A mixed-categorical correlation kernel for Gaussian process

TL;DR

This paper introduces a new Gaussian process kernel for mixed-categorical variables that improves modeling accuracy over existing methods, demonstrated through analytical and engineering benchmarks.

Contribution

A novel kernel-based approach extending exponential kernels to handle mixed-categorical variables, unifying and enhancing existing GP surrogate models.

Findings

Higher likelihood compared to state-of-the-art models

Smaller residual errors in benchmarks

Applicable to both analytical and engineering problems

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.