Bayesian Tensor Regression for Neuroimaging Data
Abstract
Multidimensional array data, or tensors, arise naturally in neuroimaging and other high-dimensional applications. We propose a parsimonious Bayesian tensor regression model for studies in which a brain image is the response and predictors are vector-valued covariates. The method extends Bayesian envelope dimension reduction to tensor responses, identifying material subspaces that contain regression information while removing variation that is immaterial to the predictors. This formulation leads naturally to a Tucker tensor decomposition and allows spatial dependence and multiple sources of uncertainty to be modeled jointly. We develop a computationally feasible Markov chain Monte Carlo algorithm based on Gibbs sampling and establish posterior consistency for the proposed model. Simulation studies demonstrate substantial gains in estimation accuracy and uncertainty quantification when meaningful dimension reduction is present. We apply the method to Human Connectome Project neuroimaging data to investigate associations between alcohol use and brain activity. The results illustrate the value of Bayesian tensor envelope regression for inference with high-dimensional, spatially dependent imaging responses.
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BibTeX
@misc{naji2026bayesian,
title = {{Bayesian Tensor Regression for Neuroimaging Data}},
author = {Zahra Naji and Montserrat Fuentes and Liangsuo Ma and Hossein Moradi Rekabdarkolaee},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.27880},
eprint = {2609.27880},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.27880},
}
RIS
TY - UNPB
TI - Bayesian Tensor Regression for Neuroimaging Data
AU - Zahra Naji
AU - Montserrat Fuentes
AU - Liangsuo Ma
AU - Hossein Moradi Rekabdarkolaee
PY - 2026
DA - 2026/09/01
PB - arXiv
DO - 10.48550/arxiv.2609.27880
UR - https://arxiv.org/abs/2609.27880
AB - Multidimensional array data, or tensors, arise naturally in neuroimaging and other high-dimensional applications. We propose a parsimonious Bayesian tensor regression model for studies in which a brain image is the response and predictors are vector-valued covariates. The method extends Bayesian envelope dimension reduction to tensor responses, identifying material subspaces that contain regression information while removing variation that is immaterial to the predictors. This formulation leads naturally to a Tucker tensor decomposition and allows spatial dependence and multiple sources of uncertainty to be modeled jointly. We develop a computationally feasible Markov chain Monte Carlo algorithm based on Gibbs sampling and establish posterior consistency for the proposed model. Simulation studies demonstrate substantial gains in estimation accuracy and uncertainty quantification when meaningful dimension reduction is present. We apply the method to Human Connectome Project neuroimaging data to investigate associations between alcohol use and brain activity. The results illustrate the value of Bayesian tensor envelope regression for inference with high-dimensional, spatially dependent imaging responses.
ER -