Shapley Value Approximation Based on k-Additive Games

TL;DR

This paper introduces SVA$k_{ ext{ADD}}$, a new approximation technique for the Shapley value that leverages $k$-additive surrogate games to improve computational efficiency in fair division and machine learning feature attribution.

Contribution

The paper presents a novel approximation method using $k$-additive surrogate games to efficiently estimate Shapley values for complex fair division problems.

Findings

SVA$k_{ ext{ADD}}$ accurately approximates Shapley values in experiments.

The method outperforms existing approximation techniques in computational efficiency.

Empirical results demonstrate the effectiveness of the $k$-additive approach.

Abstract

The Shapley value is the prevalent solution for fair division problems in which a payout is to be divided among multiple agents. By adopting a game-theoretic view, the idea of fair division and the Shapley value can also be used in machine learning to quantify the individual contribution of features or data points to the performance of a predictive model. Despite its popularity and axiomatic justification, the Shapley value suffers from a computational complexity that scales exponentially with the number of entities involved, and hence requires approximation methods for its reliable estimation. We propose SVA$k_{\text{ADD}}$, a novel approximation method that fits a $k$-additive surrogate game. By taking advantage of $k$-additivity, we are able to elicit the exact Shapley values of the surrogate game and then use these values as estimates for the original fair division problem. The efficacy of our method is evaluated empirically and compared to competing methods.