一个明显的paradise：从部分分类样本训练的分类器可能具有比完全分类样本更小的期望错误率
An Apparent Paradox: A Classifier Trained from a Partially Classified Sample May Have Smaller Expected Error Rate Than That If the Sample Were Completely Classified
摘要：
人们越来越关注使用半监督学习来形成分类器。众所周知，在一个未分类的功能与未知的类标签的（费舍尔）信息是少（弱分离类少得多）比已分类的功能，具有已知的类标签。因此，假设未分类特征的标签随机缺失或其缺失标签机制被简单地忽略，则由部分分类的样本形成的分类器的预期错误率大于如果样本被完全分类的情况。我们建议将未分类特征的标签视为缺失数据，并在这些标签不是随机缺失的情况下为其缺失引入一个框架。在文献中的几个部分分类的数据集的检查表明，未分类的功能不是随机发生的，而是倾向于集中在特征空间中的相对高熵的区域。在这里，在两个正常的类与一个共同的协方差阵的情况下，我们考虑的情况下，未分类的功能的标签的缺失可以通过一个逻辑模型，其中一个功能的缺失标签的概率取决于它的熵建模。而矛盾的是，我们表明，这样形成的分类器从部分分类的样本可能有较小的预期错误率，如果样本被完全分类。
英文摘要：
There has been increasing interest in using semi-supervised learning to form a classifier. As is well known, the (Fisher) information in an unclassified feature with unknown class label is less (considerably less for weakly separated classes) than that of a classified feature which has known class label. Hence assuming that the labels of the unclassified features are randomly missing or their missing-label mechanism is simply ignored, the expected error rate of a classifier formed from a partially classified sample is greater than that if the sample were completely classified. We propose to treat the labels of the unclassified features as missing data and to introduce a framework for their missingness in situations where these labels are not randomly missing. An examination of several partially classified data sets in the literature suggests that the unclassified features are not occurring at random but rather tend to be concentrated in regions of relatively high entropy in the feature space. Here in the context of two normal classes with a common covariance matrix we consider the situation where the missingness of the labels of the unclassified features can be modelled by a logistic model in which the probability of a missing label for a feature depends on its entropy. Rather paradoxically, we show that the classifier so formed from the partially classified sample may have smaller expected error rate that that if the sample were completely classified.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
