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

TL;DR

This paper introduces a Bayesian tensor-on-tensor model with Gaussian process priors for nonlinear, spatially-aware forecasting of Alzheimer's disease progression from MRI data.

Contribution

It develops a flexible, interpretable framework that captures nonlinearity, spatial heterogeneity, and high-dimensional image data, with an efficient MCMC algorithm.

Findings

Outperforms existing methods in simulation studies

Accurately forecasts cortical thickness in ADNI data

Predicts brain aging with biological relevance

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.