Abstract:
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In many real applications of statistical learning, a decision made from misclassification can be too costly to afford; in this case, a reject option, which defers the decision until further investigation is conducted, is preferred. In recent years, there has been much development for binary classification with a reject option. Yet, little progress has been made for the multicategory case. In this article, we propose margin-based multicategory classification methods with a reject option. In addition, and more importantly, we introduce a new and unique refine option for the multicategory problem, where the class of an observation is predicted to be from a set of class labels, whose cardinality is not necessarily one. The main advantage of both options lies in their capacity of identifying error-prone observations. Moreover, the refine option can provide more constructive information for classification by effectively ruling out implausible classes. Efficient implementations have been developed for the proposed methods. A set of simulation and real data studies has shown the usefulness of the new methods.
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