A Generalized Adaptive Joint Learning Framework for High-Dimensional Time-Varying Models

TL;DR

This paper introduces a hierarchical regularization framework called Adaptive Joint Learning (AJL) for high-dimensional, time-varying models, effectively capturing structural shifts and selecting relevant predictors in complex biomedical and econometric data.

Contribution

It proposes a two-stage screening and refinement procedure with theoretical guarantees for high-dimensional time-varying models, including changepoint detection and predictor selection.

Findings

The method achieves sure screening consistency.

It attains the oracle property in high-dimensional settings.

Validated through simulations and real data analysis.

Abstract

In modern biomedical and econometric studies, longitudinal processes are often characterized by complex time-varying associations and abrupt regime shifts that are shared across correlated outcomes. Standard functional data analysis (FDA) methods, which prioritize smoothness, often fail to capture these dynamic structural features, particularly in high-dimensional settings. This article introduces Adaptive Joint Learning (AJL), a hierarchical regularization framework designed to integrate functional variable selection with structural changepoint detection in multivariate time-varying coefficient models. Unlike standard simultaneous estimation approaches, we propose a theoretically grounded two-stage screening-and-refinement procedure. This framework first synergizes adaptive group-wise penalization with sure screening principles to robustly identify active predictors, followed by a refined fused regularization step that effectively borrows strength across multiple outcomes to detect local regime shifts. We provide a rigorous theoretical analysis of the estimator in the ultra-high-dimensional regime (p >> n). Crucially, we establish the sure screening consistency of the first stage, which serves as the foundation for proving that the refined estimator achieves the oracle property-performing as well as if the true active set and changepoint locations were known a priori. A key theoretical contribution is the explicit handling of approximation bias via undersmoothing conditions to ensure valid asymptotic inference. The proposed method is validated through comprehensive simulations and an application to Sleep-EDF data, revealing novel dynamic patterns in physiological states.