Gaussian process models for periodicity detection

TL;DR

This paper introduces a Gaussian process-based method for detecting and quantifying periodic signals in noisy data, emphasizing a novel covariance decomposition and a periodicity ratio, with applications to gene expression analysis.

Contribution

It presents a new covariance decomposition approach and a periodicity ratio for Gaussian process models, enhancing periodicity detection in noisy, limited data scenarios.

Findings

Effective detection of periodic signals in noisy data.

Application to gene expression data demonstrates practical utility.

Special focus on Matérn kernels improves model flexibility.

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.