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Cholesky-based experimental design for Gaussian process and kernel-based emulation and calibration

Harbrecht, Helmut and Jakeman, John D. and Zaspel, Peter. (2021) Cholesky-based experimental design for Gaussian process and kernel-based emulation and calibration. Communications in Computational Physics, 29 (4). pp. 1152-1185.

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Abstract

Gaussian processes and other kernel-based methods are used extensively to construct approximations of multivariate data sets. The accuracy of these approximations is dependent on the data used. This paper presents a computationally efficient algorithm to greedily select training samples that minimize the weighted L p error of kernel-based approximations for a given number of data. The method successively generates nested samples, with the goal of minimizing the error in high probability regions of densities specified by users. The algorithm presented is extremely simple and can be implemented using existing pivoted Cholesky factorization methods. Training samples are generated in batches which allows training data to be evaluated (labeled) in parallel. For smooth kernels, the algorithm performs comparably with the greedy integrated variance design but has significantly lower complexity. Numerical experiments demonstrate the efficacy of the approach for bounded, unbounded, multi-modal and non-tensor product densities. We also show how to use the proposed algorithm to efficiently generate surrogates for inferring unknown model parameters from data using Bayesian inference.
Faculties and Departments:05 Faculty of Science > Departement Mathematik und Informatik > Mathematik > Computational Mathematics (Harbrecht)
UniBasel Contributors:Harbrecht, Helmut and Zaspel, Peter
Item Type:Article, refereed
Article Subtype:Research Article
Publisher:Global Science Press
ISSN:1815-2406
e-ISSN:1991-7120
Note:Publication type according to Uni Basel Research Database: Journal article
Language:English
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Last Modified:10 Mar 2021 13:36
Deposited On:10 Mar 2021 13:35

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