LS-SVM hyperparameter selection with a nonparametric noise estimator

Abstract

This paper presents a new method for the selection of the two hyperparameters of Least Squares Support Vector Machine (LS-SVM) approximators with Gaussian Kernels. The two hyperparameters are the width σ of the Gaussian kernels and the regularization parameter λ. For different values of σ, a Nonparametric Noise Estimator (NNE) is introduced to estimate the variance of the noise on the outputs. The NNE allows the determination of the best λ for each given σ. A Leave-one-out methodology is then applied to select the best σ. Therefore, this method transforms the double optimization problem into a single optimization one. The method is tested on 2 problems: a toy example and the Pumadyn regression Benchmark. © Springer-Verlag Berlin Heidelberg 2005.