Robustness bounds on the successful adversarial examples in probabilistic models: Implications from Gaussian processes
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Abstract (arXiv)
Adversarial example (AE) is an attack method for machine learning, which is crafted by adding imperceptible perturbation to the data inducing misclassification. In the current paper, we investigated the upper bound of the probability of successful AEs based on the Gaussian Process (GP) classification, a probabilistic inference model. We proved a new upper bound of the probability of a successful AE attack that depends on AE's perturbation norm, the kernel function used in GP, and the distance of the closest pair with different labels in the training dataset. Surprisingly, the upper bound is determined regardless of the distribution of the sample dataset. We showed that our theoretical result was confirmed through the experiment using ImageNet. In addition, we showed that changing the parameters of the kernel function induces a change of the upper bound of the probability of successful AEs.
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References · 19
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- 2019Lower Bounds on Adversarial Robustness from Optimal Transportcited by 52
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- 2018The Curse of Concentration in Robust Learning: Evasion and Poisoning Attacks from Concentration of Measurecited by 44
- 2017Analyzing the Robustness of Nearest Neighbors to Adversarial Examplescited by 36
- 2018Robustness Guarantees for Bayesian Inference with Gaussian Processescited by 23
- 2019A Kernelized Manifold Mapping to Diminish the Effect of Adversarial Perturbationscited by 11
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- 2019Adversarial Vulnerability Bounds for Gaussian Process Classificationcited by 5
- 2020Understanding the Intrinsic Robustness of Image Distributions using Conditional Generative Modelscited by 5
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