  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 the present paper, we provide new
methodology for this approach. Predicting a new instance via a confidence set,
we ensure an exact control of the probability of classification. Moreover, we
show that this methodology is easily implementable and entails attractive
theoretical and numerical properties.
