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.

引入了一种基于概率鲁棒性的贝叶斯神经网络（BNNs）的测量方法，定义为在某个有界集合内是否存在另一个点，使得 BNN 的预测在这两个点之间有差异的概率，并且可以用于量化对抗样本的存在概率。通过基于概率模型的统计验证技术，开发了一个框架，可以估计具有统计保证的 BNN 的概率鲁棒性，并在 MNIST 和 GTSRB 数据集的图像分类任务上提供了实验对比。结果可以在对抗环境中量化 BNN 预测的不确定性。