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
%P 0--0
%R 10.7717/peerj-cs.50
%U http://inverseprobability.com/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.

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