Adaptive metric kernel regression

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. Finally, we benchmark the method using the DELVE environment.