Maximum Mean Discrepancy Test is Aware of Adversarial Attacks

Ruize Gao, Feng Liu, Jingfeng Zhang, Bo Han, Tongliang Liu, Gang Niu, Masashi Sugiyama
Proceedings of the 38th International Conference on Machine Learning, PMLR 139:3564-3575, 2021.

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v139-gao21b, title = {Maximum Mean Discrepancy Test is Aware of Adversarial Attacks}, author = {Gao, Ruize and Liu, Feng and Zhang, Jingfeng and Han, Bo and Liu, Tongliang and Niu, Gang and Sugiyama, Masashi}, booktitle = {Proceedings of the 38th International Conference on Machine Learning}, pages = {3564--3575}, year = {2021}, editor = {Meila, Marina and Zhang, Tong}, volume = {139}, series = {Proceedings of Machine Learning Research}, month = {18--24 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v139/gao21b/gao21b.pdf}, url = {https://proceedings.mlr.press/v139/gao21b.html}, 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.} }
Endnote
%0 Conference Paper %T Maximum Mean Discrepancy Test is Aware of Adversarial Attacks %A Ruize Gao %A Feng Liu %A Jingfeng Zhang %A Bo Han %A Tongliang Liu %A Gang Niu %A Masashi Sugiyama %B Proceedings of the 38th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2021 %E Marina Meila %E Tong Zhang %F pmlr-v139-gao21b %I PMLR %P 3564--3575 %U https://proceedings.mlr.press/v139/gao21b.html %V 139 %X 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.
APA
Gao, R., Liu, F., Zhang, J., Han, B., Liu, T., Niu, G. & Sugiyama, M.. (2021). Maximum Mean Discrepancy Test is Aware of Adversarial Attacks. Proceedings of the 38th International Conference on Machine Learning, in Proceedings of Machine Learning Research 139:3564-3575 Available from https://proceedings.mlr.press/v139/gao21b.html.

Related Material