Soft Margin Support Vector Classification as Buffered Probability Minimization

In this paper, we show that the popular C-SVM, soft-margin support vector classifier is equivalent to minimization of Buffered Probability of Exceedance (bPOE) by introducing a new SVM formulation, called the EC-SVM, which is derived as a bPOE minimization problem. Since it is derived from a simple bPOE minimization problem, the EC-SVM is simple to interpret with a meaningful free parameter, optimal objective value, and probabilistic derivation. We connect the EC-SVM to existing SVM formulations. We first show that the C-SVM, formulated with any regularization norm, produces the same set of solutions as the EC-SVM over the same parameter range. Additionally, we show that the Eν-SVM, formulated with any regularization norm, produces the same set of solutions as the EC-SVM over their entire parameter range. These equivalences, coupled with the interpretability of the EC-SVM, allow us to gain surprising new insights into the C-SVM and fully connect soft margin support