An Odd Estimator for Shapley Values

Researchers have proposed novel methods for efficient computation of Shapley values in machine learning, addressing the challenge of exact computation being generally intractable.

The Shapley value is a widely used framework for attribution in machine learning, encompassing feature importance, data valuation, and causal inference^[1]. However, its exact computation is generally intractable, necessitating efficient approximation methods. Recent studies have introduced new estimators to improve the computation of Shapley values. OddSHAP, proposed in a paper submitted on January 2, 2026^[1], performs polynomial regression solely on the odd subspace of the set function, overcoming the combinatorial explosion of higher-order approximations. Another method, TN-SHAP-G, submitted on June 1, 2026^[2], exploits structure in graph-structured inputs to compute Shapley values and higher-order interaction indices efficiently. TN-SHAP, presented in a paper revised on May 31, 2026^[3], achieves 25-1000x wall-clock speedups over KernelSHAP-IQ at comparable accuracy, with a computational complexity of O(n*poly(chi) + n^2) time using tensor networks. These advancements provide theoretical guarantees on the approximation error and tractability, enabling deterministic recovery of first- and higher-order Shapley indices without additional model queries or Monte Carlo variance.