Costa, Manon, Gadat, Sébastien, Gendre, Xavier and Klein, Thierry (2026) On-line Pick-Freeze Mirror algorithm for Sensitity Analysis. TSE Working Paper, n. 26-1751, Toulouse

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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.