On-line Pick-Freeze Mirror algorithm for Sensitity Analysis

TL;DR

This paper introduces an online stochastic mirror descent method for simultaneously estimating all Sobol' indices in sensitivity analysis, providing theoretical guarantees and demonstrating superior numerical performance.

Contribution

It presents a novel online optimization-based approach for Sobol' index estimation, with proven consistency and convergence rates, advancing sensitivity analysis techniques.

Findings

Method is consistent and converges at a quantifiable rate.

Numerical experiments show improved accuracy over classical methods.

Approach efficiently estimates all Sobol' indices simultaneously.

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 the simplex of $\R^d$, 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.