Estimating Shapley Effects in Big-Data Emulation and Regression Settings using Bayesian Additive Regression Trees

Shapley effects are a particularly interpretable approach to assessing how a function depends on its various inputs. The existing literature contains various estimators for this class of sensitivity indices in the context of nonparametric regression where the function is observed with noise, but there does not seem to be an estimator that is computationally tractable for input dimensions in the hundreds scale. This article provides such an estimator that is computationally tractable on this scale. The estimator uses a metamodel-based approach by first fitting a Bayesian Additive Regression Trees model which is then used to compute Shapley-effect estimates. This article also establishes a theoretical guarantee of posterior consistency on a large function class for this Shapley-effect estimator. Finally, this paper explores the performance of these Shapley-effect estimators on four different test functions for various input dimensions, including $p=500$.