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Maximum Mean Discrepancy Test is Aware of Adversarial Attacks
Ruize Gao · Feng Liu · Jingfeng Zhang · Bo Han · Tongliang Liu · Gang Niu · Masashi Sugiyama

Thu Jul 22 05:20 PM -- 05:25 PM (PDT) @
in Adversarial Learning 3 »

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.

Keywords: Adversarial Examples · Algorithms

Author Information

Ruize Gao (Hong Kong Baptist University)
Feng Liu (University of Technology Sydney)

I am a machine learning researcher with research interests in hypothesis testing and trustworthy machine learning. I am currently an Assistant Professor in Statistics (Data Science) at the School of Mathematics and Statistics, The University of Melbourne, Australia. We are also running the Trustworthy Machine Learning and Reasoning (TMLR) Lab where I am one of co-directors (see this page for details). In addition, I am a Visiting Scientist at RIKEN-AIP, Japan, and a Visting Fellow at DeSI Lab, Australian Artificial Intelligence Institute, University of Technology Sydney. I was the recipient of the Australian Laureate postdoctoral fellowship. I received my Ph.D. degree in computer science at the University of Technology Sydney in 2020, advised by Dist. Prof. Jie Lu and Prof. Guangquan Zhang. I was a research intern at the RIKEN-AIP, working on the robust domain adaptation project with Prof. Masashi Sugiyama, Dr. Gang Niu and Dr. Bo Han. I visited Gatsby Computational Neuroscience Unit at UCL and worked on the hypothesis testing project with Prof. Arthur Gretton, Dr. Danica J. Sutherland and Dr. Wenkai Xu. I have received the Outstanding Paper Award of NeurIPS (2022), the Outstanding Reviewer Award of NeurIPS (2021), the Outstanding Reviewer Award of ICLR (2021), the UTS-FEIT HDR Research Excellence Award (2019). My publications are mainly distributed in high-quality journals or conferences, such as Nature Communications, IEEE-TPAMI, IEEE-TNNLS, IEEE-TFS, NeurIPS, ICML, ICLR, KDD, IJCAI, and AAAI. I have served as a senior program committee (SPC) member for IJCAI, ECAI and program committee (PC) members for NeurIPS, ICML, ICLR, AISTATS, ACML, AAAI and so on. I also serve as reviewers for many academic journals, such as JMLR, IEEE-TPAMI, IEEE-TNNLS, IEEE-TFS and so on.

Jingfeng Zhang (RIKEN)
Bo Han (HKBU / RIKEN)
Tongliang Liu (The University of Sydney)
Gang Niu (RIKEN)
Gang Niu

Gang Niu is currently an indefinite-term senior research scientist at RIKEN Center for Advanced Intelligence Project.

Masashi Sugiyama (RIKEN / The University of Tokyo)

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