Trust Regions for Explanations via Black-Box Probabilistic Certification

Given the black box nature of machine learning models, a plethora of explainability methods have been developed to decipher the factors behind individual decisions. In this paper, we introduce a novel problem of black box (probabilistic) explanation certification. We ask the question: Given a black box model with only query access, an explanation for an example and a quality metric (viz. fidelity, stability), can we find the largest hypercube (i.e., $\ell_{\infty}$ ball) centered at the example such that when the explanation is applied to all examples within the hypercube, (with high probability) a quality criterion is met (viz. fidelity greater than some value)? Being able to efficiently find such a *trust region* has multiple benefits: i) insight into model behavior in a *region*, with a *guarantee*; ii) ascertained *stability* of the explanation; iii) *explanation reuse*, which can save time, energy and money by not having to find explanations for every example; and iv) a possible *meta-metric* to compare explanation methods. Our contributions include formalizing this problem, proposing solutions, providing theoretical guarantees for these solutions that are computable, and experimentally showing their efficacy on synthetic and real data.