A simple algorithm for global sensitivity analysis with Shapley effects

@article{Goda2021ASA,
  title={A simple algorithm for global sensitivity analysis with Shapley effects},
  author={Takashi Goda},
  journal={Reliab. Eng. Syst. Saf.},
  year={2021},
  volume={213},
  pages={107702}
}
  • T. Goda
  • Published 2 September 2020
  • Computer Science, Mathematics
  • Reliab. Eng. Syst. Saf.
Global sensitivity analysis aims at measuring the relative importance of different variables or groups of variables for the variability of a quantity of interest. Among several sensitivity indices, so-called Shapley effects have recently gained popularity mainly because the Shapley effects for all the individual variables are summed up to the total variance, which gives a better intepretability than the classical sensitivity indices called main effects and total effects. In this paper, assuming… 
1 Citations

Figures and Tables from this paper

Computing Shapley Effects for Sensitivity Analysis
TLDR
A new algorithm is presented that offers major improvements for the computation of Shapley effects, reducing computational burden by several orders of magnitude and makes it possible to estimate all generalized (Shapley-Owen) effects for interactions.

References

SHOWING 1-10 OF 33 REFERENCES
Shapley Effects for Global Sensitivity Analysis: Theory and Computation
TLDR
Owen proposed an alternative sensitivity measure, based on the concept of the Shapley value in game theory, and showed it always sums to the correct total variance if inputs are independent, and it is analyzed, which is called Owen's measure, in the case of dependent inputs.
Variance Reduction for Estimation of Shapley Effects and Adaptation to Unknown Input Distribution
TLDR
This work investigates the already existing estimator of Shapley effects and suggests a new one with a lower variance, and extends these estimators when the distribution of the inputs is unknown.
Sobol' Indices and Shapley Value
  • A. Owen
  • Computer Science, Mathematics
    SIAM/ASA J. Uncertain. Quantification
  • 2014
TLDR
The Shapley value of individual variables when the authors take “variance explained” as their combined value does not match either of the usual Sobol' indices, but is bracketed between them for variance explained or any totally monotone game.
Making best use of model evaluations to compute sensitivity indices
This paper deals with computations of sensitivity indices in sensitivity analysis. Given a mathematical or computational model y=f(x1,x2,…,xk), where the input factors xi's are uncorrelated with one
On Shapley Value for Measuring Importance of Dependent Inputs
  • A. Owen, C. Prieur
  • Mathematics, Computer Science
    SIAM/ASA J. Uncertain. Quantification
  • 2017
TLDR
The main goal here is to show that Shapley value removes the conceptual problems when alternatives based on the ANOVA decomposition run into conceptual and computational problems when the input variables are dependent.
Variance based sensitivity analysis of model output. Design and estimator for the total sensitivity index
TLDR
Existing and new practices for sensitivity analysis of model output are compared and recommendations on which to use are offered to help practitioners choose which techniques to use.
Global Sensitivity Analysis
TLDR
This paper demonstrates practical approaches for determining relative parameter sensitivity with respect to a model's optimal objective function value, decision variables, and other analytic functions of a solution.
Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates
Global sensitivity indices for rather complex mathematical models can be efficiently computed by Monte Carlo (or quasi-Monte Carlo) methods. These indices are used for estimating the influence of
Asymptotic normality and efficiency of two Sobol index estimators
Many mathematical models involve input parameters, which are not precisely known. Global sensitivity analysis aims to identify the parameters whose uncertainty has the largest impact on the
Variance-based sensitivity analysis of model outputs using surrogate models
TLDR
A procedure in which an adaptive sequential design is employed to derive surrogate models and estimate sensitivity indices for different sub-groups of inputs is drawn attention, which is particularly useful when there is little prior knowledge about the response surface.
...
1
2
3
4
...