Title: Adaptive metric kernel regression

Author: Cyril Goutte and Jan Larsen
Department of Mathematical Modeling - Building 321
Technical University of Denmark, DK-2800 Lyngby, Denmark
Phone: +45 4525 3921,3923
Fax: +45 4587 2599
E-mail: cg,jl@imm.dtu.dk


Kernel smoothing is a widely used non-parametric pattern recognition technique. By nature, it suffers from the curse of dimensionality and is usually difficult to apply to high input dimensions. In this contribution, we propose an algorithm that adapts the input metric used in multivariate regression by minimising a cross-validation estimate of the generalisation error. This allows to automatically adjust the importance of different dimensions. The improvement in terms of modelling performance is illustrated on a variable selection task where the adaptive metric kernel clearly outperforms the standard approach.

Preprint, appears in T. Constantinides, S.-Y. Kung, M. Niranjan and E. Wilson (eds), Neural Networks for Signal Processing VIII -- Proceedings of the 1998 IEEE Workshop (NNSP'98, Cambridge), pp. 184-193.

Download: abstract, Compressed Postscript.