Some Results in Statistical Learning Theory With Relevance to Nonlinear System Identification

摘要

Statistical Learning Theory comprises a collection of techniques that have been developed in order to theoretically analyse the performance of neural network and other "learning" algorithms. In this paper, a number of recent results in statical learning theory are summarised in the context of nonlinear system identification. A top-down approach to the problem is taken, leading to the statement of a number of characterisation resutls. Specific topics covered include empirical risk minimisation, various types of Glivenko-Cantelli classes, scale-sensitive dimensions, sample complexity and the application to dynamic system identification.