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arXiv 2102.09086cs.LG
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鲁棒性最大化的相容非参数方法

Consistent Non-Parametric Methods for Maximizing Robustness

University of California San Diego(加州大学圣地亚哥分校)

Robi Bhattacharjee, Kamalika Chaudhuri

摘要:

学习分类器对对抗性样本的鲁棒性最近受到了极大的关注。标准鲁棒学习框架的主要缺点是存在适用于所有输入的人工鲁棒半径$r$。这忽略了数据可能是高度异构的事实,在这种情况下,鲁棒性区域在某些数据区域中应该更大,而在其他区域中应该更小。在本文中,我们提出了一个新的极限分类器,称为邻域最优分类器,扩展贝叶斯最优分类器的支持外,通过使用标签的最近的支持点,解决了这个限制。然后,我们认为,该分类器的鲁棒性区域的大小最大化的约束具有精度等于贝叶斯最优。然后,我们提出了充分的条件下,一般的非参数方法,可以表示为权重函数收敛到这个极限,并表明,最近的邻居和核分类器满足它们在一定的条件下。

英文摘要:

Learning classifiers that are robust to adversarial examples has received a great deal of recent attention. A major drawback of the standard robust learning framework is there is an artificial robustness radius $r$ that applies to all inputs. This ignores the fact that data may be highly heterogeneous, in which case it is plausible that robustness regions should be larger in some regions of data, and smaller in others. In this paper, we address this limitation by proposing a new limit classifier, called the neighborhood optimal classifier, that extends the Bayes optimal classifier outside its support by using the label of the closest in-support point. We then argue that this classifier maximizes the size of its robustness regions subject to the constraint of having accuracy equal to the Bayes optimal. We then present sufficient conditions under which general non-parametric methods that can be represented as weight functions converge towards this limit, and show that both nearest neighbors and kernel classifiers satisfy them under certain conditions.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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