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摘要翻译：
ROC曲线和成本曲线是可视化分类器性能的两种常用方法，可以根据操作条件找到合适的阈值，并导出有用的聚合度量，如ROC曲线下的面积(AUC)或最优成本曲线下的面积。在本文中，我们通过在一系列操作条件下使用期望损失，提出了一些新的发现和ROC空间与成本空间之间的联系。特别地，我们表明ROC曲线可以通过一种理解阈值选择的非常自然的方式转移到成本空间，通过选择阈值使正预测的比例等于操作条件（无论是以成本比例还是倾斜的形式）。我们称这些新的曲线为{ROC成本曲线}，我们证明了用这些曲线下的面积来衡量的期望损失与AUC线性相关。这开辟了一系列新的可能性，澄清了成本曲线的概念及其与ROC分析的关系。此外，我们还证明了对于以均匀间隔方式分配分值的分类器，这些曲线等于Brier曲线。因此，这建立了AUC和Brier评分之间的第一个明确联系。
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英文标题：
《Technical Note: Towards ROC Curves in Cost Space》
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作者：
Jos\'e Hern\'andez-Orallo, Peter Flach, C\`esar Ferri
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最新提交年份：
2011
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分类信息：
一级分类：Computer Science 计算机科学
二级分类：Artificial Intelligence 人工智能
分类描述：Covers all areas of AI except Vision, Robotics, Machine Learning, Multiagent Systems, and Computation and Language (Natural Language Processing), which have separate subject areas. In particular, includes Expert Systems, Theorem Proving (although this may overlap with Logic in Computer Science), Knowledge Representation, Planning, and Uncertainty in AI. Roughly includes material in ACM Subject Classes I.2.0, I.2.1, I.2.3, I.2.4, I.2.8, and I.2.11.
涵盖了人工智能的所有领域，除了视觉、机器人、机器学习、多智能体系统以及计算和语言（自然语言处理），这些领域有独立的学科领域。特别地，包括专家系统，定理证明（尽管这可能与计算机科学中的逻辑重叠），知识表示，规划，和人工智能中的不确定性。大致包括ACM学科类I.2.0、I.2.1、I.2.3、I.2.4、I.2.8和I.2.11中的材料。
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英文摘要：
ROC curves and cost curves are two popular ways of visualising classifier performance, finding appropriate thresholds according to the operating condition, and deriving useful aggregated measures such as the area under the ROC curve (AUC) or the area under the optimal cost curve. In this note we present some new findings and connections between ROC space and cost space, by using the expected loss over a range of operating conditions. In particular, we show that ROC curves can be transferred to cost space by means of a very natural way of understanding how thresholds should be chosen, by selecting the threshold such that the proportion of positive predictions equals the operating condition (either in the form of cost proportion or skew). We call these new curves {ROC Cost Curves}, and we demonstrate that the expected loss as measured by the area under these curves is linearly related to AUC. This opens up a series of new possibilities and clarifies the notion of cost curve and its relation to ROC analysis. In addition, we show that for a classifier that assigns the scores in an evenly-spaced way, these curves are equal to the Brier Curves. As a result, this establishes the first clear connection between AUC and the Brier score.
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PDF链接：
https://arxiv.org/pdf/1107.5930
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