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

Baptiste Broto (1) , François Bachoc (2) , Marine Depecker (1)

1 CEA - Commissariat à l'énergie atomique et aux énergies alternatives
2 IMT - Institut de Mathématiques de Toulouse UMR5219

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.

Mots clés: Global sensitivity analysis; Shapley effects; Nearest Neighbour

Domaines: Statistiques [math.ST]

Baptiste Broto, François Bachoc, Marine Depecker. Variance reduction for estimation of Shapley effects and adaptation to unknown input distribution. 2018. ⟨hal-01962010v1⟩