In this paper we propose a new nonparametric regression algorithm based on Fuzzy systems with overlapping concepts. We analyze its consistency properties, showing that it is capable to reconstruct an infinite-dimensional class of function when the size of the noisy dataset grows to infinity. Moreover, convergence to the target function is guaranteed in Sobolev norms so ensuring uniform convergence also for a certain number of derivatives. The connection with Regularization Networks, Bayesian estimation and Tychonov regularization is highlighted.

Consistent Sobolev regression via fuzzy systems with overlapping concepts

FERRARI TRECATE, GIANCARLO;
2006-01-01

Abstract

In this paper we propose a new nonparametric regression algorithm based on Fuzzy systems with overlapping concepts. We analyze its consistency properties, showing that it is capable to reconstruct an infinite-dimensional class of function when the size of the noisy dataset grows to infinity. Moreover, convergence to the target function is guaranteed in Sobolev norms so ensuring uniform convergence also for a certain number of derivatives. The connection with Regularization Networks, Bayesian estimation and Tychonov regularization is highlighted.
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11571/136893
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus ND
  • ???jsp.display-item.citation.isi??? ND
social impact