Detecting Periodicities with Gaussian processes

Nicolas Durrande; James Hensman; Magnus Rattray; Neil D. Lawrence

doi:10.7717/peerj-cs.50

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Detecting Periodicities with Gaussian processes

Nicolas Durrande, James Hensman, Magnus Rattray, Neil D. Lawrence

PeerJ Computer Science, 4:e50, 2016.

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.

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Cite this Paper

BibTeX


@Article{Durrande-periodicities16,
  title = 	 {Detecting periodicities with {G}aussian processes},
  author = 	 {Durrande, Nicolas and Hensman, James and Rattray, Magnus and Lawrence, Neil D.},
  journal =      {PeerJ Computer Science},
  year = 	 {2016},
  volume = 	 {4},
  doi = 	 {10.7717/peerj-cs.50},
  pdf = 	 {https://peerj.com/articles/cs-50.pdf},
  url = 	 {/publications/durrande-periodicities16.html},
  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.}
}

Endnote

%0 Journal Article
%T Detecting Periodicities with Gaussian processes
%A Nicolas Durrande
%A James Hensman
%A Magnus Rattray
%A Neil D. Lawrence
%J PeerJ Computer Science
%D 2016	
%F Durrande-periodicities16
%R 10.7717/peerj-cs.50
%U /publications/durrande-periodicities16.html
%V 4
%X 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.

RIS


TY  - JOUR
TI  - Detecting Periodicities with Gaussian processes
AU  - Nicolas Durrande
AU  - James Hensman
AU  - Magnus Rattray
AU  - Neil D. Lawrence
DA  - 2016/04/13	
ID  - Durrande-periodicities16
VL  - 4
SP  - e50
DO  - 10.7717/peerj-cs.50
L1  - https://peerj.com/articles/cs-50.pdf
UR  - /publications/durrande-periodicities16.html
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.
ER  -

APA


Durrande, N., Hensman, J., Rattray, M. & Lawrence, N.D.. (2016). Detecting Periodicities with Gaussian processes. PeerJ Computer Science 4:e50 doi:10.7717/peerj-cs.50 Available from /publications/durrande-periodicities16.html.