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A Kalman filtering algorithm for regularization networks

Regularization networks are nonparametric estimators obtained from the application of Tychonov regularization or Bayes estimation to the hypersurface reconstruction problem. With the usual algorithm, the computation of the weights scales as O(n/sup 3/) where n is the number of data. 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. The procedure applies also to smoothing splines and, in a multidimensional context, to additive regularization networks.