Robustness of learning algorithms using hinge loss with outlier indicators

We propose a unified formulation of robust learning methods for classification and regression problems. In the learning methods, the hinge loss is used with outlier indicators in order to detect outliers in the observed data. To analyze the robustness property, we evaluate the breakdown point of the learning methods in the situation that the outlier ratio is not necessarily small. Although minimization of the hinge loss with outlier indicators is a non-convex optimization problem, we prove that any local optimal solution of our learning algorithms has the robustness property. The theoretical findings are confirmed in numerical experiments.