# Weighted Euclidean Distance Matrices over Mixed Continuous and Categorical Inputs for Gaussian Process Models

arXiv: https://arxiv.org/abs/2503.02630 · HTML: https://mlsanity.com/paper/2503.02630/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 25 of its 52 references that are in the map.
- First posted on arXiv 4 Mar 2025.

## Builds on (most cited first, 25 of 25)

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- [A mixed-categorical correlation kernel for Gaussian process](https://mlsanity.com/paper/2211.08262/) (2022)
- [Framework and Benchmarks for Combinatorial and Mixed-variable Bayesian Optimization](https://mlsanity.com/paper/2306.09803/) (2023)
- [Black-box Mixed-Variable Optimisation using a Surrogate Model that Satisfies Integer Constraints](https://mlsanity.com/paper/2006.04508/) (2020)
- [Batch Bayesian Optimization for Replicable Experimental Design](https://mlsanity.com/paper/2311.01195/) (2023)
- [Uncertainty Quantification for Bayesian Optimization](https://mlsanity.com/paper/2002.01569/) (2020)
- [Measuring the robustness of Gaussian processes to kernel choice](https://mlsanity.com/paper/2106.06510/) (2021)

## Abstract (arXiv)

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.