Sequential dimension reduction for learning features of expensive black-box functions

Learning a feature of an expensive black-box function (optimum, contour line,...) is a difficult task when the dimension increases. A classical approach is two-stage. First, sensitivity analysis is performed to reduce the dimension of the input variables. Second, the feature is estimated by considering only the selected influential variables. This approach can be computationally expensive and may lack flexibility since dimension reduction is done once and for all. In this paper, we propose a so called Split-and-Doubt algorithm that performs sequentially both dimension reduction and feature oriented sampling. The 'split' step identifies influential variables. This selection relies on new theoretical results on Gaussian process regression. We prove that large correlation lengths of covariance functions correspond to inactive variables. Then, in the 'doubt' step, a doubt function is used to update the subset of influential variables. Numerical tests show the efficiency of the Split-and-Doubt algorithm.

Mots clés

62K99 62F15 Bayesian optimization AMS subject classifications 62L05 Surrogate modeling Design of experiments Variable selection Bayesian optimization

Domaines

Applications [stat.AP]

Fichier principal

main.pdf (410.29 Ko)

boxplotsperiteration.jpg (40.57 Ko)

boxplotsperiteration.png (6.68 Ko)

Ackley20D40iterboxlot.pdf (28.03 Ko)

Ackley20D40itermean.pdf (21.59 Ko)

Borhole25Dboxlot.pdf (22.55 Ko)

Borhole25Dmean.pdf (19.17 Ko)

Branin25Dboxlot.pdf (29.21 Ko)

Branin25Dmean.pdf (20.59 Ko)

IDEAL_cos2pi_constrastxstar.pdf (51.46 Ko)

IDEAL_cos2pix2_1.pdf (183.23 Ko)

IDEAL_cos_krigx1.pdf (175.73 Ko)

IDEAL_loglik2.pdf (179.33 Ko)

IDEAL_loglik2bad.pdf (175.61 Ko)

IDEAL_loglikcos2pi_10_tr.pdf (178.12 Ko)

Rosenbrock20_5D_largerboxlot.pdf (42.8 Ko)

Rosenbrock20_5D_largermean.pdf (25.29 Ko)

harmtann15Dboxlot.pdf (26.85 Ko)

harmtann15Dmean.pdf (20.24 Ko)

hartmannbydimnewcolorcode.pdf (23.32 Ko)

legend.pdf (14.5 Ko)

meancomputingTime.pdf (18.02 Ko)

rosenbrock_missperc.pdf (5.7 Ko)

rosenperc_inf_var.pdf (5.34 Ko)

Origine	Fichiers produits par l'(les) auteur(s)

Format	Figure, Image
Origine	Fichiers produits par l'(les) auteur(s)

Format	Figure, Image

Origine	Fichiers produits par l'(les) auteur(s)

Malek BEN SALEM : Connectez-vous pour contacter le contributeur

https://hal.science/hal-01688329

Soumis le : mercredi 27 février 2019-11:09:48

Dernière modification le : mardi 27 août 2024-12:48:37

Archivage à long terme le : mardi 28 mai 2019-12:18:16

Dates et versions

hal-01688329 , version 1 (19-01-2018)

hal-01688329 , version 2 (27-02-2019)

Identifiants

HAL Id : hal-01688329 , version 2

Citer

Malek Ben Salem, François Bachoc, Olivier Roustant, Fabrice Gamboa, Lionel Tomaso. Sequential dimension reduction for learning features of expensive black-box functions. 2019. ⟨hal-01688329v2⟩

Exporter

BibTeX XML-TEI Dublin Core DC Terms EndNote DataCite

Collections

PRES_CLERMONT CNRS FAYOL-ENSMSE LIMOS DEMO-ENSMSE INSA-GROUPE CLERMONT-AUVERGNE-INP UNIV-UT3 UT3-TOULOUSEINP

627 Consultations

1707 Téléchargements