In this paper, we propose a probabilistic reduced-dimensional vector autoregressive (PredVAR) model with oblique projections. This model partitions the measurement space into a dynamic subspace and a static subspace that do not need to be orthogonal. The partition allows us to apply an oblique projection to extract dynamic latent variables (DLVs) from high-dimensional data with maximized predictability. We develop an alternating iterative PredVAR algorithm that exploits the interaction between updating the latent VAR dynamics and estimating the oblique projection, using expectation maximization (EM) and a statistical constraint. In addition, the noise covariance matrices are estimated as a natural outcome of the EM method. A simulation case study of the nonlinear Lorenz oscillation system illustrates the advantages of the proposed approach over two alternatives.

翻译：本文提出一种基于斜投影的概率性降维向量自回归（PredVAR）模型。该模型将测量空间划分为动态子空间和静态子空间，两者无需满足正交性。这种划分允许应用斜投影从高维数据中提取动态潜变量（DLVs），并实现最大可预测性。我们开发了一种交替迭代的PredVAR算法，通过期望最大化（EM）方法和统计约束，利用潜变量VAR动力学更新与斜投影估计之间的交互作用。此外，噪声协方差矩阵作为EM方法的自然结果被估计得出。在非线性洛伦兹振荡系统的仿真案例研究中，所提方法相较于两种替代方案展示了显著优势。