Robust ν-support vector machine based on worst-case conditional value-at-risk minimization

Abstract

By minimizing the conditional expectation of random loss in the 1−β worst case, the performance of the ν-support vector machine (SVM) severely depends on its assumption on the underlying distribution. This paper proposes a robust ν-SVM based on worst-case conditional value-at-risk (WCCVaR) minimization, which assumes that the underlying distribution comes from a certain set of potential distributions and minimizes the maximum CVaR associated with these distributions. The problem can be transformed into a quadratic programme and handle nonlinear classification problems. Experiments on six data sets clearly show that the robust approach can achieve superior results than the ν-SVM.

Keywords:

• Kernel methods
• ν-support vector machine
• conditional value-at-risk
• robust programming

AMS Subject Classification :

• 90C15
• 90C20
• 97R40

Acknowledgements

The author thanks the anonymous referees for their valuable comments and suggestions, which improved the technical content and the presentation of this paper. The work was supported by Social Sciences Foundation of Chinese Ministry of Education (10YJC790265), Zhejiang Natural Science Foundation (Y7080205), Zhejiang Province Universities Social Sciences Key Base (Finance) and National Natural Science Foundation of China (71101127).