A mixed-categorical correlation kernel for Gaussian process
This work addresses a specific challenge in meta-modeling for engineering and analytical applications, representing an incremental improvement over existing kernel-based methods.
The paper tackles the problem of building Gaussian process surrogates for mixed-categorical variables by proposing a new kernel that extends continuous exponential kernels, resulting in higher likelihood and smaller residual error compared to state-of-the-art models on analytical and engineering problems.
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.