Axiomatic Explainer Locality With Optimal Transport

Joshua Bone, Aria Masoomi, Jennifer Dy

Keywords: Interpretability, Explainability, Optimal Transport, Wasserstein

Abstract: Explainability methods have been notoriously difficult to evaluate and compare. Because of this, practitioners are often left guessing as to which explainer they should use for their task. Locality is one critical property of explainers which grants insight into the diversity of produced explanations. In this paper, we define a set of axioms which align with natural intuition regarding globalness, the inverse of locality. We then introduce a novel measure of globalness, Wasserstein Globalness, which uses optimal transport to quantify how local or global a given explainer is. Finally, we provide theoretical results describing the sample complexity of Wasserstein Globalness, and experimentally demonstrate how globalness can be used to effectively compare explainers. These results illustrate connections between both explainer fidelity and explainer robustness.

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