ShaplEIG: Bayesian Experimental Design for Shapley Value Estimation
2026-06-01 • Machine Learning
Machine Learning
AI summaryⓘ
The authors address a problem with Shapley values, a way to fairly measure contributions, which is usually very slow to calculate exactly. They propose ShaplEIG, a method that uses a smart guessing technique (Gaussian processes) to estimate values and picks which groups to check next based on how much new information they expect to gain. This approach makes the process much faster without losing accuracy by reducing complicated calculations to simpler ones. Their tests show that ShaplEIG works better than other methods when only a small number of evaluations are possible.
Shapley valuesinterpretable machine learningBayesian experimental designGaussian processadaptive samplingvalue functioncoalitionselementary symmetric polynomialssample efficiencyfeature importance
Authors
David Rundel, Fabian Fumagalli, Maximilian Muschalik, Bernd Bischl, Matthias Feurer
Abstract
Shapley values are a principled attribution measure widely used in interpretable machine learning, but their exact computation scales exponentially with the number of players, motivating a wide range of approximation methods based on value function evaluations of sampled coalitions. This raises the question of whether approximation accuracy can be improved by adaptively selecting coalitions for evaluation based on previous evaluations. This is particularly relevant in settings where the value function is costly and the number of evaluations is severely limited, such as retraining-based feature importance, data valuation, and hyperparameter importance. For this purpose, we propose ShaplEIG, a Bayesian experimental design approach that approximates the expensive value function using a Gaussian process surrogate and adaptively selects coalitions based on their expected information gain about the Shapley values. By the linearity of the Shapley values in the value function, we show that the expected information gain is available in closed form. Furthermore, we propose an efficient computation scheme that reduces the complexity from exponential to polynomial in the number of players via elementary symmetric polynomials. In extensive experiments across diverse costly applications, our method consistently improves sample efficiency in the low-budget regime over state-of-the-art baselines.