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# Detecting periodicities with Gaussian processes

Nicolas Durrande, James Hensman, Magnus Rattray, Neil D. Lawrence, 4:0-0, 2016.

#### 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.

#### Cite this Paper

BibTeX

```
@InProceedings{pmlr-v-durrande-periodicities16,
title = {Detecting periodicities with {G}aussian processes},
author = {Nicolas Durrande and James Hensman and Magnus Rattray and Neil D. Lawrence},
pages = {0--0},
year = {},
editor = {},
volume = {4},
url = {http://inverseprobability.com/publications/durrande-periodicities16.html},
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.}
}
```

Endnote

```
%0 Conference Paper
%T Detecting periodicities with Gaussian processes
%A Nicolas Durrande
%A James Hensman
%A Magnus Rattray
%A Neil D. Lawrence
%B
%C Proceedings of Machine Learning Research
%D
%E
%F pmlr-v-durrande-periodicities16
%I PMLR
%J Proceedings of Machine Learning Research
%P 0--0
%R 10.7717/peerj-cs.50
%U http://inverseprobability.com
%V
%W PMLR
%X 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.
```

RIS

```
TY - CPAPER
TI - Detecting periodicities with Gaussian processes
AU - Nicolas Durrande
AU - James Hensman
AU - Magnus Rattray
AU - Neil D. Lawrence
BT -
PY -
DA -
ED -
ID - pmlr-v-durrande-periodicities16
PB - PMLR
SP - 0
DP - PMLR
EP - 0
DO - 10.7717/peerj-cs.50
L1 -
UR - http://inverseprobability.com/publications/durrande-periodicities16.html
AB - 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.
ER -
```

APA

`Durrande, N., Hensman, J., Rattray, M. & Lawrence, N.D.. (). Detecting periodicities with Gaussian processes. `*, in PMLR* :0-0

#### Related Material

BibTeX

```
@InProceedings{/durrande-periodicities16,
title = {Detecting periodicities with {G}aussian processes},
author = {Nicolas Durrande and James Hensman and Magnus Rattray and Neil D. Lawrence},
pages = {0--0},
year = {},
editor = {},
volume = {4},
url = {http://inverseprobability.com/publications/durrande-periodicities16.html},
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.}
}
```

Endnote

```
%0 Conference Paper
%T Detecting periodicities with Gaussian processes
%A Nicolas Durrande
%A James Hensman
%A Magnus Rattray
%A Neil D. Lawrence
%B
%C Proceedings of Machine Learning Research
%D
%E
%F /durrande-periodicities16
%I PMLR
%J Proceedings of Machine Learning Research
%P 0--0
%R 10.7717/peerj-cs.50
%U http://inverseprobability.com
%V
%W PMLR
%X 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.
```

RIS

```
TY - CPAPER
TI - Detecting periodicities with Gaussian processes
AU - Nicolas Durrande
AU - James Hensman
AU - Magnus Rattray
AU - Neil D. Lawrence
BT -
PY -
DA -
ED -
ID - /durrande-periodicities16
PB - PMLR
SP - 0
DP - PMLR
EP - 0
DO - 10.7717/peerj-cs.50
L1 -
UR - http://inverseprobability.com/publications/durrande-periodicities16.html
AB - 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.
ER -
```

APA

`Durrande, N., Hensman, J., Rattray, M. & Lawrence, N.D.. (). Detecting periodicities with Gaussian processes. `*, in PMLR* :0-0