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

TL;DR

This paper introduces FACD, a novel statistical framework for analyzing associations between high-dimensional longitudinal datasets, effectively capturing time-varying cross-covariance structures and identifying relevant features.

Contribution

The paper presents FACD, a new efficient method for high-dimensional longitudinal data analysis that adaptively learns temporal structures and performs feature selection.

Findings

FACD outperforms existing methods in simulations.

Applied to multi-omic data, it identified dynamic associations.

Theoretical guarantees support its statistical validity.

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.