Sensitivity indices for independent groups of variables

Baptiste Broto (1) , François Bachoc (2) , Marine Depecker (1) , Jean-Marc Martinez (3)

1 LI3A (CEA, LIST) - Intelligence Artificielle et Apprentissage Automatique (CEA, LIST)
2 IMT - Institut de Mathématiques de Toulouse UMR5219
3 DM2S - Département de Modélisation des Systèmes et Structures

In this paper, we study sensitivity indices for independent groups of variables and we look at the particular case of block-additive models. We show in this case that most of the Sobol indices are equal to zero and that Shapley effects can be estimated more efficiently. We then apply this study to Gaussian linear models, and we provide an efficient algorithm to compute the theoretical sensitivity indices. In numerical experiments, we show that this algorithm compares favourably to other existing methods. We also use the theoretical results to improve the estimation of the Shapley effects for general models, when the inputs form independent groups of variables.

Domaines: Probabilités [math.PR]; Statistiques [math.ST]

Baptiste Broto, François Bachoc, Marine Depecker, Jean-Marc Martinez. Sensitivity indices for independent groups of variables. Mathematics and Computers in Simulation, 2019, 163, pp.19-31. ⟨10.1016/j.matcom.2019.02.008⟩. ⟨hal-01680687v3⟩