Probabilistic Global Robustness Verification of Arbitrary Supervised Machine Learning Models

Many works have been devoted to evaluating the robustness of a classifier in the neighborhood of single points of input data. Recently, in particular, probabilistic settings have been considered, where robustness is defined in terms of random perturbations of input data. In this paper, we consider robustness on the entire input domain as opposed to single points of input. For the first time, we provide formal guarantees on the probability of robustness, given a random input and a random perturbation, based only on sampling or in combination with existing pointwise methods. We prove that the error becomes arbitrarily small for enough input data. This is applicable to any classification or regression model and any random input perturbation. We then illustrate the resulting bounds and compare them against the state of the art for models trained on the MNIST, California Housing, and ImageNet datasets.