Detecting periodicities with Gaussian processes

[edit]

Nicolas Durrande, Ecole des Mines, St-Etienne
James Hensman, University of Lancaster
Magnus Rattray, University of Manchester
Neil D. Lawrence, University of Sheffield

PeerJ Computer Science 4, pp 0-0

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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.


@Article{durrande-periodicities16,
  title = 	 {Detecting periodicities with {G}aussian processes},
  journal =  	 {PeerJ Computer Science},
  author = 	 {Nicolas Durrande and James Hensman and Magnus Rattray and Neil D. Lawrence},
  pages = 	 {0},
  year = 	 {2016},
  volume = 	 {4},
  month = 	 {00},
  edit = 	 {https://github.com/lawrennd//publications/edit/gh-pages/_posts/2016-04-13-durrande-periodicities16.md},
  url =  	 {http://inverseprobability.com/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.},
  key = 	 {Durrande-periodicities16},
  doi = 	 {10.7717/peerj-cs.50},
  linkpdf = 	 {https://peerj.com/articles/cs-50.pdf},
  OPTgroup = 	 {}
 

}
%T Detecting periodicities with Gaussian processes
%A Nicolas Durrande and James Hensman and Magnus Rattray and Neil D. Lawrence
%B 
%C PeerJ Computer Science
%D 
%F durrande-periodicities16
%J PeerJ Computer Science	
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%R 10.7717/peerj-cs.50
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%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.
TY  - CPAPER
TI  - Detecting periodicities with Gaussian processes
AU  - Nicolas Durrande
AU  - James Hensman
AU  - Magnus Rattray
AU  - Neil D. Lawrence
PY  - 2016/04/13
DA  - 2016/04/13	
ID  - durrande-periodicities16	
SP  - 0
EP  - 0
DO  - 10.7717/peerj-cs.50
L1  - https://peerj.com/articles/cs-50.pdf
UR  - http://inverseprobability.com/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  -

Durrande, N., Hensman, J., Rattray, M. & Lawrence, N.D.. (2016). Detecting periodicities with Gaussian processes. PeerJ Computer Science 4:0-0