Kernel-based Measures of Association Between Inputs and Outputs Using ANOVA

Matieyendou Lamboni ()
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Matieyendou Lamboni: University of Guyane

Sankhya A: The Indian Journal of Statistics, 2024, vol. 86, issue 2, No 6, 790-826

Abstract: Abstract ANOVA decomposition of a function with random input variables provides ANOVA functionals (AFs), which contain information about the contributions of the input variables on the output variable(s). By embedding AFs into an appropriate reproducing kernel Hilbert space regarding their distributions, we propose an efficient statistical test of independence between the input variables and output variable(s). The resulting test statistic leads to new dependence measures of association between inputs and outputs that allow for i) dealing with any distribution of AFs, including the Cauchy distribution, ii) accounting for the necessary or desirable moments of AFs and the interactions among the input variables. In uncertainty quantification for mathematical models, a number of existing measures are special cases of this framework. We then provide unified and general global sensitivity indices and their consistent estimators, including asymptotic distributions. For Gaussian-distributed AFs, we obtain Sobol’ indices and dependent generalized sensitivity indices using quadratic kernels.

Keywords: Dimension reduction; Independence tests; Kernel methods; Reducing uncertainties; Non-independent input variables; Primary 62H20; 49Q12; Secondary 78M05; 65C60 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s13171-024-00354-w

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