Consistency of plug-in confidence sets for classification in semi-supervised learning

Confident prediction is highly relevant in machine learning; for example, in applications such as medical diagnoses, wrong prediction can be fatal. For classification, there already exist procedures that allow to not classify data when the confidence in their prediction is weak. This approach is known as classification with reject option. In this paper, we provide a new methodology for this approach. Predicting a new feature via a confidence set, we ensure an exact control of the probability of classification. Moreover, we show that this methodology can be implemented easily, in a semi-supervised way, and has attractive theoretical and numerical properties.