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

2025-06-20

AI Summary

Modeling high-dimensional longitudinal functional data—such as multimodal neuroimaging—faces concurrent challenges of high resolution, structural complexity, and computational burden. Method: We propose a Bayesian semiparametric orthogonal Tucker decomposition mixture model. It introduces the first Tucker decomposition framework for covariance tensors; incorporates graph Laplacian smoothing priors to estimate semi-orthogonal mode matrices; and employs cumulative shrinkage priors to enable semi-automatic rank selection while ensuring posterior convergence. Contribution/Results: Simulations demonstrate substantially improved accuracy and stability over state-of-the-art methods. Applied to the ADNI cohort, our model uncovers, for the first time, dynamic spatiotemporal gradients of localized brain atrophy throughout Alzheimer’s disease progression—yielding clinically interpretable insights while scaling efficiently to thousand-subject datasets.

Technology Category

• Machine Learning: Matrix & Tensor Methods
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding
• 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: On-Device user modeling, personalization, and recommendation
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics

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.

Problem

• Modeling complex multidimensional functional data with high resolution
• Reducing computational demands via dimension reduction techniques
• Analyzing brain changes in Alzheimer's Disease progression

Innovation

• Bayesian semiparametric orthogonal Tucker factorization
• Graph-Laplacian-based smoothness prior approximation
• Cumulative shrinkage strategy for sparsity