Maximum Mean Discrepancy Test is Aware of Adversarial Attacks
Ruize Gao,u00a0Feng Liu,u00a0Jingfeng Zhang,u00a0Bo Han,u00a0Tongliang Liu,u00a0Gang Niu,u00a0Masashi Sugiyama
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 attacksu2013the 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 affirmativeu2013the 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.
