In this paper, we study a classification problem in which sample labels are randomly corrupted. In this scenario, there is an unobservable sample with noise-free labels. However, before being observed, the true labels are independently flipped with a probability $\rho\in[0,0.5)$, and the random label noise can be class-conditional. Here, we address two fundamental problems raised by this scenario. The first is how to best use the abundant surrogate loss functions designed for the traditional classification problem when there is label noise. We prove that any surrogate loss function can be used for classification with noisy labels by using importance reweighting, with consistency assurance that the label noise does not ultimately hinder the search for the optimal classifier of the noise-free sample. The other is the open problem of how to obtain the noise rate $\rho$. We show that the rate is upper bounded by the conditional probability $P(y|x)$ of the noisy sample. Consequently, the rate can be estimated, because the upper bound can be easily reached in classification problems. Experimental results on synthetic and real datasets confirm the efficiency of our methods.

本文研究了一个分类问题，其中样本标签被随机损坏。我们解决了如何在有标签噪声的情况下最好地利用传统分类问题的丰富代理损失函数，通过重要性重新加权来使用任何代理损失函数进行带有噪声标签的分类，以及如何获得噪声率的问题。

通过重要性加权对带噪声标签的数据进行分类