Variance reduction for estimation of Shapley effects and adaptation to unknown input distribution

TL;DR

This paper introduces new variance-reduced estimators for Shapley effects, applicable when input distributions are known or unknown, along with their asymptotic properties.

Contribution

It proposes novel estimators with lower variance for Shapley effects and extends these estimators to unknown input distributions.

Findings

New estimators with reduced variance for known input distributions

Extension of estimators to unknown input distributions

Asymptotic properties of the proposed estimators

Abstract

The Shapley effects are global sensitivity indices: they quantify the impact of each input variable on the output variable in a model. In this work, we suggest new estimators of these sensitivity indices. When the input distribution is known, we investigate the already existing estimator and suggest a new one with a lower variance. Then, when the distribution of the inputs is unknown, we extend these estimators. Finally, we provide asymptotic properties of the estimators studied in this article.