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A probabilistic Taylor expansion with Gaussian processes

Karvonen, Toni ; Cockayne, Jon ; Tronarp, Filip LU and Särkkä, Simo (2023) In 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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; ; and
organization
publishing date
type
Contribution to journal
publication status
published
subject
in
Transactions on Machine Learning Research
volume
2023
external identifiers
  • scopus:86000119210
ISSN
2835-8856
language
English
LU publication?
yes
id
419b544d-9645-40c4-82a6-1ad653823e40
date added to LUP
2025-06-05 11:29:38
date last changed
2025-06-05 11:30:01
@article{419b544d-9645-40c4-82a6-1ad653823e40,
  abstract     = {{<p>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.</p>}},
  author       = {{Karvonen, Toni and Cockayne, Jon and Tronarp, Filip and Särkkä, Simo}},
  issn         = {{2835-8856}},
  language     = {{eng}},
  series       = {{Transactions on Machine Learning Research}},
  title        = {{A probabilistic Taylor expansion with Gaussian processes}},
  volume       = {{2023}},
  year         = {{2023}},
}