Aumann-SHAP: The Geometry of Counterfactual Interaction Explanations in Machine Learning

arXiv:2603.14014v2 Announce Type: replace Abstract: We introduce Aumann-SHAP, an interaction-aware framework that decomposes counterfactual transitions by restricting the model to a local hypercube connecting baseline and counterfactual features. Each hypercube is discretized into a grid to construct an induced micro-player cooperative game in which elementary grid-step moves become players. Shapley and LES values on this TU-micro-game yield geometry-aware within-pot attributions that converge to the diagonal Aumann--Shapley / Integrated Gradients limit under grid refinement, and recover equal-split Shapley as the degenerate $m=1$ special case. An exact grid-state closed form gives polynomial-time computation for fixed interaction order. On a synthetic benchmark with known ground truth, equal-split Shapley carries an irreducible bias while Aumann-SHAP converges to the correct decomposition. On German Credit, interaction geometry changes feature priority rankings in $12.3\%$ of instances. On UCI Heart Disease, equal-split misattributes a cholesterol suppressor as a positive contributor, which is a sign error Aumann-SHAP corrects. On MNIST, game-theoretic attribution reaches target confidence with $3.5\times$ fewer edits than magnitude-based ordering, with micro-game Shapley achieving the best efficiency across all budgets.

Abstract:We introduce Aumann-SHAP, an interaction-aware framework that decomposes counterfactual transitions by restricting the model to a local hypercube connecting baseline and counterfactual features. Each hypercube is discretized into a grid to construct an induced micro-player cooperative game in which elementary grid-step moves become players. Shapley and LES values on this TU-micro-game yield geometry-aware within-pot attributions that converge to the diagonal Aumann--Shapley / Integrated Gradients limit under grid refinement, and recover equal-split Shapley as the degenerate $m=1$ special case. An exact grid-state closed form gives polynomial-time computation for fixed interaction order. On a synthetic benchmark with known ground truth, equal-split Shapley carries an irreducible bias while Aumann-SHAP converges to the correct decomposition. On German Credit, interaction geometry changes feature priority rankings in $12.3\%$ of instances. On UCI Heart Disease, equal-split misattributes a cholesterol suppressor as a positive contributor, which is a sign error Aumann-SHAP corrects. On MNIST, game-theoretic attribution reaches target confidence with $3.5\times$ fewer edits than magnitude-based ordering, with micro-game Shapley achieving the best efficiency across all budgets.

Machine Learning (cs.LG); Computer Science and Game Theory (cs.GT)

arXiv:2603.14014 [cs.LG]

(or arXiv:2603.14014v2 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2603.14014 Focus to learn more arXiv-issued DOI via DataCite

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Aumann-SHAP: The Geometry of Counterfactual Interaction Explanations in Machine Learning

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