A Polynomial-Time Axiomatic Alternative to SHAP for Feature Attribution

TL;DR

This paper introduces a new, efficient, and theoretically justified feature attribution method called ESENSC_rev2, which approximates SHAP values with better scalability for high-dimensional data.

Contribution

It proposes a polynomial-time, axiomatic alternative to SHAP, combining closed-form rules to improve scalability while maintaining theoretical soundness.

Findings

ESENSC_rev2 closely approximates exact SHAP values.

The method significantly improves computational efficiency in high-dimensional settings.

Theoretical analysis confirms the unique axiomatic characterization of ESENSC_rev2.

Abstract

In this paper, we provide a theoretically grounded and computationally efficient alternative to SHAP. To this end, we study feature attribution through the lens of cooperative game theory by formulating a class of XAI--TU games. Building on this formulation, we investigate equal-surplus-type and proportional-allocation-type attribution rules and propose a low-cost attribution rule, ESENSC_rev2, constructed by combining two polynomial-time closed-form rules while ensuring the null-player property in the XAI--TU domain. Extensive experiments on tabular prediction tasks demonstrate that ESENSC_rev2 closely approximates exact SHAP while substantially improving scalability as the number of features increases. These empirical results indicate that equal-surplus-type attribution rules can achieve favorable trade-offs between computational cost and approximation accuracy in high-dimensional explainability settings. To provide theoretical foundations for these findings, we establish an axiomatic characterization showing that ESENSC_rev2 is uniquely determined by efficiency, the null-player axiom, a restricted differential marginality principle, an intermediate inessential-game property, and axioms that reduce computational requirements. Our results suggest that axiomatically justified and computationally efficient attribution rules can serve as practical and theoretically principled substitutes for SHAP-based approximations in modern explainability pipelines.