Tensor Regression with Applications in Neuroimaging Data Analysis

• 成果类型: Article
• 署名作者: Zhou, Hua; Li, Lexin; Zhu, Hongtu
• 署名单位: North Carolina State University; University of North Carolina; University of North Carolina Chapel Hill; University of North Carolina; University of North Carolina Chapel Hill
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2013.776499
• 发表日期: 2013
• 页码: 540-552
• 关键词: logistic-regression; variable selection; DECOMPOSITION; matrix; models; CLASSIFICATION

摘要

Classical regression methods treat covariates as a vector and estimate a corresponding vector of regression coefficients. Modem applications in medical imaging generate covariates of more complex form such as multidimensional arrays (tensors). Traditional statistical and computational methods are proving insufficient for analysis of these high-throughput data due to their ultrahigh dimensionality as well as complex structure. In this article, we propose a new family of tensor regression models that efficiently exploit the special structure of tensor covariates. Under this framework, ultrahigh dimensionality is reduced to a manageable level, resulting in efficient estimation and prediction. A fast and highly scalable estimation algorithm is proposed for maximum likelihood estimation and its associated asymptotic properties are studied. Effectiveness of the new methods is demonstrated on both synthetic and real MRI imaging data. Supplementary materials for this article are available online.