Predictive Linear-Gaussian Models of Stochastic Dynamical Systems
This work addresses the challenge of continuous observation modeling in dynamical systems for researchers in machine learning and control theory, representing an incremental extension of predictive state representations.
The authors tackled the problem of modeling stochastic dynamical systems with continuous observations by developing Predictive Linear-Gaussian (PLG) models, which subsume Linear Dynamical System models while using fewer parameters and outperforming Expectation Maximization algorithms in preliminary empirical results, especially as model dimension increases.
Models of dynamical systems based on predictive state representations (PSRs) are defined strictly in terms of observable quantities, in contrast with traditional models (such as Hidden Markov Models) that use latent variables or statespace representations. In addition, PSRs have an effectively infinite memory, allowing them to model some systems that finite memory-based models cannot. Thus far, PSR models have primarily been developed for domains with discrete observations. Here, we develop the Predictive Linear-Gaussian (PLG) model, a class of PSR models for domains with continuous observations. We show that PLG models subsume Linear Dynamical System models (also called Kalman filter models or state-space models) while using fewer parameters. We also introduce an algorithm to estimate PLG parameters from data, and contrast it with standard Expectation Maximization (EM) algorithms used to estimate Kalman filter parameters. We show that our algorithm is a consistent estimation procedure and present preliminary empirical results suggesting that our algorithm outperforms EM, particularly as the model dimension increases.