Hoeffding decomposition of functions of random dependent variables

Marouane Il Idrissi, Nicolas Bousquet, Fabrice Gamboa, Bertrand Iooss, Jean-Michel Loubes

Abstract: Highlights•Generalization of FANOVA through direct-sum decomposition of Lebesgue spaces.•Geometric interpretation of non-linear dependencies using Hilbert space theory.•Suitable importance quantification tools when variables are dependent.•Analytical illustrations for Bernoulli and Gaussian variables.