Despite their numerous successes, there are many scenarios where adversarial
risk metrics do not provide an appropriate measure of robustness. For example,
test-time perturbations may occur in a probabilistic manner rather than being
generated by an explicit adversary, while the poor train--test generalization
of adversarial metrics can limit their usage to simple problems. Motivated by
this, we develop a probabilistic robust risk framework, the statistically
robust risk (SRR), which considers pointwise corruption distributions, as
opposed to worst-case adversaries. The SRR provides a distinct and
complementary measure of robust performance, compared to natural and
adversarial risk. We show that the SRR admits estimation and training schemes
which are as simple and efficient as for the natural risk: these simply require
noising the inputs, but with a principled derivation for exactly how and why
this should be done. Furthermore, we demonstrate both theoretically and
experimentally that it can provide superior generalization performance compared
with adversarial risks, enabling application to high-dimensional datasets.

为了解决在某些场景下对抗风险无法提供适当的强健度度量的问题，我们开发了一个概率强健风险框架（SRR），它考虑到逐点损坏分布而不是最坏情况下的对手。我们展示了 SRR 的评估和训练方案与自然风险相当简单且高效，能提供优秀的泛化性能，适用于高维数据集。