Abstract

Kernel-based regularization methods (KRMs) has opened up a new paradigm for system identification in comparison with classic identification methods. The KRM has two key issues: kernel design and hyperparameter estimation. Kernel design is to parameterize prior knowledge of dynamic systems and hyperparameter estimation is to estimate the hyperparameters in the parameterization by the data. This talk focuses on the asymptotic optimality of the kernel-based regularization methods (KRMs). We will 1) introduce the optimality criteria and the corresponding optimal hyperparameter estimators; 2) present the theoretical advantages over least square estimators; 3) investigate the asymptotic optimality of practical estimators, e.g., empirical Bayes, Stein’s unbiased risk estimator, and cross validation.