A mixed-categorical correlation kernel for Gaussian process

Paul Saves (1, 2) , Y. Diouane (3) , Nathalie Bartoli (2) , T. Lefebvre (2) , J. Morlier (4)

1 ISAE-SUPAERO - Institut Supérieur de l'Aéronautique et de l'Espace
2 DTIS, ONERA, Université de Toulouse [Toulouse]
3 EPM - École Polytechnique de Montréal
4 ICA - Institut Clément Ader

Recently, there has been a growing interest for mixed-categorical meta-models based on Gaussian process (GP) surrogates. In this setting, several existing approaches use different strategies either by using continuous kernels (e.g., continuous relaxation and Gower distance based GP) or by using a direct estimation of the correlation matrix. In this paper, we present a kernel-based approach that extends continuous exponential kernels to handle mixed-categorical variables. The proposed kernel leads to a new GP surrogate that generalizes both the continuous relaxation and the Gower distance based GP models. We demonstrate, on both analytical and engineering problems, that our proposed GP model gives a higher likelihood and a smaller residual error than the other kernel-based state-of-the-art models. Our method is available in the open-source software SMT.

Mots clés: Gaussian process; Mixed-categorical; Continuous relaxation; Hypersphere decomposition; Bayesian optimization; Surrogate modeling toolbox; I-GAIA

Domaines: Statistiques [stat]; Optimisation et contrôle [math.OC]

Paul Saves, Y. Diouane, Nathalie Bartoli, T. Lefebvre, J. Morlier. A mixed-categorical correlation kernel for Gaussian process. Neurocomputing, inPress, ⟨10.1016/j.neucom.2023.126472⟩. ⟨hal-04130877v2⟩