标题： 关于本杰明-霍尔伯格的对抗鲁棒性 显示英文标题

标题： On the Adversarial Robustness of Benjamini Hochberg

摘要： Benjamini-Hochberg（BH）过程广泛用于控制多重检验中的误检率（FDR）。这种控制的应用在药物发现、法医学、异常检测以及特别是机器学习中比比皆是，从非参数离群点检测到分布外检测和一类分类方法均有涉及。考虑到这种控制可能在关键的安全/安全情境中被依赖，我们研究了其对抗鲁棒性。 更具体地说，我们研究了在什么条件下BH表现出对抗鲁棒性，在什么条件下它不表现出对抗鲁棒性，提出了一个简单且易于实现的对抗测试扰动算法类，并进行了计算实验。通过我们的算法，我们证明了存在一些条件，其中只需较少的测试分数扰动（甚至只有一个），就可以显著破坏BH的控制，并提供了关于FDR对抗调整的非渐近保证。我们的技术分析涉及将BH过程重新表述为“球入箱”过程的组合重述，并与广义选票问题建立联系，以促进信息论方法推导非渐近下界。 显示英文摘要

摘要： The Benjamini-Hochberg (BH) procedure is widely used to control the false detection rate (FDR) in multiple testing. Applications of this control abound in drug discovery, forensics, anomaly detection, and, in particular, machine learning, ranging from nonparametric outlier detection to out-of-distribution detection and one-class classification methods. Considering this control could be relied upon in critical safety/security contexts, we investigate its adversarial robustness. More precisely, we study under what conditions BH does and does not exhibit adversarial robustness, we present a class of simple and easily implementable adversarial test-perturbation algorithms, and we perform computational experiments. With our algorithms, we demonstrate that there are conditions under which BH's control can be significantly broken with relatively few (even just one) test score perturbation(s), and provide non-asymptotic guarantees on the expected adversarial-adjustment to FDR. Our technical analysis involves a combinatorial reframing of the BH procedure as a ``balls into bins'' process, and drawing a connection to generalized ballot problems to facilitate an information-theoretic approach for deriving non-asymptotic lower bounds.