Predictive Linear-Gaussian Models of Stochastic Dynamical Systems

TL;DR

This paper introduces the Predictive Linear-Gaussian (PLG) model, a new observable-based approach for continuous dynamical systems that generalizes Kalman filters with fewer parameters and improved estimation algorithms.

Contribution

The paper develops the PLG model for continuous observations, demonstrating its advantages over traditional models and providing a novel estimation algorithm.

Findings

PLG models generalize Kalman filters with fewer parameters.

The proposed estimation algorithm is consistent and outperforms EM in high dimensions.

Preliminary results show improved accuracy of PLG over EM-based methods.

Abstract

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.