Generalized Hoeffding-Sobol Decomposition for Dependent Variables -Application to Sensitivity Analysis

By Gaelle Chastaing, Fabrice Gamboa, Clémentine Prieur. 2011

181 citations recorded by the source corpus.

In this paper, we consider a regression model built on dependent variables. This regression modelizes an input output relationship. Under boundedness assumptions on the joint distribution function of the input variables, we show that a generalized Hoeffding-Sobol decomposition is available. This leads to new indices measuring the sensitivity of the output with respect to the input variables. We also study and discuss the estimation of these new indices.

Subfields: Computational Mechanics, Statistical and Nonlinear Physics, Statistics and Probability

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Citations in the corpus

Visualizing the effects of predictor variables in black box supervised learning models (2016, background): “Follow-up work in Li and Rabitz (2012), Chastaing et al. (2012) and Rahman (2014) improved the solution techniques, sometimes restricting the component ANOVA functions to be expansions in basis functions such as polynomials and splines, but these are more restrictive (perhaps negating the benefits…”
The Future of Sensitivity Analysis: An essential discipline for systems modeling and policy support (2020, unknown): “Recently, several methods have been developed to account for such properties, including extensions of the Hoeffding--Sobol ’ decomposition (Chastaing et al., 2012), regression-based methods (Xu and Gertner, 2008), copula-based methods (Kucherenko, 2012; Do and Razavi, 2020; Sheikholeslami et al.,…”
A Generalized ANOVA Dimensional Decomposition for Dependent Probability Measures (2014, unknown): “[12], and Chastaing et al [3], are available for models with dependent or correlated input.”
Please Stop Permuting Features: An Explanation and Alternatives (2019, methodology): “Chastaing et al. (2012) modified the estimation technique to include smoothing methods. Similar structures were used in Mentch and Hooker (2017) to test for feature interactions. A key problem for these methods is the need to jointly estimate f1(x1) and the high dimensional f−1(x−1), requiring speci”
A Review on Global Sensitivity Analysis Methods (2014, unknown): “SA for dependent inputs has also been discussed by several authors (Saltelli and Tarantola [77], Jacques et al. [39], Xu and Gertner [93], Da Veiga et al. [17],Gauchi et al. [27], Li et al. [54], Chastaing et al. [14]), but this issue remains misunderstood.”
SHAPLEY EFFECTS FOR SENSITIVITY ANALYSIS WITH CORRELATED INPUTS: COMPARISONS WITH SOBOL' INDICES, NUMERICAL ESTIMATION AND APPLICATIONS (2017, unknown): “Then, in [33], the authors deﬁned a new variable importance measure based on the decomposition of Stone.”
Generalized Sobol sensitivity indices for dependent variables: numerical methods (2013, methodology): “The goal of this paper is to complement the work done in [1] by providing an eﬃcient numerical method for the estimation of the generalized Sobol sensitivity indices.”