Durrande, N., Hensman, J., Rattray, M. et al. (1 more author) (2016) Detecting periodicities with Gaussian processes. PeerJ Computer Science, 2. e50. ISSN 2376-5992
Abstract
We consider the problem of detecting and quantifying the periodic component of a function given noise-corrupted observations of a limited number of input/output tuples. Our approach is based on Gaussian process regression, which provides a flexible non-parametric framework for modelling periodic data. We introduce a novel decomposition of the covariance function as the sum of periodic and aperiodic kernels. This decomposition allows for the creation of sub-models which capture the periodic nature of the signal and its complement. To quantify the periodicity of the signal, we derive a periodicity ratio which reflects the uncertainty in the fitted sub-models. Although the method can be applied to many kernels, we give a special emphasis to the Matérn family, from the expression of the reproducing kernel Hilbert space inner product to the implementation of the associated periodic kernels in a Gaussian process toolkit. The proposed method is illustrated by considering the detection of periodically expressed genes in the arabidopsis genome.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2016 Durrande et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, reproduction and adaptation in any medium and for any purpose provided that it is properly attributed. For attribution, the original author(s), title, publication source (PeerJ Computer Science) and either DOI or URL of the article must be cited. |
Keywords: | RKHS; Harmonic analysis; Circadian rhythm; Gene expression; Matérn kernels |
Dates: |
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Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Engineering (Sheffield) > Department of Computer Science (Sheffield) |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 14 Mar 2018 15:39 |
Last Modified: | 14 Mar 2018 15:39 |
Published Version: | https://doi.org/10.7717/peerj-cs.50 |
Status: | Published |
Publisher: | PeerJ |
Refereed: | Yes |
Identification Number: | 10.7717/peerj-cs.50 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:128528 |