没有调整的量化是否有效？
Does quantification without adjustments work?
摘要：
分类是基于对对象特征的观察来预测对象的类标签的任务。相比之下，量化被定义为确定目标数据集中不同类别标签的普遍性的任务。最简单的量化方法是Classify & Count，其中分类器针对训练集的分类进行优化，并应用于目标数据集以预测类别标签。在二进制量化的情况下，预测的阳性标记的数量然后被用作目标数据集中阳性类别的流行率的估计。由于Classify & Count在量化方面的性能较差，因此其结果通常会进行调整。然而，一些研究人员最近提出，如果Classify & Count是基于专门训练用于量化的分类器，那么它实际上可以在没有调整的情况下工作。我们讨论了这一主张的理论基础，并探讨了其潜力和局限性的数值例子的基础上的副正态模型与等方差。为了确定一个最佳的量词在副正规设置，我们引入了局部贝叶斯最优性的概念。作为旁注，我们给出了Ye等人（2012）的一个定理的完整证明。
英文摘要：
Classification is the task of predicting the class labels of objects based on the observation of their features. In contrast, quantification has been defined as the task of determining the prevalences of the different sorts of class labels in a target dataset. The simplest approach to quantification is Classify & Count where a classifier is optimised for classification on a training set and applied to the target dataset for the prediction of class labels. In the case of binary quantification, the number of predicted positive labels is then used as an estimate of the prevalence of the positive class in the target dataset. Since the performance of Classify & Count for quantification is known to be inferior its results typically are subject to adjustments. However, some researchers recently have suggested that Classify & Count might actually work without adjustments if it is based on a classifer that was specifically trained for quantification. We discuss the theoretical foundation for this claim and explore its potential and limitations with a numerical example based on the binormal model with equal variances. In order to identify an optimal quantifier in the binormal setting, we introduce the concept of local Bayes optimality. As a side remark, we present a complete proof of a theorem by Ye et al. (2012).
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