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Activity Number: 195 - Section on Statistics in Imaging Student Paper Award Winners
Type: Topic Contributed
Date/Time: Monday, August 8, 2022 : 2:00 PM to 3:50 PM
Sponsor: Section on Statistics in Imaging
Abstract #321007
Title: Reduced-Rank Tensor-on-Tensor Regression and Tensor-Variate Analysis of Variance
Author(s): Carlos Llosa* and Ranjan Maitra
Companies: Iowa State University and Iowa State University
Keywords: Kronecker separable model; tensor regression; multilinear statistics; tensor decomposition

Fitting regression models with many multivariate responses and covariates can be challenging, but such responses and covariates sometimes have tensor-variate structure. We extend the classical multivariate regression model to exploit such 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 framework enables us to formulate 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.

Authors who are presenting talks have a * after their name.

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