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Machine learning methods have significantly improved in their predictivecapabilities, but at the same time they are becoming more complex and lesstransparent. As a result, explainers are often relied on to provideinterpretability to these black-box prediction models. As crucial diagnosticstools, it is important that these explainers themselves are robust. In thispaper we focus on one particular aspect of robustness, namely that an explainershould give similar explanations for similar data inputs. We formalize thisnotion by introducing and defining explainer astuteness, analogous toastuteness of prediction functions. Our formalism allows us to connectexplainer robustness to the predictor's probabilistic Lipschitzness, whichcaptures the probability of local smoothness of a function. We provide lowerbound guarantees on the astuteness of a variety of explainers (e.g., SHAP,RISE, CXPlain) given the Lipschitzness of the prediction function. Thesetheoretical results imply that locally smooth prediction functions lendthemselves to locally robust explanations. We evaluate these resultsempirically on simulated as well as real datasets.

Analyzing Explainer Robustness via Lipschitzness of Prediction Functions