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.

翻译：最近，基于高斯过程代理模型的混合类别元模型引起了越来越多的关注。在此背景下，现有多种方法采用不同策略，要么使用连续核（例如基于连续松弛和高尔距离的高斯过程），要么直接估计相关矩阵。本文提出一种基于核的方法，将连续指数核拓展至处理混合类别变量。所提出的核衍生出一种新的高斯过程代理模型，该模型同时泛化了基于连续松弛和高尔距离的高斯过程模型。通过分析问题与工程问题的验证，我们证明所提出的高斯过程模型相比其他基于核的最优模型具有更高的似然性和更小的残差误差。该方法已在开源软件SMT中实现。