G. De Nicolao and G. Ferrari-Trecate. Regularization networks: Fast weight calculation via Kalman filtering. IEEE Trans. Neural Networks , 12(2):228--235, 2001. Link to IEEE Trans. Neural Networks
Regularization networks are nonparametric estimators obtained fromthe application of Tychonov regularization or Bayes estimation tothe hypersurface reconstruction problem. Their main drawback isthat 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 ofmonodimensional problems, the complexity can be reduced to $O(n)$by a suitable algorithm based on spectral factorization and Kalmanfiltering. Moreover, the procedure applies also to smoothingsplines.