Fast uncertainty reduction strategies relying on Gaussian process models

Clément Chevalier 1, 2, 3, 4
4 ReDICE - The ReDICE Consortium
IMT - Institut de Mathématiques de Toulouse UMR5219, Mines Saint-Étienne MSE - École des Mines de Saint-Étienne, UNS - Université Nice Sophia Antipolis, Inria - Institut National de Recherche en Informatique et en Automatique, University of Bern
Abstract : This work deals with sequential and batch-sequential evaluation strategies of real-valued functions under limited evaluation budget, using Gaussian process models. Optimal Stepwise Uncertainty Reduction (SUR) strategies are investigated for two diff erent problems, motivated by real test cases in nuclear safety. First we consider the problem of identifying the excursion set above a given threshold T of a real-valued function f. Then we study the question of finding the set of "safe controlled con gurations", i.e. the set of controlled inputs where the function remains below T, whatever the value of some others non-controlled inputs. New SUR strategies are presented, together with effi cient procedures and formulas to compute and use them in real-world applications. The use of fast formulas to recalculate quickly the posterior mean or covariance function of a Gaussian process (referred to as the "kriging update formulas") does not only provide substantial computational savings. It is also one of the key tools to derive closed-form formulas enabling a practical use of computationally-intensive sampling strategies. A contribution in batch-sequential optimization (with the multi-points Expected Improvement) is also presented.
Liste complète des métadonnées

Cited literature [192 references]  Display  Hide  Download

https://tel.archives-ouvertes.fr/tel-00879082
Contributor : Chevalier Clément <>
Submitted on : Thursday, October 31, 2013 - 4:55:37 PM
Last modification on : Friday, April 12, 2019 - 4:23:35 PM
Document(s) archivé(s) le : Saturday, February 1, 2014 - 4:30:33 AM

Identifiers

  • HAL Id : tel-00879082, version 1

Citation

Clément Chevalier. Fast uncertainty reduction strategies relying on Gaussian process models. Statistics [math.ST]. Universität Bern, 2013. English. ⟨tel-00879082⟩

Share

Metrics

Record views

828

Files downloads

851