Research Article

Non-parametric regression with wavelet kernels

  1. Alain Rakotomamonjy*,
  2. Xavier Mary,
  3. Stéphane Canu

Article first published online: 23 MAR 2005

DOI: 10.1002/asmb.533

Issue

Applied Stochastic Models in Business and Industry

Applied Stochastic Models in Business and Industry

Special Issue: Statistical Learning

Volume 21, Issue 2, pages 153–163, March/April 2005

Additional Information

How to Cite

Rakotomamonjy, A., Mary, X. and Canu, S. (2005), Non-parametric regression with wavelet kernels. Appl. Stochastic Models Bus. Ind., 21: 153–163. doi: 10.1002/asmb.533

Author Information

  1. P.S.I FRE CNRS 2645, INSA de Rouen, Avenue de l'université, 76801 Saint Etienne du Rouvray, France

*P.S.I FRE CNRS 2645, INSA de Rouen, Avenue de l'université, 76801 Saint Etienne du Rouvray, France

Publication History

  1. Issue published online: 23 MAR 2005
  2. Article first published online: 23 MAR 2005

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Keywords:

  • reproducing kernel;
  • wavelet;
  • regression;
  • regularization networks

Abstract

This paper introduces a method to construct a reproducing wavelet kernel Hilbert spaces for non-parametric regression estimation when the sampling points are not equally spaced. Another objective is to make high-dimensional wavelet estimation problems tractable. It then provides a theoretical foundation to build reproducing kernel from operators and a practical technique to obtain reproducing kernel Hilbert spaces spanned by a set of wavelets. A multiscale approximation technique that aims at taking advantage of the multiresolution structure of wavelets is also described. Examples on toy regression and a real-world problem illustrate the effectiveness of these wavelet kernels. Copyright © 2005 John Wiley & Sons, Ltd.

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