Predictive Linear-Gaussian Models of Stochastic Dynamical Systems
  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.
