  Selective classification (or classification with a reject option) pairs a
classifier with a selection function to determine whether or not a prediction
should be accepted. This framework trades off coverage (probability of
accepting a prediction) with predictive performance, typically measured by
distributive loss functions. In many application scenarios, such as credit
scoring, performance is instead measured by ranking metrics, such as the Area
Under the ROC Curve (AUC). We propose a model-agnostic approach to associate a
selection function to a given probabilistic binary classifier. The approach is
specifically targeted at optimizing the AUC. We provide both theoretical
justifications and a novel algorithm, called AUCROSS, to achieve such a goal.
Experiments show that our method succeeds in trading-off coverage for AUC,
improving over existing selective classification methods targeted at optimizing
accuracy.
