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Gaussian process learning via Fisher scoring of Vecchia’s approximation

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Abstract

We derive a single-pass algorithm for computing the gradient and Fisher information of Vecchia’s Gaussian process loglikelihood approximation, which provides a computationally efficient means for applying the Fisher scoring algorithm for maximizing the loglikelihood. The advantages of the optimization techniques are demonstrated in numerical examples and in an application to Argo ocean temperature data. The new methods find the maximum likelihood estimates much faster and more reliably than an optimization method that uses only function evaluations, especially when the covariance function has many parameters. This allows practitioners to fit nonstationary models to large spatial and spatial–temporal datasets.

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Acknowledgements

This work was supported by the National Science Foundation under Grant Nos. 1613219 and 1916208 and the National Institutes of Health under Grant No. R01ES027892.

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  1. Department of Statistics and Data Science, Cornell University, Ithaca, USA

    Joseph Guinness

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  1. Joseph Guinness
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Correspondence to Joseph Guinness.

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Extended timing results

Extended timing results

This section contains histograms of timing results for \(|g(i)| = 20\) and 30, and \(n = 4900\) and 10,000 (Figs. 3, 4, 5, 6).

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Guinness, J. Gaussian process learning via Fisher scoring of Vecchia’s approximation. Stat Comput 31, 25 (2021). https://doi.org/10.1007/s11222-021-09999-1

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  • DOI: https://doi.org/10.1007/s11222-021-09999-1

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