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The Shapley value is one of the most widely used measures of featureimportance partly as it measures a feature's average effect on a model'sprediction. We introduce joint Shapley values, which directly extend Shapley'saxioms and intuitions: joint Shapley values measure a set of features' averagecontribution to a model's prediction. We prove the uniqueness of joint Shapleyvalues, for any order of explanation. Results for games show that joint Shapleyvalues present different insights from existing interaction indices, whichassess the effect of a feature within a set of features. The joint Shapleyvalues provide intuitive results in ML attribution problems. With binaryfeatures, we present a presence-adjusted global value that is more consistentwith local intuitions than the usual approach.

Joint Shapley values: a measure of joint feature importance