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.

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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.

Item Type:
Journal Article
Journal or Publication Title:
PeerJ Computer Science
Subjects:
ID Code:
83542
Deposited By:
Deposited On:
14 Dec 2016 09:16
Refereed?:
Yes
Published?:
Published
Last Modified:
12 Aug 2020 05:47