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The Shapley Taylor Interaction Index

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Document pages: 21 pages

Abstract: The attribution problem, that is the problem of attributing a model sprediction to its base features, is well-studied. We extend the notion ofattribution to also apply to feature interactions.The Shapley value is a commonly used method to attribute a model s predictionto its base features. We propose a generalization of the Shapley value calledShapley-Taylor index that attributes the model s prediction to interactions ofsubsets of features up to some size k. The method is analogous to how thetruncated Taylor Series decomposes the function value at a certain point usingits derivatives at a different point. In fact, we show that the Shapley Taylorindex is equal to the Taylor Series of the multilinear extension of theset-theoretic behavior of the model.We axiomatize this method using the standard Shapley axioms -- linearity,dummy, symmetry and efficiency -- and an additional axiom that we call theinteraction distribution axiom. This new axiom explicitly characterizes howinteractions are distributed for a class of functions that model pureinteraction.We contrast the Shapley-Taylor index against the previously proposed ShapleyInteraction index (cf. [9]) from the cooperative game theory literature. Wealso apply the Shapley Taylor index to three models and identify interestingqualitative insights.

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