Computing Shapley Effects for Sensitivity Analysis

Plischke, Elmar; Rabitti, Giovanni; Borgonovo, Emanuele

doi:10.1137/19m1304738

Cited by 22 publications

(23 citation statements)

References 45 publications

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“…More recently, [13] proposed a subset aggregation procedure which leads to a significant reduction of the variance of Shapley effect estimation. Let us also cite the algorithm proposed in [17] based on the Möbius inverse, which offers a computationally efficient alternative for the estimation of Shapley effects, the simple Monte Carlo sampling-based algorithm proposed in [18] focused on independent inputs but which can be extended with a loss of efficiency to the dependent framework. The main advantage of the subset aggregation procedure introduced in [13] is that it has a version, based on nearest-neighbors, which does not require the ability to sample from the exact conditional distributions of the input parameters.…”

Section: Introductionmentioning

confidence: 99%

Global sensitivity analysis with aggregated Shapley effects, application to avalanche hazard assessment

Heredia

Prieur

Eckert

2022

Reliability Engineering & System Safety

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Section: Introductionmentioning

confidence: 99%

Global sensitivity analysis with aggregated Shapley effects, application to avalanche hazard assessment

Heredia

Prieur

Eckert

2022

Reliability Engineering & System Safety

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“…In the context of game theory, the authors of [8] presented a first algorithm to estimate the Shapley effects which was improved by [48] in sensitivity analysis by reducing the number of calls to the function φ. New approaches [5,38,18] and surrogate-model-based strategies [25,2] were explored to reduce even more the estimation cost of these indices while the articles [4,6] were focused on the estimation of the Shapley effects with independent groups of variable.…”

Section: Shapley Effect Estimation Schemesmentioning

confidence: 99%

Shapley effect estimation in reliability-oriented sensitivity analysis with correlated inputs by importance sampling

Demange-Chryst¹,

Bachoc²,

Mitard³

2022

Preprint

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Reliability-oriented sensitivity analysis aims at combining both reliability and sensitivity analyses by quantifying the influence of each input variable of a numerical model on a quantity of interest related to its failure. In particular, target sensitivity analysis focuses on the occurrence of the failure, and more precisely aims to determine which inputs are more likely to lead to the failure of the system. The Shapley effects are quantitative global sensitivity indices which are able to deal with correlated input variables. They have been recently adapted to the target sensitivity analysis framework. In this article, we investigate two importance-sampling-based estimation schemes of these indices which are more efficient than the existing ones when the failure probability is small. Moreover, an extension to the case where only an i.i.d. input/output N -sample distributed according to the importance sampling auxiliary distribution is proposed. This extension allows to estimate the Shapley effects only with a data set distributed according to the importance sampling auxiliary distribution stemming from a reliability analysis without additional calls to the numerical model. In addition, we study theoretically the absence of bias of some estimators as well as the benefit of importance sampling. We also provide numerical guidelines and finally, realistic test cases show the practical interest of the proposed methods.

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“…To fully understand factor prioritization the ability to parse out the mutual information between two inputs when dependencies exist is necessary. Furthermore, in general it is not the case that the introduction of correlations will strictly decrease the Shapley indicator, as the nature of the input-output map and input dependency structure both play a role [16,19].…”

Section: Linear System With Variance-based Measurementioning

confidence: 99%

“…Key advances to GSA include the introduction of momentindependent sensitivity analysis (MISA) [7], multivariate-output aggregation [8,9,10], goal-oriented GSA [11], and frameworks for systems with input-input correlations [12,13]. In particular, Shapley effects have been of growing interest as a method when dependencies exist amongst the inputs [14,15,13,16,17,18,19].…”

Section: Introductionmentioning

confidence: 99%

Kernel-based Global Sensitivity Analysis Obtained from a Single Data Set

Barr¹,

Rabitz²

2022

Preprint

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Results from global sensitivity analysis (GSA) often guide the understanding of complicated input-output systems. Kernel-based GSA methods have recently been proposed for their capability of treating a broad scope of complex systems. In this paper we develop a new set of kernel GSA tools when only a single set of input-output data is available. Three key advances are made: (1) A new numerical estimator is proposed that demonstrates an empirical improvement over previous procedures. (2) A computational method for generating inner statistical functions from a single data set is presented. (3) A theoretical extension is made to define conditional sensitivity indices, which reveal the degree that the inputs carry shared information about the output when inherent input-input correlations are present. Utilizing these conditional sensitivity indices, a decomposition is derived for the output uncertainty based on what is called the optimal learning sequence of the input variables, which remains consistent when correlations exist between the input variables. While these advances cover a range of GSA subjects, a common single data set numerical solution is provided by a technique known as the conditional mean embedding of distributions.The new methodology is implemented on benchmark systems to demonstrate the provided insights.

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Computing Shapley Effects for Sensitivity Analysis

Cited by 22 publications

References 45 publications

Global sensitivity analysis with aggregated Shapley effects, application to avalanche hazard assessment

Global sensitivity analysis with aggregated Shapley effects, application to avalanche hazard assessment

Shapley effect estimation in reliability-oriented sensitivity analysis with correlated inputs by importance sampling

Kernel-based Global Sensitivity Analysis Obtained from a Single Data Set

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