Probabilistic Lipschitzness and the Stable Rank for Comparing Explanation Models
This work addresses the need for robust evaluation metrics in explainable AI, providing theoretical insights and practical heuristics for researchers and practitioners, though it is incremental in building on existing probabilistic Lipschitzness concepts.
The authors tackled the problem of comparing the effectiveness of explainability models for neural networks by proving theoretical lower bounds on the probabilistic Lipschitzness of methods like Integrated Gradients, LIME, and SmoothGrad, and introduced a novel metric, normalized astuteness, to assess robustness.
Explainability models are now prevalent within machine learning to address the black-box nature of neural networks. The question now is which explainability model is most effective. Probabilistic Lipschitzness has demonstrated that the smoothness of a neural network is fundamentally linked to the quality of post hoc explanations. In this work, we prove theoretical lower bounds on the probabilistic Lipschitzness of Integrated Gradients, LIME and SmoothGrad. We propose a novel metric using probabilistic Lipschitzness, normalised astuteness, to compare the robustness of explainability models. Further, we prove a link between the local Lipschitz constant of a neural network and its stable rank. We then demonstrate that the stable rank of a neural network provides a heuristic for the robustness of explainability models.