Robustness of classifiers to uniform $\ell_p$ and Gaussian noise

Jean-Yves Franceschi, Alhussein Fawzi, Omar Fawzi
Proceedings of the Twenty-First International Conference on Artificial Intelligence and Statistics, PMLR 84:1280-1288, 2018.

Abstract

We study the robustness of classifiers to various kinds of random noise models. In particular, we consider noise drawn uniformly from the $\ell_p$ ball for $p ∈[1, ∞]$ and Gaussian noise with an arbitrary covariance matrix. We characterize this robustness to random noise in terms of the distance to the decision boundary of the classifier. This analysis applies to linear classifiers as well as classifiers with locally approximately flat decision boundaries, a condition which is satisfied by state-of-the-art deep neural networks. The predicted robustness is verified experimentally.

Cite this Paper


BibTeX
@InProceedings{pmlr-v84-franceschi18a, title = {Robustness of classifiers to uniform $\ell_p$ and Gaussian noise}, author = {Jean-Yves Franceschi and Alhussein Fawzi and Omar Fawzi}, booktitle = {Proceedings of the Twenty-First International Conference on Artificial Intelligence and Statistics}, pages = {1280--1288}, year = {2018}, editor = {Amos Storkey and Fernando Perez-Cruz}, volume = {84}, series = {Proceedings of Machine Learning Research}, month = {09--11 Apr}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v84/franceschi18a/franceschi18a.pdf}, url = { http://proceedings.mlr.press/v84/franceschi18a.html }, abstract = {We study the robustness of classifiers to various kinds of random noise models. In particular, we consider noise drawn uniformly from the $\ell_p$ ball for $p ∈[1, ∞]$ and Gaussian noise with an arbitrary covariance matrix. We characterize this robustness to random noise in terms of the distance to the decision boundary of the classifier. This analysis applies to linear classifiers as well as classifiers with locally approximately flat decision boundaries, a condition which is satisfied by state-of-the-art deep neural networks. The predicted robustness is verified experimentally.} }
Endnote
%0 Conference Paper %T Robustness of classifiers to uniform $\ell_p$ and Gaussian noise %A Jean-Yves Franceschi %A Alhussein Fawzi %A Omar Fawzi %B Proceedings of the Twenty-First International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2018 %E Amos Storkey %E Fernando Perez-Cruz %F pmlr-v84-franceschi18a %I PMLR %P 1280--1288 %U http://proceedings.mlr.press/v84/franceschi18a.html %V 84 %X We study the robustness of classifiers to various kinds of random noise models. In particular, we consider noise drawn uniformly from the $\ell_p$ ball for $p ∈[1, ∞]$ and Gaussian noise with an arbitrary covariance matrix. We characterize this robustness to random noise in terms of the distance to the decision boundary of the classifier. This analysis applies to linear classifiers as well as classifiers with locally approximately flat decision boundaries, a condition which is satisfied by state-of-the-art deep neural networks. The predicted robustness is verified experimentally.
APA
Franceschi, J., Fawzi, A. & Fawzi, O.. (2018). Robustness of classifiers to uniform $\ell_p$ and Gaussian noise. Proceedings of the Twenty-First International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 84:1280-1288 Available from http://proceedings.mlr.press/v84/franceschi18a.html .

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