Shapley Curves: A Smoothing Perspective
This work addresses the problem of improving statistical inference for Shapley values in explainable AI, providing foundational tools for researchers and practitioners, though it is incremental in building on existing smoothing and estimation methods.
The paper tackles the limited statistical understanding of Shapley values as a variable importance measure by introducing population-level Shapley curves to measure true variable importance based on conditional expectation and covariate distribution, deriving minimax convergence rates and asymptotic normality for estimation strategies, and proposing a novel wild bootstrap procedure for finite sample inference, with numerical studies confirming theoretical findings and an empirical application analyzing vehicle price factors.
This paper fills the limited statistical understanding of Shapley values as a variable importance measure from a nonparametric (or smoothing) perspective. We introduce population-level \textit{Shapley curves} to measure the true variable importance, determined by the conditional expectation function and the distribution of covariates. Having defined the estimand, we derive minimax convergence rates and asymptotic normality under general conditions for the two leading estimation strategies. For finite sample inference, we propose a novel version of the wild bootstrap procedure tailored for capturing lower-order terms in the estimation of Shapley curves. Numerical studies confirm our theoretical findings, and an empirical application analyzes the determining factors of vehicle prices.