提出更宽松的噪声假设，提升分类模型的理论可靠性。
Beyond Tsybakov: Model Margin Noise and $\mathcal{H}$-Consistency Bounds
- 引入依赖假设与贝叶斯分类器差距的新型噪声条件
- 在弱于Tsybakov条件下仍能获得更强一致性边界
- 适用于常见损失函数，对中等噪声情形有平滑过渡
我们提出一种新的分类低噪声条件——模型边际噪声（MM noise），并在此条件下推导出改进的$ \mathcal{H}$-一致性边界。相较于Tsybakov噪声条件，MM噪声更弱：它由给定假设与贝叶斯分类器之间的差异决定，而非分布固有的最小边际值。因此，即使在Tsybakov不成立时，MM噪声仍可能成立。该假设依赖性使二分类与多分类场景下的$ \mathcal{H}$-一致性边界得到增强。我们的结果在相同有利指数下扩展了Mao、Mohri与Zhong（2025a）的结论，且比Tsybakov条件更弱；在中间噪声水平下可平滑介于线性和平方根之间。我们还为常见代理损失族实例化这些边界，并提供示意表格。
原文摘要 · Abstract (English)
We introduce a new low-noise condition for classification, the Model Margin Noise (MM noise) assumption, and derive enhanced $\mathcal{H}$-consistency bounds under this condition. MM noise is weaker than Tsybakov noise condition: it is implied by Tsybakov noise condition but can hold even when Tsybakov fails, because it depends on the discrepancy between a given hypothesis and the Bayes-classifier rather than on the intrinsic distributional minimal margin (see Figure 1 for an illustration of an explicit example). This hypothesis-dependent assumption yields enhanced $\mathcal{H}$-consistency bounds for both binary and multi-class classification. Our results extend the enhanced $\mathcal{H}$-consistency bounds of Mao, Mohri, and Zhong (2025a) with the same favorable exponents but under a weaker assumption than the Tsybakov noise condition; they interpolate smoothly between linear and square-root regimes for intermediate noise levels. We also instantiate these bounds for common surrogate loss families and provide illustrative tables.
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