Quantification is the task of estimating, given a set \(\sigma \) of unlabelled items and a set of classes \({\mathcal {C}}=\{c_{1}, \ldots , c_{|{\mathcal {C}}|}\}\), the prevalence (or “relative frequency”) in \(\sigma \) of each class \(c_{i}\in {\mathcal {C}}\). While quantification may in principle be solved by classifying each item in \(\sigma \) and counting how many such items have been labelled with \(c_{i}\), it has long been shown that this “classify and count” method yields suboptimal quantification accuracy. As a result, quantification is no longer considered a mere byproduct of classification, and has evolved as a task of its own. While the scientific community has devoted a lot of attention to devising more accurate quantification methods, it has not devoted much to discussing what properties an evaluation measure for quantification (EMQ) should enjoy, and which EMQs should be adopted as a result. This paper lays down a number of interesting properties that an EMQ may or may not enjoy, discusses if (and when) each of these properties is desirable, surveys the EMQs that have been used so far, and discusses whether they enjoy or not the above properties. As a result of this investigation, some of the EMQs that have been used in the literature turn out to be severely unfit, while others emerge as closer to what the quantification community actually needs. However, a significant result is that no existing EMQ satisfies all the properties identified as desirable, thus indicating that more research is needed in order to identify (or synthesize) a truly adequate EMQ.

中文翻译：

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量化评估措施：公理化方法

给定一组未标记项目的\（\ sigma \）和一组类别的\（{\ mathcal {C}} = \ {c_ {1}，\ ldots，c_ {| {\ mathcal {C}} |} \} \），{{mathcal {C}} \）中每个类\（c_ {i} \\的\（\ sigma \）的患病率（或“相对频率” ）。量化原则上可以通过将\（\ sigma \）中的每个项目分类并计算用\（c_ {i} \）标记了多少个此类项目来解决。，早就表明，这种“分类和计数”方法会产生次优的量化精度。结果，量化不再仅仅是分类的副产品，而是作为其自身任务而发展的。尽管科学界投入了大量精力来设计更准确的量化方法，但它并没有花太多时间讨论评估评估方法的量化特性（EMQ）应该享有，因此应采用哪些EMQ。本文列出了EMQ可能享受或可能不享受的一些有趣属性，讨论了每个属性是否（以及何时）是理想的，调查了迄今已使用的EMQ，并讨论了它们是否享受上述乐趣。属性。这项调查的结果是，文献中使用的某些EMQ严重不合适，而另一些EMQ则更加接近量化社区的实际需求。但是，一个重要的结果是，没有现有的EMQ能够满足所有确定为所需的属性，因此表明需要进行更多的研究才能确定（或综合）一个真正合适的EMQ。