Latent variable Gaussian process models: A rank-based analysis and an alternative approach (bibtex)
Bibtex Entry:
@article{tao2021latent,
author = {Tao, Siyu and Apley, Daniel W. and Plumlee, Matthew and Chen, Wei},
title = {Latent variable Gaussian process models: A rank-based analysis and an alternative approach},
journal = {International Journal for Numerical Methods in Engineering},
volume = {122},
number = {15},
pages = {4007-4026},
keywords = {computer experiments, latent variables, metamodeling, mixed variables, response surface modeling},
doi = {https://doi.org/10.1002/nme.6690},
url = {https://onlinelibrary.wiley.com/doi/abs/10.1002/nme.6690},
eprint = {https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6690},
abstract = {Abstract Gaussian process (GP) models have been extended to emulate expensive computer simulations with both qualitative/categorical and quantitative/continuous variables. Latent variable (LV) GP models, which have been recently developed to map each qualitative variable to some underlying numerical LVs, have strong physics-based justification and have achieved promising performance. Two versions use LVs in Cartesian (LV-Car) space and hyperspherical (LV-sph) space, respectively. Despite their success, the effects of these different LV structures are still poorly understood. This article illuminates this issue with two contributions. First, we develop a theorem on the effect of the ranks of the qualitative factor correlation matrices of mixed-variable GP models, from which we conclude that the LV-sph model restricts the interactions between the input variables and thus restricts the types of response surface data with which the model can be consistent. Second, following a rank-based perspective like in the theorem, we propose a new alternative model named LV-mix that combines the LV-based correlation structures from both LV-Car and LV-sph models to achieve better model flexibility than them. Through extensive case studies, we show that LV-mix achieves higher average accuracy compared with the existing two.},
year = {2021}
}