Bayesian Tensor-on-Tensor Varying Coefficient Model for Forecasting Alzheimer's Disease Progression

2026-04-08

AI Summary

This study addresses the challenges of modeling the nonlinear evolution, spatial structure, and individual heterogeneity inherent in high-dimensional neuroimaging data across the progression of Alzheimer’s disease. To this end, we propose a Bayesian tensor-on-tensor varying coefficient model that, for the first time, integrates spatial heterogeneity, nonlinear time-varying effects, and tensor-structured data within an interpretable Bayesian framework. The approach employs Gaussian process priors to capture voxel-wise nonlinear trajectories, combines low-rank tensor decomposition with a spatial block-to-voxel mapping to model local neighborhood dependencies, and leverages a parallelized MCMC algorithm for efficient inference. Experiments on ADNI data demonstrate that our method significantly outperforms existing approaches in forecasting future cortical thickness and brain age, achieving superior performance in estimation accuracy, computational efficiency, predictive capability, and scalability.

Abstract

We propose a novel tensor-on-tensor modeling framework that flexibly models nonlinear voxel-level relationships using Gaussian process (GP) priors, while incorporating the spatial structure of the output tensor through low-rank tensor-based coefficients. Spatial heterogeneity is captured through patch-to-voxel mappings, enabling each output voxel to depend on its spatial neighborhood. The proposed interpretable and flexible Bayesian tensor-on-tensor framework is able to capture nonlinearity, spatial information, and spatial heterogeneity. We develop an efficient Markov chain Monte Carlo (MCMC) algorithm that exploits parallel structure to sample voxel-specific GP atoms and update low-rank tensor coefficients. Extensive simulations reveal advantages of the proposed approach over existing methods in terms of coefficient estimation, inference, prediction, and scalability to high-dimensional images. Applied to longitudinal image prediction with T1-weighted MRIs from the Alzheimer's Disease Neuroimaging Initiative (ADNI), the proposed method can accurately forecast future cortical thickness. The predicted images also enable reliable prediction of brain aging, underscoring their biological relevance. Overall, the ADNI analysis highlights the model's ability to forecast future neurobiological changes that has important implications for early detection of AD.

Problem

• Alzheimer's Disease
• disease progression forecasting
• neuroimaging
• cortical thickness prediction
• brain aging

Innovation

• Bayesian tensor-on-tensor model
• Gaussian process prior
• spatial heterogeneity
• low-rank tensor coefficient
• MCMC algorithm