G. De Nicolao and G. Ferrari-Trecate. Consistent identification of NARX models via regularization networks. IEEE Trans. Autom. Contr. - Special Section on Neural Networks in Control, Identification, and Decision Making , 44(11):2045--2049, 1999. Link to IEEE Trans. AC
Generalization networks are nonparametric estimators obtained from the application ofTychonov 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.