Bayesian Semiparametric Orthogonal Tucker Factorized Mixed Models for Multi-dimensional Longitudinal Functional Data

TL;DR

This paper presents a new Bayesian semiparametric model for analyzing complex multidimensional longitudinal functional data, combining tensor decomposition, dimension reduction, and scalable inference to uncover insights in neuroimaging studies.

Contribution

It introduces a novel orthogonal Tucker factorized mixed model with scalable inference and theoretical guarantees, advancing analysis of high-dimensional longitudinal functional data.

Findings

Demonstrates superior performance over existing methods in simulations.

Reveals new neuroimaging insights into Alzheimer's disease progression.

Provides a scalable framework for complex longitudinal data analysis.

Abstract

We introduce a novel longitudinal mixed model for analyzing complex multidimensional functional data, addressing challenges such as high-resolution, structural complexities, and computational demands. Our approach integrates dimension reduction techniques, including basis function representation and Tucker tensor decomposition, to model complex functional (e.g., spatial and temporal) variations, group differences, and individual heterogeneity while drastically reducing model dimensions. The model accommodates multiplicative random effects whose marginalization yields a novel Tucker-decomposed covariance-tensor framework. To ensure scalability, we employ semi-orthogonal mode matrices implemented via a novel graph-Laplacian-based smoothness prior with low-rank approximation, leading to an efficient posterior sampling method. A cumulative shrinkage strategy promotes sparsity and enables semiautomated rank selection. We establish theoretical guarantees for posterior convergence and demonstrate the method's effectiveness through simulations, showing significant improvements over existing techniques. Applying the method to Alzheimer's Disease Neuroimaging Initiative (ADNI) neuroimaging data reveals novel insights into local brain changes associated with disease progression, highlighting the method's practical utility for studying cognitive decline and neurodegenerative conditions.