In many real-world classification problems, the labels of training examples
are randomly corrupted. Most previous theoretical work on classification with
label noise assumes that the two classes are separable, that the label noise is
independent of the true class label, or that the noise proportions for each
class are known. In this work, we give conditions that are necessary and
sufficient for the true class-conditional distributions to be identifiable.
These conditions are weaker than those analyzed previously, and allow for the
classes to be nonseparable and the noise levels to be asymmetric and unknown.
The conditions essentially state that a majority of the observed labels are
correct and that the true class-conditional distributions are "mutually
irreducible," a concept we introduce that limits the similarity of the two
distributions. For any label noise problem, there is a unique pair of true
class-conditional distributions satisfying the proposed conditions, and we
argue that this pair corresponds in a certain sense to maximal denoising of the
observed distributions.
Our results are facilitated by a connection to "mixture proportion
estimation," which is the problem of estimating the maximal proportion of one
distribution that is present in another. We establish a novel rate of
convergence result for mixture proportion estimation, and apply this to obtain
consistency of a discrimination rule based on surrogate loss minimization.
Experimental results on benchmark data and a nuclear particle classification
problem demonstrate the efficacy of our approach.

该研究针对训练样本标签随机出错的分类问题，提出一种新的判别方法：通过对杂质标签的最大去噪实现真实类别条件分布的识别，其基础概念是相互不可约的真实类别条件分布，另外，相关实验表明，该方法在标杆数据和核粒子分类问题上具有有效性。