A probabilistic Taylor expansion with Gaussian processes
A probabilistic Taylor expansion with Gaussian processes
We study a class of Gaussian processes for which the posterior mean, for a particular choice of data, replicates a truncated Taylor expansion of any order. The data consist of derivative evaluations at the expansion point and the prior covariance kernel belongs to the class of Taylor kernels, which can be written in a certain power series form. We discuss and prove some results on maximum likelihood estimation of parameters of Taylor kernels. The proposed framework is a special case of Gaussian process regression based on data that is orthogonal in the reproducing kernel Hilbert space of the covariance kernel.
Karvonen, Toni
bb48042f-45d1-4f44-841b-0817f45961d8
Cockayne, Jon
da87c8b2-fafb-4856-938d-50be8f0e4a5b
Tronarp, Filip
e51d70a4-6cec-4bd9-b065-142c180e2439
Särkkä, Simo
5402acd1-808a-4428-8900-adcac00b709a
1 September 2023
Karvonen, Toni
bb48042f-45d1-4f44-841b-0817f45961d8
Cockayne, Jon
da87c8b2-fafb-4856-938d-50be8f0e4a5b
Tronarp, Filip
e51d70a4-6cec-4bd9-b065-142c180e2439
Särkkä, Simo
5402acd1-808a-4428-8900-adcac00b709a
Karvonen, Toni, Cockayne, Jon, Tronarp, Filip and Särkkä, Simo
(2023)
A probabilistic Taylor expansion with Gaussian processes.
Transactions on Machine Learning Research, 2023.
Abstract
We study a class of Gaussian processes for which the posterior mean, for a particular choice of data, replicates a truncated Taylor expansion of any order. The data consist of derivative evaluations at the expansion point and the prior covariance kernel belongs to the class of Taylor kernels, which can be written in a certain power series form. We discuss and prove some results on maximum likelihood estimation of parameters of Taylor kernels. The proposed framework is a special case of Gaussian process regression based on data that is orthogonal in the reproducing kernel Hilbert space of the covariance kernel.
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Published date: 1 September 2023
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Local EPrints ID: 502449
URI: http://eprints.soton.ac.uk/id/eprint/502449
PURE UUID: d769b8b4-cd0d-4f76-82ff-5575c3a11d5a
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Date deposited: 26 Jun 2025 16:59
Last modified: 27 Jun 2025 02:05
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Author:
Toni Karvonen
Author:
Filip Tronarp
Author:
Simo Särkkä
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