Latent vector autoregressive modeling and feature analysis of high dimensional and noisy data from dynamic systems

In this article, a novel latent vector autoregressive (LaVAR) modeling algorithm with a canonical correlation analysis (CCA) objective is proposed to estimate a fully-interacting reduced-dimensional dynamic model. This algorithm is an advancement of the dynamic inner canonical correlation analysis (DiCCA) algorithm, which builds univariate latent autoregressive models that are noninteracting. The dynamic latent variable scores of the proposed algorithm are guaranteed to be orthogonal with a descending order of predictability, retaining the properties of DiCCA. Further, the LaVAR-CCA algorithm solves multiple latent variables simultaneously with a statistical interpretation of the profile likelihood. The Lorenz oscillator with noisy measurements and an application case study on an industrial dataset are used to illustrate the superiority of the proposed algorithm. The reduced-dimensional latent dynamic model has numerous potential applications for prediction, feature analysis, and diagnosis of systems with rich measurements.