Detecting periodicities with Gaussian processes

Durrande, Nicolas and Hensman, James and Rattray, Magnus and Lawrence, Neil D. (2016) Detecting periodicities with Gaussian processes. PeerJ Computer Science, 2: e50.

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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.

Item Type:
Journal Article
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PeerJ Computer Science
?? rkhsharmonic analysiscircadian rhythmgene expressionmatérn kernels ??
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14 Dec 2016 09:16
Last Modified:
15 Jul 2024 16:40