Parsimonious Tensor Response Regression

• 成果类型: Article
• 署名作者: Li, Lexin; Zhang, Xin
• 署名单位: University of California System; University of California Berkeley; State University System of Florida; Florida State University
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2016.1193022
• 发表日期: 2017
• 页码: 1131-1146
• 关键词: multivariate linear-regression; simultaneous dimension reduction; longitudinal neuroimaging data; least-squares regression; reduced-rank regression; variable selection; models; predictors; ENVELOPES; algorithm

摘要

Aiming at abundant scientific and engineering data with not only high dimensionality but also complex structure, we study the regression problem with a multidimensional array (tensor) response and a vector predictor. Applications include, among others, comparing tensor images across groups after adjusting for additional covariates, which is of central interest in neuroimaging analysis. We propose parsimonious tensor response regression adopting a generalized sparsity principle. It models all voxels of the tensor response jointly, while accounting for the inherent structural information among the voxels. It effectively reduces the number of free parameters, leading to feasible computation and improved interpretation. We achieve model estimation through a nascent technique called the envelope method, which identifies the immaterial information and focuses the estimation based upon the material information in the tensor response. We demonstrate that the resulting estimator is asymptotically efficient, and it enjoys a competitive finite sample performance. We also illustrate the new method on two real neuroimaging studies. Supplementary materials for this article are available online.