Analyzing the Effects of Classifier Lipschitzness on Explainers

Zulqarnain Khan, Aria Masoomi, Davin Hill, Jennifer Dy

Keywords: Explainers, Explanation, Robustness, Astuteness, Lipschitz, Blackbox, Classifiers

Abstract: Machine learning methods are getting increasingly better at making predictions, but at the same time they are also becoming more complicated and less transparent. As a result, explanation methods are often relied on to provide interpretability to these complicated and often black-box prediction models. As crucial diagnostics tools, it is important that these explainer methods themselves are reliable. In this paper we focus on one particular aspect of reliability, namely that an explainer should give similar explanations for similar data inputs. We formalize this notion by introducing and defining explainer astuteness, analogous to astuteness of classifiers. Our formalism is inspired by the concept of probabilistic Lipschitzness, which captures the probability of local smoothness of a function. For a variety of explainers (e.g., SHAP, RISE, CXPlain, PredDiff), we provide lower bound guarantees on the astuteness of these explainers given the Lipschitzness of the prediction function. These theoretical results imply that locally smooth prediction functions lend themselves to locally robust explanations. We evaluate these results empirically on simulated as well as real datasets.

One-sentence Summary: locally smooth prediction functions lend themselves to locally robust explanations.

Community Implementations: [ 3 code implementations](https://www.catalyzex.com/paper/arxiv:2206.12481/code)