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.

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 = {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.} }
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 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.
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 - 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 -
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 http://inverseprobability.com/publications/durrande-periodicities16.html.

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