Group kernels for Gaussian process metamodels with categorical inputs

Gaussian processes (GP) are widely used as a metamodel for emulating time-consuming computer codes. We focus on problems involving categorical inputs, with a potentially large number L of levels (typically several tens), partitioned in G << L groups of various sizes. Parsimonious covariance functions, or kernels, can then be defined by block covariance matrices T with constant covariances between pairs of blocks and within blocks. We study the positive definiteness of such matrices to encourage their practical use. The hierarchical group/level structure, equivalent to a nested Bayesian linear model, provides a parameterization of valid block matrices T. The same model can then be used when the assumption within blocks is relaxed, giving a flexible parametric family of valid covariance matrices with constant covariances between pairs of blocks. The positive definiteness of T is equivalent to the positive definiteness of a smaller matrix of size G, obtained by averaging each block. The model is applied to a problem in nuclear waste analysis, where one of the categorical inputs is atomic number, which has more than 90 levels.

Mots clés

Gaussian processes Categorical data Computer experiments

Domaines

Statistiques [math.ST]

Fichier principal

groupKernels (1).pdf (1.29 Mo)

2groupes (1).pdf (83.17 Ko)

5_5_8_8_-5_4_1 (1).pdf (9.72 Ko)

5_5_8_8_-5_4_20Q2 (1).pdf (5.67 Ko)

5_5_8_8_-5_4_5 (1).pdf (9.71 Ko)

5_5_8_8_-5_4_6 (1).pdf (9.75 Ko)

5_5_8_8_-5_4_9 (1).pdf (9.71 Ko)

5_5_8_8_0_4_20Q2 (1).pdf (5.69 Ko)

5_5_8_8_5_4_20Q2 (1).pdf (5.75 Ko)

5groupesA (1).pdf (81.62 Ko)

5groupesB (1).pdf (86.45 Ko)

Appli_EnergieCorplot (1).pdf (27.89 Ko)

Appli_EnergieTransfo (1).pdf (5.71 Ko)

Appli_ShapeCorplot (1).pdf (12.04 Ko)

Appli_corplot_cas_a (1).pdf (59.26 Ko)

Appli_corplot_cas_b (1).pdf (59.71 Ko)

CS (1).pdf (80.1 Ko)

I1 (1).pdf (2.66 Ko)

I2 (1).pdf (2.66 Ko)

I3 (1).pdf (2.66 Ko)

Q2appli (1).pdf (6.08 Ko)

Q2appliRandom (1).pdf (6.16 Ko)

Q2beam (1).pdf (5.72 Ko)

Q2exempleSinusPlusSans13 (1).pdf (6.05 Ko)

anneau1 (1).pdf (3.17 Ko)

anneau2 (1).pdf (3.64 Ko)

anneau3 (1).pdf (3.68 Ko)

carre1 (1).pdf (2.65 Ko)

carre2 (1).pdf (2.64 Ko)

carre3 (1).pdf (2.64 Ko)

etoile1 (1).pdf (2.67 Ko)

etoile2 (1).pdf (2.73 Ko)

etoile3 (1).pdf (2.72 Ko)

example_13sinusoids_fig (1).pdf (11.2 Ko)

example_neg_within_corplot2 (1).pdf (58.5 Ko)

example_neg_within_corplot3 (1).pdf (54.75 Ko)

example_neg_within_fig (1).pdf (9.81 Ko)

influence_energie (1).pdf (4.72 Ko)

influence_forme (1).pdf (4.73 Ko)

influence_materiaux (1).pdf (18.81 Ko)

ordinal_cos (1).pdf (97.35 Ko)

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

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

Olivier Roustant : Connectez-vous pour contacter le contributeur

https://hal.science/hal-01702607

Soumis le : samedi 30 mars 2019-15:13:06

Dernière modification le : mardi 19 novembre 2024-09:28:02

Dates et versions

hal-01702607 , version 1 (06-02-2018)

hal-01702607 , version 2 (19-07-2018)

hal-01702607 , version 3 (30-03-2019)

Identifiants

HAL Id : hal-01702607 , version 3
ARXIV : 1802.02368

Citer

Olivier Roustant, Esperan Padonou, Yves Deville, Aloïs Clément, Guillaume Perrin, et al.. Group kernels for Gaussian process metamodels with categorical inputs. 2019. ⟨hal-01702607v3⟩

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