Statistical learning: regression by support vector machines

Summary form only given. The support vector machine (SVM) represents a universal constructive learning procedure based on the statistical learning theory. SVM can be used for both classification and regression, providing a new form of parametrization of functions. In this survey, attention is paid to the application of SVM to the regression problem. In the first part, an overview is given of the fundamental ideas of SVM approximation, starting from the classification problem. Then, it is shown how SVM can be extended to the case of regression with noisy data. A set of different loss functions and their implications on robustness of the estimation procedure is presented, together with derivation of the corresponding optimization functionals. Then, it is shown how the main idea of SVM can be applied to nonlinear models in high-dimensional spaces. An overview is then given of specific solutions of the support vector system. Experimental results illustrating the main properties of SVM applied to the regression problem are finally presented.