Detecting periodicities with gaussian processes

Nicolas Durrande, James Hensman, Magnus Rattray, Neil D. Lawrence

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Article numbere50
JournalPeerJ Computer Science
Issue number4
Publication statusPublished - 13 Apr 2016


  • Circadian rhythm
  • Gene expression
  • Harmonic analysis
  • Matérn kernels
  • RKHS


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