Cross-Validation Estimations of Hyper-Parameters of Gaussian Processes with Inequality Constraints

Abstract : In many situations physical systems may be known to satisfy inequality constraints with respect to some or all input parameters. When building a surrogate model of this system (like in the framework of computer experiments7), one should integrate such expert knowledge inside the emulator structure. We proposed a new methodology to incorporate both equality conditions and inequality constraints into a Gaussian process emulator such that all conditional simulations satisfy the inequality constraints in the whole domain6. An estimator called mode (maximum a posteriori) is calculated and satisfies the inequality constraints. Herein we focus on the estimation of covariance hyper-parameters and cross validation methods1. We prove that these methods are suited to inequality constraints. Applied to real data in two dimensions, the numerical results show that the Leave-One-Out mean square error criterion using the mode is more efficient than the usual (unconstrained) Kriging mean.
Type de document :
Communication dans un congrès
Alfred Stein, Denis Allard. Spatial Statistics conference 2015, Jun 2015, Avignon, France. Elsevier, 27, pp.Pages 38-44, 2015, 〈http://www.sciencedirect.com/science/journal/18780296/27/supp/C〉. 〈10.1016/j.proenv.2015.07.105〉
Liste complète des métadonnées

https://hal-emse.ccsd.cnrs.fr/emse-01185753
Contributeur : Florent Breuil <>
Soumis le : vendredi 21 août 2015 - 14:25:39
Dernière modification le : jeudi 11 janvier 2018 - 06:16:31

Lien texte intégral

Identifiants

Citation

Hassan Maatouk, Olivier Roustant, Yann Richet. Cross-Validation Estimations of Hyper-Parameters of Gaussian Processes with Inequality Constraints. Alfred Stein, Denis Allard. Spatial Statistics conference 2015, Jun 2015, Avignon, France. Elsevier, 27, pp.Pages 38-44, 2015, 〈http://www.sciencedirect.com/science/journal/18780296/27/supp/C〉. 〈10.1016/j.proenv.2015.07.105〉. 〈emse-01185753〉

Partager

Métriques

Consultations de la notice

194