On Shapley value for measuring importance of dependent inputs

Art Owen 1 Clémentine Prieur 2, 3
3 AIRSEA - Mathematics and computing applied to oceanic and atmospheric flows
Grenoble INP - Institut polytechnique de Grenoble - Grenoble Institute of Technology, UGA - Université Grenoble Alpes, LJK - Laboratoire Jean Kuntzmann, Inria Grenoble - Rhône-Alpes
Abstract : This paper makes the case for using Shapley value to quantify the importance of random input variables to a function. Alternatives based on the ANOVA decomposition can run into conceptual and computational problems when the input variables are dependent. Our main goal here is to show that Shapley value removes the conceptual problems. We do this with some simple examples where Shapley value leads to intuitively reasonable nearly closed form values.
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Art Owen, Clémentine Prieur. On Shapley value for measuring importance of dependent inputs. SIAM/ASA Journal on Uncertainty Quantification, ASA, American Statistical Association, 2017, 51 (1), pp.986-1002. ⟨10.1137/16M1097717⟩. ⟨hal-01379188v3⟩

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