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On-line Pick-Freeze Mirror algorithm for Sensitity Analysis

Author

Listed:
  • Costa, Manon
  • Gadat, Sébastien
  • Gendre, Xavier
  • Klein, Thierry

Abstract

The main objective of this paper is to propose a new approach for estimating the entire collection of Sobol’ indices simultaneously. Our approach exploits the fact that Sobol’ indices can be rewritten as solutions to an optimization problem over a simplex, to construct an online sequence of estimators using a stochastic mirror descent algorithm. We prove that our estimation procedure is consistent and provide a non-asymptotic upper bound for its rate of convergence. Furthermore, we demonstrate the numerical accuracy of our method and compare it with other classical estimation procedures.

Suggested Citation

  • Costa, Manon & Gadat, Sébastien & Gendre, Xavier & Klein, Thierry, 2026. "On-line Pick-Freeze Mirror algorithm for Sensitity Analysis," TSE Working Papers 26-1751, Toulouse School of Economics (TSE).
    • Handle: RePEc:tse:wpaper:131794
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    References listed on IDEAS

    as
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    2. Heredia, María Belén & Prieur, Clémentine & Eckert, Nicolas, 2021. "Nonparametric estimation of aggregated Sobol’ indices: Application to a depth averaged snow avalanche model," Reliability Engineering and System Safety, Elsevier, vol. 212(C).
    3. Liitiäinen, Elia & Corona, Francesco & Lendasse, Amaury, 2010. "Residual variance estimation using a nearest neighbor statistic," Journal of Multivariate Analysis, Elsevier, vol. 101(4), pages 811-823, April.
    4. Elmar Plischke & Emanuele Borgonovo, 2020. "Fighting the Curse of Sparsity: Probabilistic Sensitivity Measures From Cumulative Distribution Functions," Risk Analysis, John Wiley & Sons, vol. 40(12), pages 2639-2660, December.
    5. Sébastien Da Veiga & Fabrice Gamboa, 2013. "Efficient estimation of sensitivity indices," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 25(3), pages 573-595, September.
    6. Heinz H. Bauschke & Jérôme Bolte & Marc Teboulle, 2017. "A Descent Lemma Beyond Lipschitz Gradient Continuity: First-Order Methods Revisited and Applications," Mathematics of Operations Research, INFORMS, vol. 42(2), pages 330-348, May.
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