Learning with label dependent label noise has been extensively explored in both theory and practice; however, dealing with instance (i.e., feature) and label dependent label noise continues to be a challenging task. The difficulty arises from the fact that the noise rate varies for each instance, making it challenging to estimate accurately. The question of whether it is possible to learn a reliable model using only noisy samples remains unresolved. We answer this question with a theoretical analysis that provides matching upper and lower bounds. Surprisingly, our results show that, without any additional assumptions, empirical risk minimization achieves the optimal excess risk bound. Specifically, we derive a novel excess risk bound proportional to the noise level, which holds in very general settings, by comparing the empirical risk minimizers obtained from clean samples and noisy samples. Second, we show that the minimax lower bound for the 0-1 loss is a constant proportional to the average noise rate. Our findings suggest that learning solely with noisy samples is impossible without access to clean samples or strong assumptions on the distribution of the data.

本文通过理论分析探讨了在样本噪声存在的情况下，仅使用噪声样本能否学习到可靠模型的问题。作者认为，没有额外假设条件的情况下，经验风险最小化可以达到最优风险上限。此外，文章还讨论了0-1损失的极小极大下限问题，认为纯使用噪声样本无法学习。

基于实例和标签相关的标签噪声的二分类