Learning Confidence Sets using Support Vector Machines
This work addresses the need for reliable confidence sets in classification tasks, offering a flexible method for applications requiring uncertainty quantification, though it appears incremental as it builds on existing support vector machine techniques.
The paper tackled the problem of constructing confidence sets for binary classification with specific probability guarantees, proposing a support vector classifier approach that controls non-coverage rates and minimizes ambiguity, with numerical studies demonstrating its effectiveness.
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.