Explaining the Uncertain: Stochastic Shapley Values for Gaussian Process Models

TL;DR

This paper introduces a stochastic Shapley value method for Gaussian processes that captures explanation uncertainty and dependencies, providing more informative and reliable model explanations.

Contribution

It extends Shapley values to stochastic explanations for GPs, incorporating covariance structures and enabling predictive explanations for new data.

Findings

The method quantifies explanation uncertainty effectively.

It models dependencies between explanations across features.

The approach demonstrates improved interpretability in experiments.

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.