On Reject and Refine Options in Multicategory Classification
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多类别分类中的拒判与缩小候选类别选项
- 研究问题
- 当多类别分类的误判成本较高时，如何允许模型暂缓决策，或返回一个缩小的候选类别集合，以帮助识别容易出错的观测？
- 方法与思路
- 作者提出基于间隔的多类别分类方法，结合拒判和候选集合选项，并分析维度及类别数量增长时的超额风险收敛。
- 材料陈述的贡献
- 摘要称，方法能够排除不合理类别，并给出快速风险收敛、拒判及候选集合输出比例的有限样本上界，以及模拟和数据比较。
- 阅读关注点
- 应核对损失函数与拒判成本、候选集合的构造规则、低噪声条件，以及理论风险指标和实际分类表现之间的对应关系。
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- 材料为稿件版本未注明的 OpenAlex 索引摘要。具体定理条件、界的常数和数值优势未提供，也不能推断刊本变化。
原文摘要
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 often 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. On the theoretical side, we offer a novel statistical learning theory and show a fast convergence rate of the excess ℓ-risk of our methods with emphasis on diverging dimensionality and number of classes. The results can be further improved under a low noise assumption and be generalized to the excess 0-d-1 risk. Finite-sample upper bounds for the reject and reject/refine rates are also provided. A set of comprehensive simulation and real data studies has shown the usefulness of the new learning tools compared to regular multicategory classifiers. Detailed proofs of theorems and extended numerical results are included in the supplemental materials available online.