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. Medical imaging and genomic studiesgenerate 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 ultrahighdimensionality as well as complex structure. We propose a family of tensorregression models that efficiently exploit the special structure of tensorcovariates. Under this framework, ultrahigh dimensionality is reduced to a manageable level, resulting in efficient estimation and prediction. Potential of the new method is demonstrated on imaging data.