Explaining the Uncertain: Stochastic Shapley Values for Gaussian Process
  Models
Siu Lun Chau Krikamol Muandet Dino Sejdinovic
We present a novel approach for explaining Gaussian processes (GPs) that can
utilize the full analytical covariance structure present in GPs. Our method is
based on the popular solution concept of Shapley values extended to stochastic
cooperative games, resulting in explanations that are random variables. The GP
explanations generated using our approach satisfy similar favorable axioms to
standard Shapley values and possess a tractable covariance function across
features and data observations. This covariance allows for quantifying
explanation uncertainties and studying the statistical dependencies between
explanations. We further extend our framework to the problem of predictive
explanation, and propose a Shapley prior over the explanation function to
predict Shapley values for new data based on previously computed ones. Our
extensive illustrations demonstrate the effectiveness of the proposed approach.