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 regularization framework designed to simultaneously perform functional variable selection and structural changepoint detection in multivariate time-varying coefficient models. We propose a convex optimization procedure that synergizes adaptive group-wise penalization with fused regularization, effectively borrowing strength across multiple outcomes to enhance estimation efficiency. We provide a rigorous theoretical analysis of the estimator in the ultra-high-dimensional regime (p >> n), establishing non-asymptotic error bounds and proving that AJL 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 Primary Biliary Cirrhosis (PBC) data. The analysis uncovers synchronized phase transitions in disease progression and identifies a parsimonious set of time-varying prognostic markers.

翻译：在现代生物医学和计量经济学研究中，纵向过程通常表现出复杂的时变关联性和跨相关结局共享的突发性机制转换。标准的函数型数据分析方法强调平滑性，往往难以捕捉这些动态结构特征，尤其在高维场景下。本文提出了自适应联合学习框架，这是一种正则化方法，旨在多元时变系数模型中同步实现函数型变量选择与结构变点检测。我们设计了一种凸优化程序，将自适应组惩罚与融合正则化有机结合，通过跨多个结局的有效信息共享提升估计效率。我们在超高维情形下对该估计量进行了严格的理论分析，建立了非渐近误差界，并证明AJL具备Oracle性质——其表现与已知真实活跃集和变点位置时同样优异。理论贡献的关键在于通过欠平滑条件显式处理近似偏差，从而保证有效的渐近推断。通过综合模拟实验和对原发性胆汁性胆管炎数据的应用验证了所提方法的有效性。该分析揭示了疾病进展中的同步相变过程，并识别出一组精简的时变预后标志物。