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Title: Using tensor regression to select the HIV-related connections between brain's regions Authors:  Joaquin Goni - Purdue University (United States)
Jaroslaw Harezlak - Indiana University School of Public Health-Bloomington (United States)
Damian Brzyski - Indiana University Bloomington (United States) [presenting]
Beau Ances - School of Medicine Washington University in Saint Louis (United States)
Abstract: Classical regression methods treat covariates as a vector and estimate a corresponding vector of regression coefficients. In medical applications, however, very often regressors in a form of multidimensional arrays could be met. For instance, one might be interested in utilizing 2- or 3-dimensional MRI brain images to determine brain regions whose structural or functional features are associated with certain medical condition. Flattening such image array into a vector is an unsatisfactory solution, since it destroys the inherent spatial structure of the image and could be very challenging from the computational point of view. We will present the alternative approach - the tensor regression - which we are using to investigate the changes in the structure of brain's connections in the cohort of HIV-positive subjects. For each patient such connectivity information occurs in the form of p by p dimensional matrix, where p is a number of considered brain's regions and where entries indicate how strongly pairs of regions are connected. The corresponding model's coefficients are in the form of p by p dimensional matrix as well and the goal is to select the response-related entries.