Probabilistic Reduced-Dimensional Vector Autoregressive Modeling for Dynamics Prediction and Reconstruction with Oblique Projections

TL;DR

This paper introduces a probabilistic reduced-dimensional VAR model with oblique projections that effectively extracts dynamic latent variables from high-dimensional data, improving prediction and reconstruction of complex system dynamics.

Contribution

It proposes a novel PredVAR model utilizing oblique projections and an EM-based iterative algorithm for better dynamic variable extraction and noise estimation in high-dimensional data.

Findings

Outperforms alternative methods in nonlinear Lorenz system simulation

Effectively extracts dynamic latent variables with maximized predictability

Provides accurate noise covariance estimation through EM

Abstract

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.