%0 Journal Article %1 bhattacharjee2020nonparametric %A Bhattacharjee, Robi %A Chaudhuri, Kamalika %D 2020 %K bayesian generative-models non-parametric readings robustness %T When are Non-Parametric Methods Robust? %U http://arxiv.org/abs/2003.06121 %X A growing body of research has shown that many classifiers are susceptible to adversarial examples -- small strategic modifications to test inputs that lead to misclassification. In this work, we study general non-parametric methods, with a view towards understanding when they are robust to these modifications. We establish general conditions under which non-parametric methods are r-consistent -- in the sense that they converge to optimally robust and accurate classifiers in the large sample limit. Concretely, our results show that when data is well-separated, nearest neighbors and kernel classifiers are r-consistent, while histograms are not. For general data distributions, we prove that preprocessing by Adversarial Pruning (Yang et. al., 2019) -- that makes data well-separated -- followed by nearest neighbors or kernel classifiers also leads to r-consistency.

@article{bhattacharjee2020nonparametric, abstract = {A growing body of research has shown that many classifiers are susceptible to {\em{adversarial examples}} -- small strategic modifications to test inputs that lead to misclassification. In this work, we study general non-parametric methods, with a view towards understanding when they are robust to these modifications. We establish general conditions under which non-parametric methods are r-consistent -- in the sense that they converge to optimally robust and accurate classifiers in the large sample limit. Concretely, our results show that when data is well-separated, nearest neighbors and kernel classifiers are r-consistent, while histograms are not. For general data distributions, we prove that preprocessing by Adversarial Pruning (Yang et. al., 2019) -- that makes data well-separated -- followed by nearest neighbors or kernel classifiers also leads to r-consistency.}, added-at = {2020-07-16T10:44:54.000+0200}, author = {Bhattacharjee, Robi and Chaudhuri, Kamalika}, biburl = {https://www.bibsonomy.org/bibtex/26902d2bcc30ece1c56e0114a05582a8b/kirk86}, description = {[2003.06121] When are Non-Parametric Methods Robust?}, interhash = {0d97e53739604a860f3dae1687621e5f}, intrahash = {6902d2bcc30ece1c56e0114a05582a8b}, keywords = {bayesian generative-models non-parametric readings robustness}, note = {cite arxiv:2003.06121Comment: under review for ICML 2020}, timestamp = {2020-07-16T10:44:54.000+0200}, title = {When are Non-Parametric Methods Robust?}, url = {http://arxiv.org/abs/2003.06121}, year = 2020 }