A mixed-categorical correlation kernel for Gaussian process

Abstract

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.

arXiv commentPublished in Neurocomputing. 10.1016/j.neucom.2023.126472

References in corpus (4)

• Dealing with Integer-valued Variables in Bayesian Optimization with Gaussian Processes
• Dealing with Categorical and Integer-valued Variables in Bayesian Optimization with Gaussian Processes
• Latent Map Gaussian Processes for Mixed Variable Metamodeling
• Multioutput Gaussian Processes with Functional Data: A Study on Coastal Flood Hazard Assessment

Cited by in corpus (6)

• SMT 2.0: A Surrogate Modeling Toolbox with a focus on Hierarchical and Mixed Variables Gaussian Processes
• System Architecture Optimization Strategies: Dealing with Expensive Hierarchical Problems
• Surrogate-based optimization of system architectures subject to hidden constraints
• High-dimensional mixed-categorical Gaussian processes with application to multidisciplinary design optimization for a green aircraft
• A distance for mixed-variable and hierarchical domains with meta variables
• SMT-EX: An Explainable Surrogate Modeling Toolbox for Mixed-Variables Design Exploration