Probabilistic Reduced-Dimensional Vector Autoregressive Modeling with Oblique Projections
This work addresses the challenge of modeling high-dimensional time series data for applications like industrial processes, but it appears incremental as it builds on existing VAR and projection methods.
The paper tackles the problem of extracting low-dimensional dynamics from high-dimensional noisy data by proposing a probabilistic reduced-dimensional vector autoregressive (PredVAR) model, which uses an oblique projection to partition the measurement space and an EM-based algorithm for estimation, demonstrating superior performance on synthesized Lorenz system and industrial process data.
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.