The Shapley value has become a popular method to attribute the prediction of a machine-learning model on an input to its base features. The Shapley value [ 1 ] is known to be the unique method that satisfies certain desirable properties , and this motivates its use. Unfortunately, despite this uniqueness result, there are a multiplicity of Shapley values used in explaining a model's prediction. This is because there are many ways to apply the Shapley value that differ in how they reference the model, the training data, and the explanation context. In this paper, we study an approach that applies the Shapley value to conditional expectations (CES) of sets of features (cf. 2%DIFDELCMD < ]%%% ) that subsumes several prior approaches within a common framework. We provide the first algorithm for the general version of CES. We show that CES can result in counterintuitive attributions in theory and in practice (we study a diabetes prediction task); for instance, CES can assign non-zero attributions to features that are not  referenced by the model. In contrast, we show that an approach called the Baseline Shapley ( BS) does not exhibit counterintuitive attributions; we support this claim with a uniqueness (axiomatic) result. We show that BS is a special case of CES, and CES with an independent feature distribution coincides with a randomized version of BS. Thus, BS fits into the CES framework, but does not suffer from many of CES's deficiencies .
The Shapley value has become a popular method to attribute the prediction of a machine-learning model on an input to its base features. The use of the Shapley value is justified by citing [ 16 ] showing that it is theunique method that satisfies certain good properties (axioms). There are, however, a multiplicity of ways in which the Shapley value is operationalized in the attribution problem. These differ in how they reference the model, the training data, and the explanation context. %DIFDELCMD < ]%%% These give very different results, rendering the uniqueness result meaningless. Furthermore, we find that previously proposed approaches can produce counterintuitive attributions in theory and in practice---for instance, they can assign non-zero attributions to features that are not even referenced by the model. In this paper, we use the axiomatic approach to study the differences between some of the many operationalizations of the Shapley value for attribution, and propose a technique called Baseline Shapley ( BShap) that is backed by a proper uniqueness result. We also contrast BShap with Integrated Gradients, another extension of Shapley value to the continuous setting .
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show that BS is a special case of CES, and CES with an independent feature distribution coincides with a randomized version of BS. Thus, BS fits into the CES framework, but does not suffer from many of CES's deficiencies
also contrast BShap with Integrated Gradients, another extension of Shapley value to the continuous setting