A class of new Support Vector Regression models

Abstract

We propose a novel convex loss function termed as ‘ϵ-penalty loss function’, to be used in Support Vector Regression (SVR) model. The proposed ϵ-penalty loss function is shown to be optimal for a more general noise distribution. The popular ϵ-insensitive loss function and the Laplace loss function are particular cases of the proposed loss function. Making the use of the proposed loss function, we have proposed two new Support Vector Regression models in this paper. The first model which we have termed with ‘ϵ-Penalty Support Vector Regression’ (ϵ-PSVR) model minimizes the proposed loss function with L2-norm regularization. The second model minimizes the proposed loss function with L1-Norm regularization and has been termed as ‘L1-Norm Penalty Support Vector Regression’ (L1- Norm PSVR) model. The proposed loss function can offer different rates of penalization inside and outside of the ϵ-tube. This strategy enables the proposed SVR models to use the full information of the training set which make them to generalize well. Further, the numerical results obtained from the experiments carried out on various artificial, benchmark datasets and financial time series datasets show that the proposed SVR models own better generalization ability than existing SVR models.