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Adversarially robust machine learning has re- ceived much recent attention. However, prior attacks and defenses for non-parametric clas- sifiers have been developed in an ad-hoc or classifier-specific basis. In this work, we take a holistic look at adversarial examples for non- parametric classifiers, including nearest neigh- bors, decision trees, and random forests. We provide a general defense method, adversar- ial pruning, that works by preprocessing the dataset to become well-separated. To test our defense, we provide a novel attack that applies to a wide range of non-parametric classifiers. Theoretically, we derive an optimally robust classifier, which is analogous to the Bayes Op- timal. We show that adversarial pruning can be viewed as a finite sample approximation to this optimal classifier. We empirically show that our defense and attack are either better than or competitive with prior work on non- parametric classifiers. Overall, our results pro- vide a strong and broadly-applicable baseline for future work on robust non-parametrics.
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Consistent Non-Parametric Methods for Maximizing Robustness
Learning classifiers that are robust to adversarial examples has received a great deal of recent attention. A major drawback of the standard robust learning framework is there is an artificial robustness radius r that applies to all inputs. This ignores the fact that data may be highly heterogeneous, in which case it is plausible that robustness regions should be larger in some regions of data, and smaller in others. In this paper, we address this limitation by proposing a new limit classifier, called the neighborhood optimal classifier, that extends the Bayes optimal classifier outside its support by using the label of the closest in-support point. We then argue that this classifier maximizes the size of its robustness regions subject to the constraint of having accuracy equal to the Bayes optimal. We then present sufficient conditions under which general non-parametric methods that can be represented as weight functions converge towards this limit, and show that both nearest neighbors and kernel classifiers satisfy them under certain condition
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- Award ID(s):
- 1804829
- PAR ID:
- 10333539
- Date Published:
- Journal Name:
- Advances in neural information processing systems
- ISSN:
- 1049-5258
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Accepted Manuscript1.0
- Conference Paper:
- The DOI is not currently available.
