In this paper, we propose a probabilistic reduced-dimensional vector autoregressive (PredVAR) model to extract low-dimensional dynamics from high-dimensional noisy data. The model utilizes an oblique projection to partition the measurement space into a subspace that accommodates the reduced-dimensional dynamics and a complementary static subspace. An optimal oblique decomposition is derived for the best predictability regarding prediction error covariance. Building on this, we develop an iterative PredVAR algorithm using maximum likelihood and the expectation-maximization (EM) framework. This algorithm alternately updates the estimates of the latent dynamics and optimal oblique projection, yielding dynamic latent variables with rank-ordered predictability and an explicit latent VAR model that is consistent with the outer projection model. The superior performance and efficiency of the proposed approach are demonstrated using data sets from a synthesized Lorenz system and an industrial process from Eastman Chemical.

翻译：本文提出一种概率性降维多变量自回归（PredVAR）模型，旨在从高维含噪数据中提取低维动态特性。该模型利用斜投影将测量空间划分为容纳降维动态特性的子空间与互补的静态子空间。我们推导出基于预测误差协方差最优可预测性的最优斜分解方法。在此基础上，结合最大似然估计与期望最大化（EM）框架，开发了迭代式PredVAR算法。该算法交替更新潜变量动态特性与最优斜投影的估计值，生成具有秩序化可预测性的动态潜变量，以及与外部投影模型一致的外显潜变量VAR模型。通过源自合成洛伦兹系统与伊士曼化学工业过程的数据集，验证了所提方法的卓越性能与高效性。