Global Sensitivity Analysis aims at explaining how much each random variable contributes to the variance of the output of a black-box model. The standard approach – namely Sobol indices – computes the contribution of each subset of variables but requires that the variables are independent. The Shapley effect (based on the Shapley value) has been defined for dependent variables, but gives the contribution of each variable individually instead of the contribution of subsets of variables. The aim of this work is to propose a novel approach for dependent variables that defines the level of contribution of each subset of variables so that they sum up to the total variance of the output of the model. We show that we come up with known concepts – namely the Banzhaf values and interaction indices, up to a multiplicative factor.

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Contribution of Subsets of Variables in Global Sensitivity Analysis with Dependent Variables

  • Christophe Labreuche

摘要

Global Sensitivity Analysis aims at explaining how much each random variable contributes to the variance of the output of a black-box model. The standard approach – namely Sobol indices – computes the contribution of each subset of variables but requires that the variables are independent. The Shapley effect (based on the Shapley value) has been defined for dependent variables, but gives the contribution of each variable individually instead of the contribution of subsets of variables. The aim of this work is to propose a novel approach for dependent variables that defines the level of contribution of each subset of variables so that they sum up to the total variance of the output of the model. We show that we come up with known concepts – namely the Banzhaf values and interaction indices, up to a multiplicative factor.