mlsanityData to 7 Oct 2026

A mixed-categorical correlation kernel for Gaussian process

arXiv 2211.08262 ↗First posted 15 Nov 2022math.OC cs.LG stat.MLcited by 19

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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.

Key facts. Cited by 19 papers in the map (data through 7 Oct 2026). Builds on 11 of its 57 references that are in the map. First posted on arXiv 15 Nov 2022.

Builds on

11 of 57 references.

References · 11

  1. 2015Scalable Bayesian Optimization Using Deep Neural Networkscited by 284
  2. 2017Dealing with Integer-valued Variables in Bayesian Optimization with Gaussian Processescited by 65
  3. 2019Bayesian Optimization for Categorical and Category-Specific Continuous Inputscited by 28
  4. 2021Latent Map Gaussian Processes for Mixed Variable Metamodelingcited by 23
  5. 2018Group kernels for Gaussian process metamodels with categorical inputscited by 22
  6. 2021Constrained Discrete Black-Box Optimization using Mixed-Integer Programmingcited by 16
  7. 2018Efficient global optimization of constrained mixed variable problemscited by 11
  8. 2021Deep Gaussian Process Emulation using Stochastic Imputationcited by 11
  9. 2020Black-box Mixed-Variable Optimisation using a Surrogate Model that Satisfies Integer Constraintscited by 9
  10. 2021A comparison of mixed-variables Bayesian optimization approachescited by 6
  11. 2020Multioutput Gaussian Processes with Functional Data: A Study on Coastal Flood Hazard Assessmentcited by 5

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 2; 2024: 1; 2025: 11; 2026: 5.

19 papers.

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  1. 2023SMT 2.0: A Surrogate Modeling Toolbox with a focus on Hierarchical and Mixed Variables Gaussian Processescited by 27
  2. 2023High-dimensional mixed-categorical Gaussian processes with application to multidisciplinary design optimization for a green aircraftcited by 8
  3. 2025Surrogate Modeling and Explainable Artificial Intelligence for Complex Systems: A Workflow for Automated Simulation Explorationcited by 6
  4. 2024A distance for mixed-variable and hierarchical domains with meta variablescited by 4
  5. 2025SMT-EX: An Explainable Surrogate Modeling Toolbox for Mixed-Variables Design Explorationcited by 4
  6. 2025Surrogate-based optimization of system architectures subject to hidden constraintscited by 3
  7. 2025Multi-objective Bayesian Optimization With Mixed-categorical Design Variables for Expensive-to-evaluate Aeronautical Applicationscited by 3
  8. 2025Modeling Hierarchical Spaces: A Review and Unified Framework for Surrogate-Based Architecture Designcited by 3
  9. 2025Bayesian Optimization of a Lightweight and Accurate Neural Network for Aerodynamic Performance Predictioncited by 2
  10. 2025Distributional encoding for Gaussian process regression with qualitative inputscited by 1
  11. 2025System-of-systems Modeling and Optimization: An Integrated Framework for Intermodal Mobilitycited by 1
  12. 2025Weighted Euclidean Distance Matrices over Mixed Continuous and Categorical Inputs for Gaussian Process Modelscited by 0
7 more
  1. 2025Frequency-aware Surrogate Modeling With SMT Kernels For Advanced Data Forecastingcited by 0
  2. 2025Global Sensitivity Analysis for Engineering Design Based on Individual Conditional Expectationscited by 0
  3. 2026Multi-fidelity approaches for general constrained Bayesian optimization with application to aircraft designcited by 0
  4. 2026Transfer Learning in Bayesian Optimization for Aircraft Designcited by 0
  5. 2026Modeling Temporal scRNA-seq Data with Latent Gaussian Process and Optimal Transportcited by 0
  6. 2026Efficient multidisciplinary design via Bayesian optimizationcited by 0
  7. 2026Hierarchical Bayesian optimization of an aircraft-based multi-agent system-of-systemscited by 0