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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https://hal.inria.fr/hal-00805468
Contributor : Nicolas Durrande <>
Submitted on : Thursday, August 18, 2016 - 3:54:38 PM
Last modification on : Tuesday, October 23, 2018 - 2:36:08 PM

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  • HAL Id : hal-00805468, version 3
  • ARXIV : 1303.7090

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

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