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Abstract:
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In this paper, we propose a new large-margin classifier under the classification with confidence umbrella. Classification with confidence refers to a group of classifiers which have overlapping regions with specified coverage probabilities for different classes. In particular, our proposed classifier entails two classification boundaries. The regions outside of the two boundaries belong to the two classes respectively with high probability while the region between boundaries is an ambiguity region which could belong to either class. By introducing a new type of functional margin, we obtain a support vector classifier that, with high probability, satisfies simultaneously two properties: (1) the probability of making Type I and Type II error is controlled; (2) it has the smallest ambiguity region among all the classifiers satisfying (1). Theoretical properties of the proposed method are investigated. An efficient algorithm is developed and numerical studies are conducted with both simulated and real data.
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