 We study interactionsamong players in cooperative games. We propose a new interaction index called Shapley-Taylor interaction index . It decomposes the value of the game into terms that model the interactions between subsets of players, analogous to how the Taylor series represents a function in terms of its derivatives of various orders . We axiomatize the method using the standard Shapley axioms--linearity , dummy, symmetry and efficiency--and also an additional axiom that we call the interaction distribution axiom. This new axiom explicitly characterizes how inter-actions are distributed for a class of games called interactiongames . We contrast the Shapley-Taylor interaction index against the previously pro-posed Shapley Interaction index and the Banzhaf interaction index (cf. [ 2 ])  .
The attribution problem, that is the problem of attributing a model's prediction to its base features, is well-studied. We extend the notion of attribution to also apply to feature interactions. The Shapley value is a commonly used method to attribute a model's prediction to its base features. We propose a generalization of the Shapley value called Shapley-Taylor index that attributes the model's prediction to interactions of subsets of features up to some size k. The method is analogous to how the truncated Taylor Series decomposes the function value at a certain point using its derivatives at a different point. In fact, we show that the Shapley Taylor index is equal to the Taylor Series of the multilinear extension of the set-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 the interaction distribution axiom. This new axiom explicitly characterizes how interactions are distributed for a class of functions that model pure interaction . We contrast the Shapley-Taylor index against the previously proposed Shapley Interaction index (cf. [ 9 ]) from the cooperative game theory literature. We also apply the Shapley Taylor index to three models and identify interesting qualitative insights .
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The attribution problem, that is the problem of attributing a model's prediction to its base features, is well-studied. We extend the notion of attribution to also apply to feature interactions. The Shapley value is a commonly used method to attribute a model's prediction to its base features.
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study interactionsamong players in cooperative games. We
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new interaction index
generalization of the Shapley value
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interaction index . It decomposes the value of the game into terms that model the interactions between subsets of players,
index that attributes the model's prediction to interactions of subsets of features up to some size k. The method is
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Taylor series represents a function in terms of its derivatives of various orders
truncated Taylor Series decomposes the function value at a certain point using its derivatives at a different point. In fact, we show that the Shapley Taylor index is equal to the Taylor Series of the multilinear extension of the set-theoretic behavior of the model
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the
this
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axioms--linearity
axioms -- linearity
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efficiency--and also
efficiency -- and
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inter-actions
interactions
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games called interactiongames
functions that model pure interaction
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interaction
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pro-posed
proposed
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and the Banzhaf interaction index
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2
9
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from the cooperative game theory literature. We also apply the Shapley Taylor index to three models and identify interesting qualitative insights