LS-SVM hyperparameter selection with a nonparametric noise estimator
Amaury Lendasse, Yongnan Ji, Nima Reyhani and Michel Verleysen
Artificial Neural Networks: Biological Inspirations – ICANN 2005, 15th International Conference, Warsaw, Poland, September 11-15, 2005, Proceedings, Part II
Lecture Notes in Computer Science
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.