Adversarial Risk via Optimal Transport and Optimal Couplings

被引:14
|
作者
Pydi, Muni Sreenivas [1 ]
Jog, Varun [2 ]
机构
[1] Univ Wisconsin, Dept Elect & Comp Engn, 1415 Johnson Dr, Madison, WI 53706 USA
[2] Univ Cambridge, Dept Pure Math & Math Stat, Cambridge CB3 0WB, England
关键词
Couplings; Standards; Measurement; Kernel; Perturbation methods; Loss measurement; Q measurement; Machine learning; statistical learning; robustness; couplings; information theory; DEEP NEURAL-NETWORKS; ROBUST; ALGORITHMS; GO;
D O I
10.1109/TIT.2021.3100107
中图分类号
TP [自动化技术、计算机技术];
学科分类号
0812 ;
摘要
Modern machine learning algorithms perform poorly on adversarially manipulated data. Adversarial risk quantifies the error of classifiers in adversarial settings; adversarial classifiers minimize adversarial risk. In this paper, we analyze adversarial risk and adversarial classifiers from an optimal transport perspective. We show that the optimal adversarial risk for binary classification with 0-1 loss is determined by an optimal transport cost between the probability distributions of the two classes. We develop optimal transport plans (probabilistic couplings) for univariate distributions such as the normal, the uniform, and the triangular distribution. We also derive optimal adversarial classifiers in these settings. Our analysis leads to algorithm-independent fundamental limits on adversarial risk, which we calculate for several real-world datasets. We extend our results to general loss functions under convexity and smoothness assumptions.
引用
收藏
页码:6031 / 6052
页数:22
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