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Title: Reduced-rank tensor-on-tensor regression and tensor-variate analysis of variance Authors:  Ranjan Maitra - Iowa State University (United States) [presenting]
Carlos Llosa-Vite - Iowa State University (United States)
Abstract: Fitting regression models with many multivariate responses and covariates can be challenging, but such responses and covariates sometimes have a tensor-variate structure. We extend the classical multivariate regression model to exploit such a structure in two ways: first, we impose four types of low-rank tensor formats on the regression coefficients. Second, we model the errors using the tensor-variate normal distribution that imposes a Kronecker separable format on the covariance matrix. We obtain maximum likelihood estimators via block-relaxation algorithms and derive their computational complexity and asymptotic distributions. Our regression framework enables us to formulate a tensor-variate analysis of variance (TANOVA) methodology. This methodology, when applied in a one-way TANOVA layout, enables us to identify cerebral regions significantly associated with the interaction of suicide attempters or non-attemptor ideators and positive-, negative- or death-connoting words in a functional Magnetic Resonance Imaging study. Another application uses three-way TANOVA on the Labeled Faces in the Wild image dataset to distinguish facial characteristics related to ethnic origin, age group and gender.