Associating High-Dimensional Longitudinal Datasets through an Efficient Cross-Covariance Decomposition

2026-01-19

AI Summary

Modeling time-varying covariance structures in high-dimensional longitudinal data pairs is challenging due to the high dimensionality and complex dynamic dependencies. To address this, this work proposes a Functional Aggregation Cross-Covariance Decomposition (FACD) framework that adaptively learns temporal structures in a nonparametric manner without pre-specifying the form of time dynamics. By integrating high-dimensional statistical estimation with feature screening, FACD enables efficient association analysis and cross-dataset identification of key variables. The method overcomes limitations of conventional low-dimensional or explicitly parameterized approaches, demonstrating superior performance over existing methods in simulation studies. It has been successfully applied to a human acute exercise multi-omics study, uncovering time-varying cross-omics associations among blood molecular biomarkers.

Technology Category

• Machine Learning: Multi-instance/Multi-view Learning
• Application Domains: Humanities & Computational Social Science
• Data Mining & Knowledge Management: Mining of Spatial, Temporal or Spatio-Temporal Data

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
• Web Mining and Content Analysis: Mining multimedia, multimodal, multilingual, cross-lingual Web data

Abstract

Understanding associations between paired high-dimensional longitudinal datasets is a fundamental yet challenging problem that arises across scientific domains, including longitudinal multi-omic studies. The difficulty stems from the complex, time-varying cross-covariance structure coupled with high dimensionality, which complicates both model formulation and statistical estimation. To address these challenges, we propose a new framework, termed Functional-Aggregated Cross-covariance Decomposition (FACD), tailored for canonical cross-covariance analysis between paired high-dimensional longitudinal datasets through a statistically efficient and theoretically grounded procedure. Unlike existing methods that are often limited to low-dimensional data or rely on explicit parametric modeling of temporal dynamics, FACD adaptively learns temporal structure by aggregating signals across features and naturally accommodates variable selection to identify the most relevant features associated across datasets. We establish statistical guarantees for FACD and demonstrate its advantages over existing approaches through extensive simulation studies. Finally, we apply FACD to a longitudinal multi-omic human study, revealing blood molecules with time-varying associations across omic layers during acute exercise.

Problem

• high-dimensional
• longitudinal data
• cross-covariance
• multi-omic
• time-varying associations

Innovation

• cross-covariance decomposition
• high-dimensional longitudinal data
• adaptive temporal learning
• feature selection
• multi-omic integration