G. De Nicolao and G. Ferrari-Trecate. Regularization networks: Fast weight calculation via Kalman filtering. Technical Report AUT00-09, Automatic Control Lab, ETH Zurich, Switzerland, 2000. http://control.ethz.ch/
Regularization networks are nonparametric estimators obtained from the application of Tychonov regularization or Bayes estimation to the hypersurface reconstruction problem. Their main drawback is that the computation of the weights scales as $O(n^3)$ where $n$ is the number of data. 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 on spectral factorization and Kalman filtering. Moreover, the procedure applies also to smoothing splines.