  Prediction credibility measures, in the form of confidence intervals or
probability distributions, are fundamental in statistics and machine learning
to characterize model robustness, detect out-of-distribution samples
(outliers), and protect against adversarial attacks. To be effective, these
measures should (i) account for the wide variety of models used in practice,
(ii) be computable for trained models or at least avoid modifying established
training procedures, (iii) forgo the use of data, which can expose them to the
same robustness issues and attacks as the underlying model, and (iv) be
followed by theoretical guarantees. These principles underly the framework
developed in this work, which expresses the credibility as a risk-fit
trade-off, i.e., a compromise between how much can fit be improved by
perturbing the model input and the magnitude of this perturbation (risk). Using
a constrained optimization formulation and duality theory, we analyze this
compromise and show that this balance can be determined counterfactually,
without having to test multiple perturbations. This results in an unsupervised,
a posteriori method of assigning prediction credibility for any (possibly
non-convex) differentiable model, from RKHS-based solutions to any architecture
of (feedforward, convolutional, graph) neural network. Its use is illustrated
in data filtering and defense against adversarial attacks.
