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.Comment: 27 pages, 4 figure
