Analyzing Explainer Robustness via Probabilistic Lipschitzness of Prediction Functions

TL;DR

This paper introduces a formal framework linking the robustness of explanation methods to the probabilistic Lipschitzness of prediction functions, providing theoretical guarantees and empirical validation for explanation stability.

Contribution

It formalizes explainer robustness through explainer astuteness and connects it to the predictor's probabilistic Lipschitzness, offering new theoretical bounds and empirical insights.

Findings

Locally smooth prediction functions lead to robust explanations.

Theoretical lower bounds on explainer astuteness based on Lipschitzness.

Empirical validation on simulated and real datasets supports the theory.

Abstract

Machine learning methods have significantly improved in their predictive capabilities, but at the same time they are becoming more complex and less transparent. As a result, explainers are often relied on to provide interpretability to these black-box prediction models. As crucial diagnostics tools, it is important that these explainers themselves are robust. In this paper we focus on one particular aspect of robustness, 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 prediction functions. Our formalism allows us to connect explainer robustness to the predictor's probabilistic Lipschitzness, which captures the probability of local smoothness of a function. We provide lower bound guarantees on the astuteness of a variety of explainers (e.g., SHAP, RISE, CXPlain) 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.