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A Latent Variable Approach to Gaussian Process Modeling with Qualitative and Quantitative Factors

arXiv 1806.07504 ↗First posted 19 Jun 2018stat.ML cs.LGcited by 30

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Abstract (arXiv)

Computer simulations often involve both qualitative and numerical inputs. Existing Gaussian process (GP) methods for handling this mainly assume a different response surface for each combination of levels of the qualitative factors and relate them via a multiresponse cross-covariance matrix. We introduce a substantially different approach that maps each qualitative factor to an underlying numerical latent variable (LV), with the mapped value for each level estimated similarly to the correlation parameters. This provides a parsimonious GP parameterization that treats qualitative factors the same as numerical variables and views them as effecting the response via similar physical mechanisms. This has strong physical justification, as the effects of a qualitative factor in any physics-based simulation model must always be due to some underlying numerical variables. Even when the underlying variables are many, sufficient dimension reduction arguments imply that their effects can be represented by a low-dimensional LV. This conjecture is supported by the superior predictive performance observed across a variety of examples. Moreover, the mapped LVs provide substantial insight into the nature and effects of the qualitative factors.

Key facts. Cited by 30 papers in the map (data through 14 Oct 2026). First posted on arXiv 19 Jun 2018.

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Citing papers per year: 2021: 5; 2022: 8; 2023: 4; 2024: 8; 2025: 5.

30 papers.

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  1. 2022Bayesian Optimization over Discrete and Mixed Spaces via Probabilistic Reparameterizationcited by 37
  2. 2023SMT 2.0: A Surrogate Modeling Toolbox with a focus on Hierarchical and Mixed Variables Gaussian Processescited by 29
  3. 2021Latent Map Gaussian Processes for Mixed Variable Metamodelingcited by 23
  4. 2022Multi-Fidelity Cost-Aware Bayesian Optimizationcited by 20
  5. 2021Data Fusion with Latent Map Gaussian Processescited by 16
  6. 2022Multi-fidelity wavelet neural operator with application to uncertainty quantificationcited by 12
  7. 2023A Latent Variable Approach for Non-Hierarchical Multi-Fidelity Adaptive Samplingcited by 10
  8. 2021Data-Driven Multiscale Design of Cellular Composites with Multiclass Microstructures for Natural Frequency Maximizationcited by 9
  9. 2022t-METASET: Tailoring Property Bias of Large-Scale Metamaterial Datasets through Active Learningcited by 9
  10. 2023Rapid Design of Top-Performing Metal-Organic Frameworks with Qualitative Representations of Building Blockscited by 8
  11. 2021A comparison of mixed-variables Bayesian optimization approachescited by 6
  12. 2022Uncertainty-Aware Mixed-Variable Machine Learning for Materials Designcited by 6
18 more
  1. 2024A distance for mixed-variable and hierarchical domains with meta variablescited by 5
  2. 2022Hybrid Parameter Search and Dynamic Model Selection for Mixed-Variable Bayesian Optimizationcited by 4
  3. 2022Fully Bayesian inference for latent variable Gaussian process modelscited by 4
  4. 2024CAGES: Cost-Aware Gradient Entropy Search for Efficient Local Multi-Fidelity Bayesian Optimizationcited by 4
  5. 2024Interpretable Multi-Source Data Fusion Through Latent Variable Gaussian Processcited by 3
  6. 2024Heterogenous Multi-Source Data Fusion Through Input Mapping and Latent Variable Gaussian Processcited by 1
  7. 2024Gearing Gaussian process modeling and sequential design towards stochastic simulatorscited by 1
  8. 2025Distributional encoding for Gaussian process regression with qualitative inputscited by 1
  9. 2021Scalable mixed-domain Gaussian process modeling and model reduction for longitudinal datacited by 0
  10. 2022Multi-objective robust optimization using adaptive surrogate models for problems with mixed continuous-categorical parameterscited by 0
  11. 2023Bayesian Quality-Diversity approaches for constrained optimization problems with mixed continuous, discrete and categorical variablescited by 0
  12. 2024Transfer Learning Bayesian Optimization to Design Competitor DNA Molecules for Use in Diagnostic Assayscited by 0
  13. 2024Adaptive Catalyst Discovery Using Multicriteria Bayesian Optimization with Representation Learningcited by 0
  14. 2024Emerging Microelectronic Materials by Design: Navigating Combinatorial Design Space with Scarce and Dispersed Datacited by 0
  15. 2025Weighted Euclidean Distance Matrices over Mixed Continuous and Categorical Inputs for Gaussian Process Modelscited by 0
  16. 2025Flow Battery Manifold Design with Heterogeneous Inputs Through Generative Adversarial Neural Networkscited by 0
  17. 2025A reproducible comparative study of categorical kernels for Gaussian process regression, with new clustering-based nested kernelscited by 0
  18. 2025ARCO-BO: Adaptive Resource-aware COllaborative Bayesian Optimization for Heterogeneous Multi-Agent Designcited by 0