Detecting periodicities with Gaussian processes - Archive ouverte HAL Access content directly
Journal Articles PeerJ Computer Science Year : 2016

Detecting periodicities with Gaussian processes

(1, 2, 3, 4) , (5) , (6) , (7, 8)
1
2
3
4
5
6
7
8

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.

Dates and versions

emse-01351044 , version 1 (02-08-2016)

Identifiers

Cite

Nicolas Durrande, James Hensman, Magnus Rattray, Neil D. Lawrence. Detecting periodicities with Gaussian processes. PeerJ Computer Science, 2016, 2, ⟨10.7717/peerj-cs.50⟩. ⟨emse-01351044⟩
185 View
0 Download

Altmetric

Share

Gmail Facebook Twitter LinkedIn More