Kernel methods for regression model based on variable selection

Abstract

The aim of this paper is to get a sufficiently smooth regression function using kernel method based on the concept of variable selection for regression model. It is essential point that the procedure does not contain the concept of the regularisation. The criterion of the variable selection is a simple AIC. On the other hand, Fisher's linear discriminant function (LDF) for two groups is known as the linear regression function which has dichotomous independent variable. Then kernel Fisher's LDF can be also discussed by the use of variable selection. In this paper, we show that the variable selection method for kernel linear models is also useful and simpler method than several regularisation methods.