Certified Calibration: Bounding Worst-Case Calibration under Adversarial Attacks

Since neural classifiers are known to be sensitive to adversarial perturbations that alter their accuracy, certification methods have been developed to provide provable guarantees on the insensitivity of their predictions to such perturbations. However, in safety-critical applications, the frequentist interpretation of the confidence of a classifier (also known as model calibration) can be of utmost importance. This property can be measured via the Brier Score or the Expected Calibration Error. We show that attacks can significantly harm calibra- tion, and thus propose certified calibration providing worst-case bounds on calibration under adversarial perturbations. Specifically, we produce analytic bounds for the Brier score and approximate bounds via the solution of a mixed-integer program on the Expected Calibration Error.