Robustness of classifiers to uniform $\ell\_p$ and Gaussian noise
This provides a theoretical framework for understanding robustness in machine learning, applicable to linear and deep neural network classifiers, but it is incremental as it builds on existing concepts of decision boundaries.
The paper tackles the problem of characterizing classifier robustness to random noise, specifically uniform ℓ_p and Gaussian noise, by relating it to the distance to the decision boundary, and verifies this experimentally.
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 $p \in [1, \infty]$ 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.