title: Tensor Regression with Applications in Neuroimaging Data Analysis.
abstract: Classical regression methods treat covariates as a vector and estimate a corresponding vector of regression coefficients. Modern 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.
authors.affiliation: Department of Statistics, North Carolina State University, Raleigh, NC 27695-8203 ( hua zhou@ncsu.edu ).
authors.forename: Hua
authors.initials: H
authors.lastname: Zhou
authors.affiliation: Department of Statistics, North Carolina State University, Raleigh, NC 27695-8203.
authors.forename: Lexin
authors.initials: L
authors.lastname: Li
authors.affiliation: Department of Biostatistics and Biomedical Research Imaging Center, University of North Carolina, Chapel Hill, NC 27599-7420 ( hzhu@bios.unc.edu ).
authors.forename: Hongtu
authors.initials: H
authors.lastname: Zhu
keywords: Brain imaging; dimension reduction; generalized linear model (GLM); magnetic resonance imaging (MRI); multidimensional array; tensor regression