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Detecting periodicities with Gaussian processes

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Detecting periodicities with Gaussian processes. / Durrande, Nicolas; Hensman, James; Rattray, Magnus; Lawrence, Neil D.

In: PeerJ Computer Science, Vol. 2, e50, 13.04.2016.

Research output: Contribution to journalJournal article

Harvard

Durrande, N, Hensman, J, Rattray, M & Lawrence, ND 2016, 'Detecting periodicities with Gaussian processes', PeerJ Computer Science, vol. 2, e50. https://doi.org/10.7717/peerj-cs.50

APA

Durrande, N., Hensman, J., Rattray, M., & Lawrence, N. D. (2016). Detecting periodicities with Gaussian processes. PeerJ Computer Science, 2, [e50]. https://doi.org/10.7717/peerj-cs.50

Vancouver

Durrande N, Hensman J, Rattray M, Lawrence ND. Detecting periodicities with Gaussian processes. PeerJ Computer Science. 2016 Apr 13;2. e50. https://doi.org/10.7717/peerj-cs.50

Author

Durrande, Nicolas ; Hensman, James ; Rattray, Magnus ; Lawrence, Neil D. / Detecting periodicities with Gaussian processes. In: PeerJ Computer Science. 2016 ; Vol. 2.

Bibtex

@article{be03cb4f56384e88ab23a3a486243537,
title = "Detecting periodicities with Gaussian processes",
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 Mat{\'e}rn 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.",
keywords = "RKHS, Harmonic analysis, Circadian rhythm, Gene expression, Mat{\'e}rn kernels",
author = "Nicolas Durrande and James Hensman and Magnus Rattray and Lawrence, {Neil D.}",
year = "2016",
month = "4",
day = "13",
doi = "10.7717/peerj-cs.50",
language = "English",
volume = "2",
journal = "PeerJ Computer Science",
issn = "2376-5992",
publisher = "PeerJ Inc.",

}

RIS

TY - JOUR

T1 - Detecting periodicities with Gaussian processes

AU - Durrande, Nicolas

AU - Hensman, James

AU - Rattray, Magnus

AU - Lawrence, Neil D.

PY - 2016/4/13

Y1 - 2016/4/13

N2 - 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.

AB - 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.

KW - RKHS

KW - Harmonic analysis

KW - Circadian rhythm

KW - Gene expression

KW - Matérn kernels

U2 - 10.7717/peerj-cs.50

DO - 10.7717/peerj-cs.50

M3 - Journal article

VL - 2

JO - PeerJ Computer Science

JF - PeerJ Computer Science

SN - 2376-5992

M1 - e50

ER -