An Odd Estimator for Shapley Values

TL;DR

This paper introduces OddSHAP, a novel estimator for Shapley values that leverages the odd component of set functions, providing a theoretical foundation and achieving state-of-the-art accuracy in approximations.

Contribution

It offers a fundamental theoretical justification for paired sampling and proposes OddSHAP, which isolates the odd component for more accurate Shapley value estimation.

Findings

OddSHAP outperforms existing estimators in accuracy.

Theoretical proof links paired sampling to the odd component filtering.

Benchmark results demonstrate state-of-the-art performance.

Abstract

The Shapley value is a ubiquitous framework for attribution in machine learning, encompassing feature importance, data valuation, and causal inference. However, its exact computation is generally intractable, necessitating efficient approximation methods. While the most effective and popular estimators leverage the paired sampling heuristic to reduce estimation error, the theoretical mechanism driving this improvement has remained opaque. In this work, we provide an elegant and fundamental justification for paired sampling: we prove that the Shapley value depends exclusively on the odd component of the set function, and that paired sampling orthogonalizes the regression objective to filter out the irrelevant even component. Leveraging this insight, we propose OddSHAP, a novel consistent estimator that performs polynomial regression solely on the odd subspace. By utilizing the Fourier basis to isolate this subspace and employing a proxy model to identify high-impact interactions, OddSHAP overcomes the combinatorial explosion of higher-order approximations. Through an extensive benchmark evaluation, we find that OddSHAP achieves state-of-the-art estimation accuracy.