In many applications, the training data, from which one needs to learn a classifier, is corrupted with label noise. Many standard algorithms such as SVM perform poorly in presence of label noise. In this paper we investigate the robustness of risk minimization to label noise. We prove a sufficient condition on a loss function for the risk minimization under that loss to be tolerant to uniform label noise. We show that the $0-1$ loss, sigmoid loss, ramp loss and probit loss satisfy this condition though none of the standard convex loss functions satisfy it. We also prove that, by choosing a sufficiently large value of a parameter in the loss function, the sigmoid loss, ramp loss and probit loss can be made tolerant to non-uniform label noise also if we can assume the classes to be separable under noise-free data distribution. Through extensive empirical studies, we show that risk minimization under the $0-1$ loss, the sigmoid loss and the ramp loss has much better robustness to label noise when compared to the SVM algorithm.

本文研究了在训练数据中存在标签噪声的情况下，风险最小化的鲁棒性。我们探讨了一种损失函数对于噪声的容忍度，并证明了 0-1 损失、Sigmoid 损失、Ramp 损失和 Probit 损失满足该条件，其中选择足够大的参数可以使其对非均匀标签噪声具有容忍度。在大量实证研究中，与 SVM 算法相比，我们证明了使用 0-1 损失、Sigmoid 损失和 Ramp 损失的风险最小化更加鲁棒。

将风险最小化技术应用于标签噪声的容错性