Least Ambiguous Set-Valued Classifiers With Bounded Error Levels
提出一种多类集值分类框架，在保证用户定义的覆盖率或置信度（真实标签在输出集中的概率）的同时最小化模糊性（输出集的期望大小），并给出基于现有单标签分类器的估计方法。
In most classification tasks, there are observations that are ambiguous and therefore difficult to correctly label. Set-valued classifiers output sets of plausible labels rather than a single label, thereby giving a more appropriate and informative treatment to the labeling of ambiguous instances. We introduce a framework for multiclass set-valued classification, where the classifiers guarantee user-defined levels of coverage or confidence (the probability that the true label is contained in the set) while minimizing the ambiguity (the expected size of the output). We first derive oracle classifiers assuming the true distribution to be known. We show that the oracle classifiers are obtained from level sets of the functions that define the conditional probability of each class. Then we develop estimators with good asymptotic and finite sample properties. The proposed estimators build on existing single-label classifiers. The optimal classifier can sometimes output the empty set, but we provide two solutions to fix this issue that are suitable for various practical needs. Supplementary materials for this article are available online.