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

A support vector machine (SVM) stable to data outliers is proposed in three closely related formulations, and relationships between those formulations are established. The SVM is based on the value-at-risk (VaR) measure, which discards a specified percentage of data viewed as outliers (extreme samples), and is referred to as -SVM. Computational experiments show that compared to the -SVM, the VaR-SVM has a superior out-of-sample performance on datasets with outliers.