Publication details


G. Ferrari-Trecate and R. Rovatti. Consistent Sobolev regression via fuzzy systems with overlapping concepts. Technical Report AUT00-10, Automatic Control Laboratory, ETH Zurich, Switzerland, 2000.


In this paper we propose a new nonparametric regression algorithm based on Fuzzy systemswith overlapping concepts. We analyze its consistency properties, showing that it iscapable 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 inSobolev norms so ensuring uniform convergence also for a certain number of derivatives. Theconnection with Regularization Networks with Tychonov regularization is highlighted.