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：移动健康已成为追踪个体健康状况的重要方式，这得益于智能手机和可穿戴设备的普及与强大功能。然而，由于从个体收集的不规则多变量测量数据，移动健康中普遍存在的异构、多分辨率数据处理带来了巨大挑战。本文提出了一种针对不规则多分辨率时间序列数据的个性化动态潜在因子模型，用于对低分辨率时间序列的未采样测量值进行插值。该方法的主要优势在于能够通过将多分辨率数据映射到潜在空间，整合多个不规则时间序列和多个受试者。此外，所提出的个性化动态潜在因子模型能够通过个性化动态潜在因子捕获异构的纵向信息。在理论上，我们给出了所提估计量的积分插值误差界，并利用B样条逼近方法推导了收敛速度。仿真研究和智能手表数据的应用均证明了该方法相较于现有方法的优异性能。