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We consider objective evaluation measures of saliency explanations forcomplex black-box machine learning models. We propose simple robust variants oftwo notions that have been considered in recent literature: (in)fidelity, andsensitivity. We analyze optimal explanations with respect to both thesemeasures, and while the optimal explanation for sensitivity is a vacuousconstant explanation, the optimal explanation for infidelity is a novelcombination of two popular explanation methods. By varying the perturbationdistribution that defines infidelity, we obtain novel explanations byoptimizing infidelity, which we show to out-perform existing explanations inboth quantitative and qualitative measurements. Another salient question giventhese measures is how to modify any given explanation to have better valueswith respect to these measures. We propose a simple modification based onlowering sensitivity, and moreover show that when done appropriately, we couldsimultaneously improve both sensitivity as well as fidelity.

On the (In)fidelity and Sensitivity for Explanations