Bayesian Scalar-on-Tensor Quantile Regression for Longitudinal Data on Alzheimer's Disease

2026-03-17

AI Summary

This study addresses key challenges in longitudinal Alzheimer’s disease research—namely, skewed distributions of cognitive scores, high-dimensional neuroimaging data, and dynamically evolving brain–behavior relationships—that are poorly captured by conventional mean regression models. To overcome these limitations, the authors propose the first Bayesian scalar-on-tensor quantile regression framework. This approach preserves voxel-wise spatial structure via low-rank tensor decomposition and jointly models both visit-invariant and visit-specific effects. Efficient feature selection is achieved through multiway shrinkage priors combined with marginal variable selection priors. A tailored MCMC algorithm enables full posterior inference via complete conditional distributions. Simulations demonstrate that the method substantially outperforms existing approaches in parameter estimation, variable selection, and predictive accuracy. Applied to real Alzheimer’s data, it uncovers more nuanced and comprehensive patterns of association between brain regions and cognitive performance.

Technology Category

• Machine Learning: Matrix & Tensor Methods
• Cognitive Modeling & Cognitive Systems: Adaptive Behavior
• Reasoning under Uncertainty: Relational Probabilistic Models

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for heterogeneous, signed, attributed, multi-relational, temporal, higher-order, and annotated Web-related graphs
• User Modeling, Personalization and Recommendation: Studies of user behavior, including longitudinal effects of personalized systems
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

As a general and robust alternative to traditional mean regression models, quantile regression avoids the assumption of normally distributed errors, making it a versatile choice when modeling outcomes such as cognitive scores that typically have skewed distributions. Motivated by an application to Alzheimer's disease data where the aim is to explore how brain-behavior associations change over time, we propose a novel Bayesian tensor quantile regression for high-dimensional longitudinal imaging data. The proposed approach distinguishes between effects that are consistent across visits and patterns unique to each visit, contributing to the overall longitudinal trajectory. A low-rank decomposition is employed on the tensor coefficients which reduces dimensionality and preserves spatial configurations of the imaging voxels. We incorporate multiway shrinkage priors to model the visit-invariant tensor coefficients and variable selection priors on the tensor margins of the visit-specific effects. For posterior inference, we develop a computationally efficient Markov chain Monte Carlo sampling algorithm. Simulation studies reveal significant improvements in parameter estimation, feature selection, and prediction performance when compared with existing approaches. In the analysis of the Alzheimer's disease data, the flexibility of our modeling approach brings new insights as it provides a fuller picture of the relationship between the imaging voxels and the quantile distributions of the cognitive scores.

Problem

• quantile regression
• longitudinal data
• tensor regression
• Alzheimer's disease
• high-dimensional imaging

Innovation

• Bayesian tensor regression
• quantile regression
• longitudinal imaging data
• low-rank decomposition
• multiway shrinkage priors