Mobile health has emerged as a major success for 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. Our theory provides a bound on the integrated interpolation error and the convergence rate for 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性与强大功能，已成为追踪个体健康状态的重要成功范例。然而，由于从个体收集的多变量测量数据存在非规则性，移动健康领域中普遍出现的异构、多分辨率数据带来了重大挑战。本文针对非规则多分辨率时间序列数据，提出一种个体化动态潜在因子模型，用于对低分辨率时间序列中未采样的测量值进行插值。该方法的核心优势在于，通过将多分辨率数据映射至潜在空间，能够整合多个非规则时间序列及多个受试对象。此外，所提出的个体化动态潜在因子模型可通过个体化动态潜在因子捕获异构纵向信息。理论分析给出了综合插值误差的界以及B样条逼近方法的收敛速率。仿真实验与智能手表数据应用均表明，所提方法相较于现有方法具有更优性能。