# A mixed-categorical correlation kernel for Gaussian process

arXiv: https://arxiv.org/abs/2211.08262 · HTML: https://mlsanity.com/paper/2211.08262/

## Key facts

- Cited by 19 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 57 references that are in the map.
- First posted on arXiv 15 Nov 2022.

## Builds on (most cited first, 11 of 11)

- [Scalable Bayesian Optimization Using Deep Neural Networks](https://mlsanity.com/paper/1502.05700/) (2015)
- [Dealing with Integer-valued Variables in Bayesian Optimization with Gaussian Processes](https://mlsanity.com/paper/1706.03673/) (2017)
- [Bayesian Optimization for Categorical and Category-Specific Continuous Inputs](https://mlsanity.com/paper/1911.12473/) (2019)
- [Group kernels for Gaussian process metamodels with categorical inputs](https://mlsanity.com/paper/1802.02368/) (2018)
- [Latent Map Gaussian Processes for Mixed Variable Metamodeling](https://mlsanity.com/paper/2102.03935/) (2021)
- [Constrained Discrete Black-Box Optimization using Mixed-Integer Programming](https://mlsanity.com/paper/2110.09569/) (2021)
- [Efficient global optimization of constrained mixed variable problems](https://mlsanity.com/paper/1806.03975/) (2018)
- [Deep Gaussian Process Emulation using Stochastic Imputation](https://mlsanity.com/paper/2107.01590/) (2021)
- [Black-box Mixed-Variable Optimisation using a Surrogate Model that Satisfies Integer Constraints](https://mlsanity.com/paper/2006.04508/) (2020)
- [A comparison of mixed-variables Bayesian optimization approaches](https://mlsanity.com/paper/2111.01533/) (2021)
- [Multioutput Gaussian Processes with Functional Data: A Study on Coastal Flood Hazard Assessment](https://mlsanity.com/paper/2007.14052/) (2020)

## Built on by (most cited first, 19 of 19)

- [SMT 2.0: A Surrogate Modeling Toolbox with a focus on Hierarchical and Mixed Variables Gaussian Processes](https://mlsanity.com/paper/2305.13998/) (2023)
- [High-dimensional mixed-categorical Gaussian processes with application to multidisciplinary design optimization for a green aircraft](https://mlsanity.com/paper/2311.06130/) (2023)
- [Surrogate Modeling and Explainable Artificial Intelligence for Complex Systems: A Workflow for Automated Simulation Exploration](https://mlsanity.com/paper/2510.16742/) (2025)
- [A distance for mixed-variable and hierarchical domains with meta variables](https://mlsanity.com/paper/2405.13073/) (2024)
- [SMT-EX: An Explainable Surrogate Modeling Toolbox for Mixed-Variables Design Exploration](https://mlsanity.com/paper/2503.19496/) (2025)
- [Multi-objective Bayesian Optimization With Mixed-categorical Design Variables for Expensive-to-evaluate Aeronautical Applications](https://mlsanity.com/paper/2504.09930/) (2025)
- [Modeling Hierarchical Spaces: A Review and Unified Framework for Surrogate-Based Architecture Design](https://mlsanity.com/paper/2506.22621/) (2025)
- [Bayesian Optimization of a Lightweight and Accurate Neural Network for Aerodynamic Performance Prediction](https://mlsanity.com/paper/2503.19479/) (2025)
- [Surrogate-based optimization of system architectures subject to hidden constraints](https://mlsanity.com/paper/2504.08721/) (2025)
- [Distributional encoding for Gaussian process regression with qualitative inputs](https://mlsanity.com/paper/2506.04813/) (2025)
- [System-of-systems Modeling and Optimization: An Integrated Framework for Intermodal Mobility](https://mlsanity.com/paper/2507.08715/) (2025)
- [Weighted Euclidean Distance Matrices over Mixed Continuous and Categorical Inputs for Gaussian Process Models](https://mlsanity.com/paper/2503.02630/) (2025)
- [Frequency-aware Surrogate Modeling With SMT Kernels For Advanced Data Forecasting](https://mlsanity.com/paper/2507.09694/) (2025)
- [Global Sensitivity Analysis for Engineering Design Based on Individual Conditional Expectations](https://mlsanity.com/paper/2512.11946/) (2025)
- [Multi-fidelity approaches for general constrained Bayesian optimization with application to aircraft design](https://mlsanity.com/paper/2603.28987/) (2026)
- [Transfer Learning in Bayesian Optimization for Aircraft Design](https://mlsanity.com/paper/2603.28999/) (2026)
- [Modeling Temporal scRNA-seq Data with Latent Gaussian Process and Optimal Transport](https://mlsanity.com/paper/2605.20989/) (2026)
- [Efficient multidisciplinary design via Bayesian optimization](https://mlsanity.com/paper/2607.22560/) (2026)
- [Hierarchical Bayesian optimization of an aircraft-based multi-agent system-of-systems](https://mlsanity.com/paper/2609.22130/) (2026)

## Abstract (arXiv)

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.