Gaussian Process (GP) models are widely utilized as surrogate models in scientific and engineering fields. However, standard GP models are limited to continuous variables due to the difficulties in establishing correlation structures for categorical variables. To overcome this limitati on, we introduce WEighted Euclidean distance matrices Gaussian Process (WEGP). WEGP constructs the kernel function for each categorical input by estimating the Euclidean distance matrix (EDM) among all categorical choices of this input. The EDM is represented as a linear combination of several predefined base EDMs, each scaled by a positive weight. The weights, along with other kernel hyperparameters, are inferred using a fully Bayesian framework. We analyze the predictive performance of WEGP theoretically. Numerical experiments validate the accuracy of our GP model, and by WEGP, into Bayesian Optimization (BO), we achieve superior performance on both synthetic and real-world optimization problems.

翻译：高斯过程（GP）模型在科学与工程领域被广泛用作代理模型。然而，由于难以建立分类变量的相关结构，标准GP模型仅限于连续变量。为克服这一限制，本文提出加权欧几里得距离矩阵高斯过程（WEGP）。WEGP通过估计每个分类输入在其所有可能取值间的欧几里得距离矩阵（EDM）来构建该输入的核函数。该EDM表示为多个预定义基EDM的线性组合，每个基EDM通过一个正权重进行缩放。权重与其他核超参数通过完全贝叶斯框架进行推断。我们从理论上分析了WEGP的预测性能。数值实验验证了所提GP模型的准确性，并将WEGP应用于贝叶斯优化（BO），在合成与真实优化问题上均取得了优越的性能。