G. De Nicolao and G. Ferrari-Trecate. A Kalman filtering algorithm for regularization networks. Proc. American Control Conference , pages 2220--2224, 2000. Chicago, Illinois, US, 28-30 June.
Regularization networks are nonparametric estimators obtained from theapplication of Tychonov regularization or Bayes estimation to thehypersurface reconstruction problem. With the usual algorithm, thecomputation of the weights scales as $O(n^3)$ where $n$ is the number ofdata. In this paper we show that for a class of monodimensional problems,the complexity can be reduced to $O(n)$ by a suitable algorithm based onspectral factorization and Kalman filtering. The procedure applies also tosmoothing splines and, in a multidimensional context, to additiveregularization networks.