Value-at-risk support vector machine: stability to outliers

A new robust version of Support Vector Machine (SVM) based on value-at-risk (VaR) measure referred to as VaR-SVM is proposed in three closely related formulations, and relationships between those VaRSVM formulations is established. In contrast to classical SVMs (hard-margin SVM, soft-margin SVM, and ν-SVM), VaR-SVM is stable to data outliers. Computational experiments confirm that compared to ν-SVM, VaR-SVM has a superior out-of-sample performance on datasets with outliers.