  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.
