Explaining the Uncertain: Stochastic Shapley Values for Gaussian Process Models

Siu Lun Chau, Krikamol Muandet, Dino Sejdinovic

Keywords: Gaussian Processes, Shapley values, Uncertainty Modelling

TL;DR: A new SHAP algorithm design for GPs that take into account the analytical covariance and result in explanations as Gaussian processes. A Shapley kernel is also proposed for predicting Shapley values of new observations.

Abstract: 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.

Submission Number: 2112