We propose an empirical measure of the approximate accuracy of feature importance estimates in deep neural networks. Our results across several large-scale image classification datasets show that many popular interpretability methods produce estimates of feature importance that are not better than a random designation of feature importance. Only certain ensemble based approaches-VarGrad and SmoothGrad-Squared-outperform such a random assignment of importance. The manner of ensembling remains critical, we show that some approaches do no better then the underlying method but carry a far higher computational burden.
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