CVaR Minimizations in Support Vector Machines

Abstract

This chapter overview the connections between support vector machines (SVM) and conditional value at risk (CVaR) minimization and suggests further interactions beyond their similarity in appearance. It introduces several SVM formulations, whose relation to CVaR minimization. The chapter further discusses robust extensions of the CVaR formulation. It presents the dual problems of the CVaR-minimizing formulations, and shows that two kinds of robust modeling of the CVaR minimization for binary classification are tractable. Dual representations expand the range of algorithms and enrich the theory of SVM. SVMs are one of the most successful supervised learning methods that can be applied to classification or regression. The maximum margin hyperplane of hard-margin SVM classification (SVC) minimizes an upper bound of the generalization error. The support vector regression (SVR) method performs well in regression analysis and is a popular data analysis tool in machine learning and signal processing.