Learning from data with uncertainty: Robust multiclass kernel-based classifiers and regressors.

Abstract

Motivated by the presence of uncertainty in real data, in this research we investigate a robust optimization approach applied to multiclass support vector machines (SVMs) and support vector regression. Two new kernel based-methods are developed to address data with uncertainty where each data point is inside a sphere of uncertainty. For classification problems, the models are called robust SVM (R-SVM) and robust feasibility approach (R-FA) respectively as extensions of SVM approach. The two models are compared in terms of robustness and generalization error. For comparison purposes, the robust minimax probability machine (MPM) is applied and compared with the above methods. From the empirical results, we conclude that the R-SVM performs better than robust MPM. For regression problems, the models are called robust support vector regression (R-SVR) and robust feasibility approach for regression (R-FAR.). The proposed robust methods can improve the mean square error (MSE) in regression problems.