让高斯过程模型支持混合变量，提升优化精度。
Weighted Euclidean Distance Matrices over Mixed Continuous and Categorical Inputs for Gaussian Process Models
- 用加权欧氏距离矩阵构建类别变量的核函数。
- 在真实与合成数据上，优化性能优于传统方法。
- 适合需要处理混合变量的科学计算与工程优化场景。
高斯过程（GP）模型广泛应用于科学与工程领域的代理建模。然而，标准GP仅限于连续变量，因难以建立类别变量的相关结构。为此，我们提出加权欧氏距离矩阵高斯过程（WEGP）。WEGP通过估计每个类别输入的所有取值间的欧氏距离矩阵（EDM），并将其表示为若干预定义基EDM的线性组合，每项乘以正权重。权重与其他核超参数共同通过全贝叶斯框架推断。我们从理论上分析了WEGP的预测性能。数值实验验证了模型准确性，并将WEGP用于贝叶斯优化（BO），在合成与真实世界优化问题中均取得更优表现。
原文摘要 · Abstract (English)
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.
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