Detecting periodicities with Gaussian processes

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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https://hal-emse.ccsd.cnrs.fr/emse-01351044
Contributor : Florent Breuil <>
Submitted on : Tuesday, August 2, 2016 - 3:30:19 PM
Last modification on : Tuesday, May 7, 2019 - 1:21:25 AM

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Nicolas Durrande, James Hensman, Magnus Rattray, Neil D. Lawrence. Detecting periodicities with Gaussian processes. PeerJ Computer Science, PeerJ, 2016, 2, ⟨10.7717/peerj-cs.50⟩. ⟨emse-01351044⟩

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