Tight Certificates of Adversarial Robustness for Randomly Smoothed Classifiers
This work provides incremental improvements in theoretical robustness certificates for machine learning models, benefiting researchers and practitioners in adversarial machine learning.
The paper tackles the problem of certifying adversarial robustness for classifiers smoothed with random noise, extending guarantees to broader distribution classes and discrete $\ell_0$ bounded adversaries, and demonstrates empirical results with tightened guarantees under specific classifier assumptions like decision trees.
Strong theoretical guarantees of robustness can be given for ensembles of classifiers generated by input randomization. Specifically, an $\ell_2$ bounded adversary cannot alter the ensemble prediction generated by an additive isotropic Gaussian noise, where the radius for the adversary depends on both the variance of the distribution as well as the ensemble margin at the point of interest. We build on and considerably expand this work across broad classes of distributions. In particular, we offer adversarial robustness guarantees and associated algorithms for the discrete case where the adversary is $\ell_0$ bounded. Moreover, we exemplify how the guarantees can be tightened with specific assumptions about the function class of the classifier such as a decision tree. We empirically illustrate these results with and without functional restrictions across image and molecule datasets.