B - 439 Support Vector Machine Based on Conditional Value - at - Risk Minimization Akiko

A binary linear classification method, CGS method, was recently proposed by Gotoh and Takeda. The classification model was developed by introducing a risk measure known as the conditional value-at-risk (β-CVaR). CVaR minimization for the margin distribution leads to CGS problem, equivalent to ν-SVC of Schölkopf et al. in the convex case and Extended ν-SVC of Perez-Cruz et al. in the nonconvex case. The objective of this work is to investigate the properties of nonconvex CGS problem, or equivalently, Extended ν-SVC. We adopt a kernel function in the CGS problem by following SVC, and deal with its nonlinear kernel-based variants as β-SVC. We discuss theoretical aspects, mainly generalization performance, of β-SVC. The formula of generalization error includes β-CVaR or a related quantity, and the minimum β-CVaR obtained via β-SVC plays an important role to control generalization error. From a practical point of view, predictions made by β-SVC seem to be fairly reliable and accurate in comparison with those of ν-SVC. Indeed, β-SVC gave better estimations with parameter values β not permissible in ν-SVC, when several publicly available datasets were applied. We also derive a CVaR minimization problem for a regression problem, which is equivalent to ν-SVR of Schölkopf et al.