Tensor-variate Gaussian process regression for efficient emulation of complex systems: comparing regressor and covariance structures in outer product and parallel partial emulators
Tensor-variate Gaussian process regression for efficient emulation of complex systems: comparing regressor and covariance structures in outer product and parallel partial emulators
Multi-output Gaussian process regression has become an important tool in uncertainty quantification, for building emulators of computationally expensive simulators, and other areas such as multi-task machine learning. We present a holistic development of tensor-variate Gaussian process (TvGP) regression, appropriate for arbitrary dimensional outputs where a Kronecker product structure is appropriate for the covariance. We show how two common approaches to problems with two-dimensional output, outer product emulators (OPE) and parallel partial emulators (PPE), are special cases of TvGP regression and hence can be extended to higher output dimensions. Focusing on the important special case of matrix output, we investigate the relative performance of these two approaches. The key distinction is the additional dependence structure assumed by the OPE, and we demonstrate when this is advantageous through two case studies, including application to a spatial-temporal influenza simulator.
Semochkina, Dasha
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Jackson, Samuel E.
c05ee43f-7b33-4c3e-98ad-96ddc5c1bb4d
Woods, David C.
ae21f7e2-29d9-4f55-98a2-639c5e44c79c
Semochkina, Dasha
011d4fa0-cf50-4739-890e-7f453027432f
Jackson, Samuel E.
c05ee43f-7b33-4c3e-98ad-96ddc5c1bb4d
Woods, David C.
ae21f7e2-29d9-4f55-98a2-639c5e44c79c
Semochkina, Dasha, Jackson, Samuel E. and Woods, David C.
(2024)
Tensor-variate Gaussian process regression for efficient emulation of complex systems: comparing regressor and covariance structures in outer product and parallel partial emulators.
SIAM/ASA Journal on Uncertainty Quantification.
(Submitted)
Abstract
Multi-output Gaussian process regression has become an important tool in uncertainty quantification, for building emulators of computationally expensive simulators, and other areas such as multi-task machine learning. We present a holistic development of tensor-variate Gaussian process (TvGP) regression, appropriate for arbitrary dimensional outputs where a Kronecker product structure is appropriate for the covariance. We show how two common approaches to problems with two-dimensional output, outer product emulators (OPE) and parallel partial emulators (PPE), are special cases of TvGP regression and hence can be extended to higher output dimensions. Focusing on the important special case of matrix output, we investigate the relative performance of these two approaches. The key distinction is the additional dependence structure assumed by the OPE, and we demonstrate when this is advantageous through two case studies, including application to a spatial-temporal influenza simulator.
Text
2502.10319v1
- Author's Original
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Submitted date: 12 December 2024
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Local EPrints ID: 499127
URI: http://eprints.soton.ac.uk/id/eprint/499127
PURE UUID: 2594e81a-aa7d-48dc-abba-85c20fa16e0e
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Date deposited: 10 Mar 2025 17:45
Last modified: 22 Aug 2025 02:26
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Samuel E. Jackson
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