In this work, we develop a scalable approach for a flexible latent factor model for high-dimensional dynamical systems. Each latent factor process has its own correlation and variance parameters, and the orthogonal factor loading matrix can be either fixed or estimated. We utilize an orthogonal factor loading matrix that avoids computing the inversion of the posterior covariance matrix at each time of the Kalman filter, and derive closed-form expressions in an expectation-maximization algorithm for parameter estimation, which substantially reduces the computational complexity without approximation. Our approach has several applications, including noise filtering for high-dimensional time series, estimating nonseparable covariance structure between different time series, and estimating latent physical processes from real-world measurements. Extensive simulated studies illustrate higher accuracy and scalability of our approach compared to alternatives. Furthermore, by applying our method to geodetic measurements to estimate slow slip events from geodetic data in the Cascadia region, our estimated slip better agrees with independently measured seismic data of tremor events. The substantial acceleration from our method enables the use of massive noisy data for geological hazard quantification and other applications.

翻译：本文针对高维动态系统，提出了一种可扩展的灵活潜在因子模型方法。每个潜在因子过程具有独立的相关系数与方差参数，正交因子载荷矩阵可固定或通过估计确定。我们利用正交因子载荷矩阵避免了卡尔曼滤波中逐时点计算后验协方差矩阵的逆运算，并在期望最大化算法中推导出参数估计的闭式表达式，从而在不引入近似的前提下显著降低计算复杂度。该方法具有多重应用场景，包括高维时间序列的噪声滤波、不同时间序列间不可分离协方差结构的估计，以及从实际测量数据中反演潜在物理过程。大量仿真实验表明，与现有方法相比，本方法具有更高的精度与可扩展性。此外，通过将该方法应用于卡斯卡迪亚地区大地测量数据中慢滑移事件的估计，我们反演的滑移量与独立测量的震颤事件地震数据具有更优的一致性。本方法实现的显著加速效应，使得海量噪声数据可被用于地质灾害量化评估及其他应用领域。