  Adversarially robust machine learning has received much recent attention.
However, prior attacks and defenses for non-parametric classifiers 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 neighbors, decision trees, and random forests. We provide a general
defense method, adversarial 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 Optimal. 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 provide a strong and broadly-applicable
baseline for future work on robust non-parametrics. Code available at
https://github.com/yangarbiter/adversarial-nonparametrics/ .
