Towards the Unification and Robustness of Perturbation and Gradient Based Explanations

TL;DR

This paper unifies gradient-based and perturbation-based explanation methods, showing their convergence and robustness properties, supported by theoretical analysis and extensive empirical validation on synthetic and real datasets.

Contribution

It provides explicit formulas linking SmoothGrad and LIME explanations, proving their convergence and robustness, and offers finite sample complexity bounds for explanation accuracy.

Findings

SmoothGrad and LIME explanations converge in expectation with many samples.

The methods exhibit robustness properties derived from their connection.

Finite sample bounds ensure reliable explanations with limited perturbations.

Abstract

As machine learning black boxes are increasingly being deployed in critical domains such as healthcare and criminal justice, there has been a growing emphasis on developing techniques for explaining these black boxes in a post hoc manner. In this work, we analyze two popular post hoc interpretation techniques: SmoothGrad which is a gradient based method, and a variant of LIME which is a perturbation based method. More specifically, we derive explicit closed form expressions for the explanations output by these two methods and show that they both converge to the same explanation in expectation, i.e., when the number of perturbed samples used by these methods is large. We then leverage this connection to establish other desirable properties, such as robustness, for these techniques. We also derive finite sample complexity bounds for the number of perturbations required for these methods to converge to their expected explanation. Finally, we empirically validate our theory using extensive experimentation on both synthetic and real world datasets.