A1834
Title: Efficient Bayesian estimation and inference for Shapley value via experimental design
Authors: Wei Zheng - University of Tennessee (United States) [presenting]
Zheng Zhou - Beijing University of Technology (China)
Robert Mee - University of Tennessee (United States)
Yongdao Zhou - Nankai University (China)
Abstract: The Shapley value fairly allocates cooperative gains among players but requires evaluating all $2^d$ coalitions, computationally infeasible for large $d$, especially when single coalition evaluations are costly (as in AI, data science, and genomics). A Bayesian framework using Gaussian processes is proposed to infer unobserved coalition values, yielding posterior distributions over Shapley values that support both point estimation and uncertainty quantification. The posterior evaluation complexity reduces from exponential to polynomial order, and experimental design is integrated to select coalitions minimizing posterior variance. The method offers three advantages over existing approaches: (i) full statistical inference, (ii) accurate Shapley value estimation using as few as $d^2-d+1$ coalition evaluations, and (iii) robustness across diverse cooperative games. Simulations and case studies confirm superior accuracy and efficiency under comparable evaluation budgets.
