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

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

1 LI3A (CEA, LIST) - Intelligence Artificielle et Apprentissage Automatique (CEA, LIST)
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 defined in [E. Song, B. L. Nelson, and J. Staum, SIAM/ASA J. Uncertain. Quantif., 4 (2016), pp. 1060--1083] and suggest a new one with a lower variance. Then, when the distribution of the inputs is unknown, we extend these estimators. We provide asymptotic properties of the estimators studied in this article. We also apply one of these estimators to a real data set.

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. SIAM/ASA Journal on Uncertainty Quantification, 2020, 8, pp.693-716. ⟨10.1137/18M1234631⟩. ⟨hal-01962010v2⟩