A Generalized Adaptive Joint Learning Framework for High-Dimensional Time-Varying Models
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高维时变模型的广义自适应联合学习框架
- 研究问题
- 高维纵向过程中，多结果共享的时变关联与突发状态变化如何同时识别，而不被侧重平滑的估计方法掩盖？
- 方法与思路
- 作者采用两阶段筛选与精化：先用自适应组惩罚筛选变量，再通过融合正则化汇集多个结果的信息检测变点。
- 材料陈述的贡献
- 摘要称在超高维下建立筛选一致性与精化估计的预言性质，并通过欠平滑处理近似偏差以支持渐近推断。
- 阅读关注点
- 应核对共享变点结构、两阶段惩罚选择、欠平滑条件，以及预言性质对信号强度和变点间距的要求。
- 阅读边界
- 这是 arXiv 预印本，同行评审及期刊接收未经核实；摘要未列出完整理论条件，应用结果也无具体数值。
原文摘要
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.