G. De Nicolao and G. Ferrari-Trecate. Identification of NARX models using regularization networks: A consistency result. Proc. IEEE World Congr. on Computat. Intelligence , pages 2407--2412, 1998. Anchorage, Alaska, US.
Generalization networks are nonparametric estimators obtained from theapplication of Tychonov regularization or Bayes estimation to thehypersurface reconstruction problem. Under symmetry assumptions they are aparticular type of radial basis function neural networks. In the paper it isshown that such networks guarantee consistent identification of a verygeneral (infinite dimensional) class of NARX models. The proofs are based onthe theory of reproducing kernel Hilbert spaces and the notion of frequencyof time probability, by means of which it is not necessary to assume thatthe input is sampled from a stochastic process.