Tensor Partial Least Squares for the Quantile Regression Model with Multiway Neuroimaging Data

• Activity Number: 443 - Latent Variables, Causal Inference, Machine Learning and Other Topics in Mental Health Statistics
• Type: Contributed
• Date/Time: Thursday, August 12, 2021 : 4:00 PM to 5:50 PM
• Sponsor: Mental Health Statistics Section
• Author(s): Dayu Sun* and Limin Peng and Ying Guo and Amita K. Manatunga
• Companies: Emory University and Emory University and Emory University and Emory University
• Keywords: Tensor; Quantile regression; Imaging data; Partial least sqaures

Abstract

Neuroimaging data have been increasingly prevalent and are often characterized as multi-dimensional arrays, termed as tensors. Most existing tensor regression methods explore the effects of neuroimaging tensors on the average clinical outcome but fail to satisfy the practical interest in the non-average or unusual clinical phenotypes, which can be fulfilled by quantile regression. In this work, we propose a novel tensor partial least squares algorithm based on quantile covariance for the quantile regression model with tensor predictors. Our theoretical investigations show that the proposed method can substantially reduce the number of free parameters and yield consistent estimators under mild conditions. Extensive numerical studies demonstrate the proposed algorithm can satisfactorily recover the tensor coefficients with realistic sample sizes and outperform alternative methods. An application to a neuroimaging dataset from Grady Trauma Project illustrates the utility of the proposed method in practice.