Predictive Linear-Gaussian Models of Stochastic Dynamical Systems with Vector-Valued Actions and Observations

Predictive state representations use probabilities of future events as the state of a partially observable system, as opposed to most classical models, which use probabilistic statements about latent variables as state. We present a new version of the predictive linear-Gaussian model (PLG), a predictive state representation that models discrete-time dynamical systems with real-vector-valued actions and observations. This extends earlier work on PLGs in which the dynamical systems were limited to scalar observations. We show that the new PLG subsumes linear dynamical systems (LDSs, sometimes called Kalman filter models) of equal dimension. Finally, we introduce an algorithm to estimate PLG parameters from data and show that our algorithm is a consistent estimation procedure.