Detecting periodicities with Gaussian processes

Nicolas DurrandeJames HensmanMagnus RattrayNeil D. Lawrence
,  4:0-0, 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
@InProceedings{pmlr-v-durrande-periodicities16, title = {Detecting periodicities with {G}aussian processes}, author = {Nicolas Durrande and James Hensman and Magnus Rattray and Neil D. Lawrence}, pages = {0--0}, year = {}, editor = {}, volume = {4}, 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 Conference Paper %T Detecting periodicities with Gaussian processes %A Nicolas Durrande %A James Hensman %A Magnus Rattray %A Neil D. Lawrence %B %C Proceedings of Machine Learning Research %D %E %F pmlr-v-durrande-periodicities16 %I PMLR %J Proceedings of Machine Learning Research %P 0--0 %R 10.7717/peerj-cs.50 %U http://inverseprobability.com %V %W PMLR %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 - CPAPER TI - Detecting periodicities with Gaussian processes AU - Nicolas Durrande AU - James Hensman AU - Magnus Rattray AU - Neil D. Lawrence BT - PY - DA - ED - ID - pmlr-v-durrande-periodicities16 PB - PMLR SP - 0 DP - PMLR EP - 0 DO - 10.7717/peerj-cs.50 L1 - 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.. (). Detecting periodicities with Gaussian processes. , in PMLR :0-0

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