Joint Shapley values: a measure of joint feature importance

Chris Harris, Richard Pymar, Colin Rowat

Keywords: explainable AI, Shapley value, interaction index, cooperative game theory

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

One-sentence Summary: We present a direct extension of Shapley's value to sets of features, thus extending the Shapley value's intuition: a set of feature's average effect on a model's prediction

Community Implementations: [ 1 code implementation](https://www.catalyzex.com/paper/arxiv:2107.11357/code)