Integrative tensor regression for stratified data with application to neuroimaging analysis

Neuroimaging data often takes the form of tensors, traditional vector-valued regression is difficult to capture the intrinsic structure for such multi-dimensional arrays. In the field of clinical medicine, tensor regression model with tensor-valued medical image covariates and scalar responses has been well studied. Noteworthy, although the clinical manifestation of a disease may exhibit variation contingent upon factors such as geographical location, ethnicity, or other pertinent characteristics, it is imperative to acknowledge the probable existence of shared information in the underlying pathophysiology of the disease, meriting in-depth exploration. In this paper, we propose a novel integrative tensor regression model for analyzing multiple stratified neuroimaging datasets, aiming to recognize and capture both the homogeneity and heterogeneity across different strata. To this end, we utilize a Tucker decomposition of the tensor coefficients, incorporating specific assumptions on the core tensors and factor matrices, inspired by representation learning. Moreover, we generalize our approach to address the problem of tensor quantile regression across multiple stratified datasets. We propose an alternating update algorithm to estimate the coefficients and establish the asymptotic properties of the estimators under certain mild conditions. Finally, the efficacy of our method is demonstrated through experiments conducted on synthetic datasets and real stratified neuroimaging datasets related to ADHD (attention deficit hyperactivity disorder).