Gaussian process based dimension reduction for goal-oriented sequential design

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]

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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)

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https://hal.science/hal-01688329

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

Dernière modification le : vendredi 20 décembre 2024-14:20:46

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
DOI : 10.1137/18M1167930

Citer

Malek Ben Salem, François Bachoc, Olivier Roustant, Fabrice Gamboa, Lionel Tomaso. Gaussian process based dimension reduction for goal-oriented sequential design. SIAM/ASA Journal on Uncertainty Quantification, 2019, ⟨10.1137/18M1167930⟩. ⟨hal-01688329v2⟩

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