Learning with an Embedded Reject Option: A Statistical Learning Theory Perspective

The option to reject an example in order to avoid the risk of a costly potential misclassification is well-explored in the pattern recognition literature. In this paper, we look at this issue from the perspective of statistical learning theory. Specifically, we look at ways of modeling the problem of learning with an embedded reject option, in terms of minimizing an appropriately defined risk functional, and discuss the applicability thereof of some fundamental principles of learning, such as minimizing empirical risk and structural risk. Finally, we present some directions for further theoretical work on this problem.