The goal of confidence-set learning in the binary classification setting is to construct two sets, each with a specific probability guarantee to cover a class. An observation outside the overlap of the two sets is deemed to be from one of the two classes, while the overlap is an ambiguity region which could belong to either class. Instead of plug-in approaches, we propose a support vector classifier to construct confidence sets in a flexible manner. Theoretically, we show that the proposed learner can control the non-coverage rates and minimize the ambiguity with high probability. Efficient algorithms are developed and numerical studies illustrate the effectiveness of the proposed method.

Summary The paper proposes an SVM-like classification method for estimating sets containing a pre-specified amount of samples for each class. The overlap of these two sets is a region with ambiguity and should thus be small. The key results are: problem formulation and reformulation using a convex surrogate loss function. Impression The problem formulation is very interesting and the combination of theoretical and experimental results is above standard. In addition, the paper is easy to follow. My main concerns are: - What is the conceptional difference between the proposed approach and classification with reject option as in [2].

The goal of confidence-set learning in the binary classification setting is to construct two sets, each with a specific probability guarantee to cover a class. An observation outside the overlap of the two sets is deemed to be from one of the two classes, while the overlap is an ambiguity region which could belong to either class. Instead of plug-in approaches, we propose a support vector classifier to construct confidence sets in a flexible manner. Theoretically, we show that the proposed learner can control the non-coverage rates and minimize the ambiguity with high probability. Efficient algorithms are developed and numerical studies illustrate the effectiveness of the proposed method.