Robust Adversarial Classification via Abstaining

Abed AlRahman Al Makdah; Vaibhav Katewa; Fabio Pasqualetti

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arXiv · 2104.02334

Robust Adversarial Classification via Abstaining

Abed AlRahman Al Makdah·Vaibhav Katewa·Fabio Pasqualetti

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Abstract

In this work, we consider a binary classification problem and cast it into a binary hypothesis testing framework, where the observations can be perturbed by an adversary. To improve the adversarial robustness of a classifier, we include an abstain option, where the classifier abstains from making a decision when it has low confidence about the prediction. We propose metrics to quantify the nominal performance of a classifier with an abstain option and its robustness against adversarial perturbations. We show that there exist a tradeoff between the two metrics regardless of what method is used to choose the abstain region. Our results imply that the robustness of a classifier with an abstain option can only be improved at the expense of its nominal performance. Further, we provide necessary conditions to design the abstain region for a 1- dimensional binary classification problem. We validate our theoretical results on the MNIST dataset, where we numerically show that the tradeoff between performance and robustness also exist for the general multi-class classification problems.

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BibTeX RIS

Abed AlRahman Al Makdah, Vaibhav Katewa, Fabio Pasqualetti. 2021-04-06. Robust Adversarial Classification via Abstaining. https://arxiv.org/abs/2104.02334

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