estimator for a wide range of scenarios. Numerical experiments are conducted to confirm the theoretical findings, and they show that the proposed model has advantages over its existing linear counterparts.