Maximum Mean Discrepancy Test is Aware of Adversarial Attacks

Ruize Gao, Feng Liu, Jingfeng Zhang, Bo Han*, Tongliang Liu, Gang Niu*, Masashi Sugiyama

*Corresponding author for this work

Research output: Chapter in book/report/conference proceedingConference contributionpeer-review

Abstract

The maximum mean discrepancy (MMD) test could in principle detect any distributional discrepancy between two datasets. However, it has been shown that the MMD test is unaware of adversarial attacks–the MMD test failed to detect the discrepancy between natural data and adversarial data. Given this phenomenon, we raise a question: are natural and adversarial data really from different distributions? The answer is affirmative–the previous use of the MMD test on the purpose missed three key factors, and accordingly, we propose three components. Firstly, the Gaussian kernel has limited representation power, and we replace it with an effective deep kernel. Secondly, the test power of the MMD test was neglected, and we maximize it following asymptotic statistics. Finally, adversarial data may be non-independent, and we overcome this issue with the help of wild bootstrap. By taking care of the three factors, we verify that the MMD test is aware of adversarial attacks, which lights up a novel road for adversarial data detection based on two-sample tests.
Original languageEnglish
Title of host publicationProceedings of the 38th International Conference on Machine Learning
PublisherML Research Press
Pages3564-3575
Number of pages12
Publication statusPublished - 18 Jul 2021
Event38th International Conference on Machine Learning, ICML 2021 - Virtual
Duration: 18 Jul 202124 Jul 2021
https://icml.cc/Conferences/2021

Publication series

NameProceedings of Machine Learning Research
Volume139
ISSN (Print)2640-3498

Conference

Conference38th International Conference on Machine Learning, ICML 2021
Period18/07/2124/07/21
Internet address

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