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Journal Articles PeerJ Computer Science Year : 2016

Gaussian process models for periodicity detection

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 Mat\'ern 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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Dates and versions

hal-00805468 , version 1 (28-03-2013)
hal-00805468 , version 2 (16-02-2016)
hal-00805468 , version 3 (18-08-2016)

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Cite

Nicolas Durrande, James Hensman, Magnus Rattray, Neil D. Lawrence. Gaussian process models for periodicity detection. PeerJ Computer Science, 2016. ⟨hal-00805468v3⟩
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