Monte Carlo Multi-Feature Baseline Shapley (MMBS): An axiomatic attribution method for fine-grained explanations of image classification networks

This paper presents the Multi-Feature Baseline Shapley (MBS) attribution method for explaining the outcome of a neural network for a given input. MBS generalizes the Integrated Gradients (IG) and Baseline Shapley (BShap) methods by introducing a step size parameter. When the step size is set to one, MBS equals BShap, and when it is set to the number of features, MBS equals IG. MBS is an axiomatic method, which means that it was designed to satisfy certain axioms (mathematical properties). These axioms ensure that the attribution maps relate to the neural network in appealing ways, for example, by preserving linearity or symmetry. We prove that MBS satisfies eight axioms that are also satisfied by IG and BShap. To quickly approximate MBS, this paper presents the Monte Carlo Multi-Feature Baseline Shapley (MMBS) method, which is an unbiased estimator of MBS. On image classification tasks, we show that MMBS also approximates a Monte Carlo estimate for BShap while being orders of magnitude faster to compute. Furthermore, we compare MMBS to nine configurations of existing attribution methods on three image classification networks trained on either the Fashion MNIST or ImageNet1k dataset. MMBS has the best area under the deletion curve score on all three networks.