[Décompositions coalitionnelles de paramètres d’intérêt]
La compréhension du comportement d’un modèle boîte-noire, dont les entrées distribuées aléatoirement, peut s’appuyer sur la décomposition d’un paramètre d’intérêt (par exemple sa variance) en contributions allouées à chaque coalition d’entrées du modèle (i.e., sous-ensembles des entrées d’un modèle). Dans cet article, sous des hypothèses peu restrictives, nous obtenons des décompositions univoques et interprétables de quantités d’intérêt très générales. Ces résultats nous permettent notamment de retrouver des résultats connus, mais en allégeant leurs hypothèses.
Understanding the behavior of a black-box model with probabilistic inputs can be based on the decomposition of a parameter of interest (e.g., its variance) into contributions attributed to each coalition of inputs (i.e., subsets of inputs). In this paper, we produce conditions for obtaining unambiguous and interpretable decompositions of very general parameters of interest. This allows recovering known decompositions, holding under weaker assumptions than the literature states.
Accepté le :
Publié le :
Marouane Il Idrissi 1, 2, 3 ; Nicolas Bousquet 1, 3, 4 ; Fabrice Gamboa 2 ; Bertrand Iooss 1, 3, 2 ; Jean-Michel Loubes 2
CC-BY 4.0
@article{CRMATH_2023__361_G10_1653_0,
author = {Marouane Il Idrissi and Nicolas Bousquet and Fabrice Gamboa and Bertrand Iooss and Jean-Michel Loubes},
title = {On the coalitional decomposition of parameters of interest},
journal = {Comptes Rendus. Math\'ematique},
pages = {1653--1662},
publisher = {Acad\'emie des sciences, Paris},
volume = {361},
year = {2023},
doi = {10.5802/crmath.521},
language = {en},
}
TY - JOUR AU - Marouane Il Idrissi AU - Nicolas Bousquet AU - Fabrice Gamboa AU - Bertrand Iooss AU - Jean-Michel Loubes TI - On the coalitional decomposition of parameters of interest JO - Comptes Rendus. Mathématique PY - 2023 SP - 1653 EP - 1662 VL - 361 PB - Académie des sciences, Paris DO - 10.5802/crmath.521 LA - en ID - CRMATH_2023__361_G10_1653_0 ER -
%0 Journal Article %A Marouane Il Idrissi %A Nicolas Bousquet %A Fabrice Gamboa %A Bertrand Iooss %A Jean-Michel Loubes %T On the coalitional decomposition of parameters of interest %J Comptes Rendus. Mathématique %D 2023 %P 1653-1662 %V 361 %I Académie des sciences, Paris %R 10.5802/crmath.521 %G en %F CRMATH_2023__361_G10_1653_0
Marouane Il Idrissi; Nicolas Bousquet; Fabrice Gamboa; Bertrand Iooss; Jean-Michel Loubes. On the coalitional decomposition of parameters of interest. Comptes Rendus. Mathématique, Volume 361 (2023), pp. 1653-1662. doi : 10.5802/crmath.521. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.521/
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