Least Ambiguous Set-Valued Classifiers With Bounded Error Levels
Least Ambiguous Set-Valued Classifiers With Bounded Error Levels
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DOI：
10.1080/01621459.2017.1395341
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发表时间：
2019-01-02
影响因子：
3.7
通讯作者：
Wasserman, Larry
中科院分区：
文献类型：
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作者：
Sadinle, Mauricio;Lei, Jing;Wasserman, Larry
在大多数分类任务中，存在模糊的观察结果，因此难以正确标记。集值分类器输出一组合理的标签，而不是一个单一的标签，从而给出了一个更适当的和信息处理的标签模糊的情况。我们引入了一个多类集值分类的框架，其中分类器保证用户定义的覆盖率或置信度（真实标签包含在集合中的概率），同时最大限度地减少模糊性（输出的预期大小）。我们首先推导出假设真实分布已知的Oracle分类器。我们表明，甲骨文分类器是从定义每个类的条件概率的函数的水平集。然后，我们开发具有良好的渐近和有限样本性质的估计。建议的估计建立在现有的单标签分类器。最优分类器有时会输出空集，但我们提供了两种解决方案来解决这个问题，适合各种实际需要。本文的补充材料可在网上查阅。
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.