We introduce a probabilistic robustness measure for Bayesian Neural Networks (BNNs), defined as the probability that, given a test point, there exists a point within a bounded set such that the BNN prediction differs between the two. Such a measure can be used, for instance, to quantify the probability of the existence of adversarial examples. Building on statistical verification techniques for probabilistic models, we develop a framework that allows us to estimate probabilistic robustness for a BNN with statistical guarantees, i.e., with a priori error and confidence bounds. We provide experimental comparison for several approximate BNN inference techniques on image classification tasks associated to MNIST and a two-class subset of the GTSRB dataset. Our results enable quantification of uncertainty of BNN predictions in adversarial settings.
@article{arxiv.1903.01980,
title = {Statistical Guarantees for the Robustness of Bayesian Neural Networks},
author = {Luca Cardelli and Marta Kwiatkowska and Luca Laurenti and Nicola Paoletti and Andrea Patane and Matthew Wicker},
journal= {arXiv preprint arXiv:1903.01980},
year = {2019}
}