分析带噪声标签分类的误差界，揭示深度学习模型在噪声下的泛化能力极限。
The Exploration of Error Bounds in Classification with Noisy Labels
- 分解过拟合误差为统计误差与近似误差，构建理论框架。
- 针对依赖数据序列，用独立块构造法控制统计误差上界。
- 在低维流形假设下优化高维输入的近似误差，提升实用性。
大量研究表明，标签噪声会导致模型泛化性能下降，严重影响分类准确率。因此，理解深度神经网络在存在标签噪声时的分类器有效性具有重要实际意义。本文聚焦于深度学习框架中带噪声标签分类问题的过拟合误差界。我们推导了过拟合误差的上界，将其分解为统计误差和近似误差。为处理统计依赖（如混合序列），采用独立块构造法来界定误差，并利用依赖过程的分析技术。对于近似误差，将理论结果推广至向量值情形，输出空间由K维单位向量构成。最后，在低维流形假设下，进一步细化近似误差，以缓解高维输入空间带来的影响。
原文摘要 · Abstract (English)
Numerous studies have shown that label noise can lead to poor generalization performance, negatively affecting classification accuracy. Therefore, understanding the effectiveness of classifiers trained using deep neural networks in the presence of noisy labels is of considerable practical significance. In this paper, we focus on the error bounds of excess risks for classification problems with noisy labels within deep learning frameworks. We derive error bounds for the excess risk, decomposing it into statistical error and approximation error. To handle statistical dependencies (e.g., mixing sequences), we employ an independent block construction to bound the error, leveraging techniques for dependent processes. For the approximation error, we establish these theoretical results to the vector-valued setting, where the output space consists of $K$-dimensional unit vectors. Finally, under the low-dimensional manifold hypothesis, we further refine the approximation error to mitigate the impact of high-dimensional input spaces.
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