Time Varying Estimation of Tensor-On-Tensor Regression with Application in fMRI Data

• Activity Number: 215 - Contributed Poster Presentations: Section on Statistical Learning and Data Science
• Type: Contributed
• Date/Time: Tuesday, August 4, 2020 : 10:00 AM to 2:00 PM
• Sponsor: Section on Statistical Learning and Data Science
• Author(s): Pratim Guha Niyogi* and Tapabrata (Taps) Maiti
• Companies: Michigan State University and Michigan State University
• Keywords: Functional linear model; Multidimensional array; Tensor-on-Tensor regression; B-spline; CP decomposition; Functional MRI

Abstract

In fMRI studies, data structure could be visualized as time-varying multidimensional arrays (tensor), collected at different time-points on multiple objects. We consider detection of neural activation in fMRI experiments in presence of tensor valued brain images and tensor predictors where both of them are collected over same set of time. A time- varying regression model with the presence of inherent structural composition of regressors and covariates is proposed. B-spline technique is used to model the regression coefficient and the coefficients of the basis function are estimated using CP decomposition based on Lock (2018) algorithm by minimizing a penalized loss function. In this article, we have generalized the varying coefficient model from vector-valued covariates and responses, as well as, the tensor regression model. Hence, it is a logical and nontrivial extension of function-on-function concurrent linear models in complex data structure where the inherent structures of the data is considered. Efficacy of the proposed model is studied based on both simulated data for different setups and a real data set.