ASSESSING ROBUSTNESS OF CLASSIFICATION USING ANGULAR BREAKDOWN POINT.
ASSESSING ROBUSTNESS OF CLASSIFICATION USING ANGULAR BREAKDOWN POINT.
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DOI：
10.1214/17-aos1661
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发表时间：
2018-12
影响因子：
4.5
通讯作者：
Liu Y
中科院分区：
文献类型：
--
作者：
Zhao J;Yu G;Liu Y
鲁棒性是许多统计技术的理想特性。作为鲁棒性的一个重要度量，击穿点已被广泛地应用于回归问题和许多其他设置。尽管已有发展，但我们发现标准击穿点准则并不能直接适用于许多分类问题。为了更好地量化不同分类方法的鲁棒性，本文提出了一个新的击穿点准则，即角度击穿点。利用这一新的击穿点准则，我们研究了二值大余量分类技术的鲁棒性，尽管该思想适用于一般的分类方法。考虑了具有线性和核学习的有界和无界损失函数。这些研究对不同分类方法的稳健性提供了有用的见解。数值结果进一步证实了我们的理论发现。
Robustness is a desirable property for many statistical techniques. As an important measure of robustness, breakdown point has been widely used for regression problems and many other settings. Despite the existing development, we observe that the standard breakdown point criterion is not directly applicable for many classification problems. In this paper, we propose a new breakdown point criterion, namely angular breakdown point, to better quantify the robustness of different classification methods. Using this new breakdown point criterion, we study the robustness of binary large margin classification techniques, although the idea is applicable to general classification methods. Both bounded and unbounded loss functions with linear and kernel learning are considered. These studies provide useful insights on the robustness of different classification methods. Numerical results further confirm our theoretical findings.