Comptes Rendus
Probabilités, Statistiques
On the coalitional decomposition of parameters of interest
[Décompositions coalitionnelles de paramètres d’intérêt]
Comptes Rendus. Mathématique, Volume 361 (2023), pp. 1653-1662.

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.

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DOI : 10.5802/crmath.521
Classification : 62J10, 68T37, 06A07

Marouane Il Idrissi 1, 2, 3 ; Nicolas Bousquet 1, 3, 4 ; Fabrice Gamboa 2 ; Bertrand Iooss 1, 3, 2 ; Jean-Michel Loubes 2

1 EDF Lab Chatou, 6 Quai Watier, 78401 Chatou, France
2 Institut de Mathématiques de Toulouse, 31062 Toulouse, France
3 SINCLAIR AI Lab., Saclay, France
4 Sorbonne Université, LPSM, 4 place Jussieu, Paris, France
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits
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     title = {On the coalitional decomposition of parameters of interest},
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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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