System identification: theory for the user
System identification: theory for the user
An Introduction to the Kalman Filter
An Introduction to the Kalman Filter
Predictive state representations: a new theory for modeling dynamical systems
UAI '04 Proceedings of the 20th conference on Uncertainty in artificial intelligence
Learning predictive state representations in dynamical systems without reset
ICML '05 Proceedings of the 22nd international conference on Machine learning
Proceedings of the 6th international joint conference on Autonomous agents and multiagent systems
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We introduce the controlled predictive linear-Gaussian model (cPLG), a model that uses predictive state to model discrete-time dynamical systems with real-valued observations and vector-valued actions. This extends the PLG, an uncontrolled model recently introduced by Rudary et al. (2005). We show that the cPLG subsumes controlled linear dynamical systems (LDS, also called Kalman filter models) of equal dimension, but requires fewer parameters. We also introduce the predictive linear-quadratic Gaussian problem, a cost-minimization problem based on the cPLG that we show is equivalent to linear-quadratic Gaussian problems (LQG, sometimes called LQR). We present an algorithm to estimate cPLG parameters from data, and show that our algorithm is a consistent estimation procedure. Finally, we present empirical results suggesting that our algorithm performs favorably compared to expectation maximization on controlled LDS models.