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 study is motivated by inversely estimating slow slip events from geodetic data, such as continuous GPS measurements. Extensive simulated studies illustrate higher accuracy and scalability of our approach compared to alternatives. By applying our method to geodetic measurements 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：本研究提出了一种适用于高维动力系统的可扩展灵活潜因子建模方法。每个潜因子过程具有独立的相关系数与方差参数，正交因子载荷矩阵既可预设亦可估计。通过采用正交因子载荷矩阵，我们避免了卡尔曼滤波过程中每次迭代时后验协方差矩阵的求逆运算，并在期望最大化算法的参数估计中推导出闭式解表达式，从而在无需近似处理的前提下显著降低了计算复杂度。本研究的动机源于从大地测量数据（如连续GPS观测）中反演估算慢滑移事件。大量仿真实验表明，相较于现有方法，本方法具有更高的精度与可扩展性。通过将本方法应用于卡斯卡迪亚地区的大地测量数据，所得滑移估计结果与独立测量的震颤事件地震数据吻合度更佳。本方法带来的显著加速效应使得利用海量噪声数据进行地质灾害量化及其他应用成为可能。