Mobile health has emerged as a major success in tracking individual health status, due to the popularity and power of smartphones and wearable devices. This has also brought great challenges in handling heterogeneous, multi-resolution data which arise ubiquitously in mobile health due to irregular multivariate measurements collected from individuals. In this paper, we propose an individualized dynamic latent factor model for irregular multi-resolution time series data to interpolate unsampled measurements of time series with low resolution. One major advantage of the proposed method is the capability to integrate multiple irregular time series and multiple subjects by mapping the multi-resolution data to the latent space. In addition, the proposed individualized dynamic latent factor model is applicable to capturing heterogeneous longitudinal information through individualized dynamic latent factors. In theory, we provide the integrated interpolation error bound of the proposed estimator and derive the convergence rate with B-spline approximation methods. Both the simulation studies and the application to smartwatch data demonstrate the superior performance of the proposed method compared to existing methods.

翻译：移动健康凭借智能手机和可穿戴设备的普及与强大功能，已成为监测个体健康状况的重要成功范例。然而，由于个体间不规则的多元测量数据采集，移动健康中普遍存在的异质性多分辨率数据带来了巨大挑战。本文针对不规则多分辨率时间序列数据，提出了一种个体化动态潜变量模型，用于对低分辨率时间序列中未采样测量值进行插补。该方法的核心优势在于，通过将多分辨率数据映射至潜空间，能够整合多个不规则时间序列与多受试者信息。此外，所提出的个体化动态潜变量模型通过个体化动态潜因子有效捕捉纵向数据异质性信息。理论上，我们推导了所提估计量的综合插值误差界，并给出了基于B样条逼近方法的收敛速度。模拟研究与智能手表数据应用均表明，相较于现有方法，本方法具有显著优越性。