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：移动健康因智能手机与可穿戴设备的普及与强大功能，已成为追踪个体健康状况的重要成功范例。这也带来了处理异构多分辨率数据的巨大挑战，此类数据在移动健康中普遍存在，源于从个体收集的不规则多变量测量值。本文针对不规则多分辨率时间序列数据，提出一种个体化动态潜因子模型，旨在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空间，整合多个不规则时间序列及多个受试者。此外，所提出的个体化动态潜因子模型适用于通过个体化动态潜因子捕捉异构纵向信息。我们的理论为集成插值误差提供了界，并给出了B样条逼近方法的收敛速率。仿真研究及在智能手表数据中的应用均表明，与现有方法相比，所提方法具有更优越的性能。