A Study on Bayesian Learning of One-Dimensional Linear Dynamical Systems

Linear dynamical systems are widely used in such fields as system control and time-dependent data analysis. Such a system can be regarded as a statistical parametric model; where the coefficients of the state space equations are unknown and given as parameters. The properties of parameter learning have not yet been established; in spite of a wide range of applications. Therefore, this paper investigates the system from the viewpoint of learning theory. It is revealed that the system has singularities in the parameter space. The generalization error measured by the prediction accuracy for unseen data sequences is reduced, due to the presence of these singularities.