Non-Stationary Spectral Kernels

Sami Remes; Markus Heinonen; Samuel Kaski

Non-Stationary Spectral Kernels

Sami Remes, Markus Heinonen, Samuel Kaski

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Scientific › peer-review

16 Citations (Scopus)

Abstract

We propose non-stationary spectral kernels for Gaussian process regression. We propose to model the spectral density of a non-stationary kernel function as a mixture of input-dependent Gaussian process frequency density surfaces. We solve the generalised Fourier transform with such a model, and present a family of non-stationary and non-monotonic kernels that can learn input-dependent and potentially long-range, non-monotonic covariances between inputs. We derive efficient inference using model whitening and marginalized posterior, and show with case studies that these kernels are necessary when modelling even rather simple time series, image or geospatial data with non-stationary characteristics.

Original language	English
Title of host publication	Advances in Neural Information Processing Systems 30
Subtitle of host publication	Proceedings of NIPS2017
Publisher	Curran Associates, Inc.
Pages	4645-4654
Publication status	Published - 2017
MoE publication type	A4 Article in a conference publication
Event	NIPS Symposium on Interpretable Machine Learning - Long Beach, Los Angeles, United States Duration: 4 Dec 2017 → 9 Dec 2017 Conference number: 31

Publication series

Name	Advances in Neural Information Processing Systems
Publisher	Curran Associates
Volume	30
ISSN (Print)	1049-5258

Conference

Conference	NIPS Symposium on Interpretable Machine Learning
Country	United States
City	Los Angeles
Period	04/12/2017 → 09/12/2017

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@inproceedings{e29a7f5333d4498a9b65a236acc2301b,

title = "Non-Stationary Spectral Kernels",

abstract = "We propose non-stationary spectral kernels for Gaussian process regression. We propose to model the spectral density of a non-stationary kernel function as a mixture of input-dependent Gaussian process frequency density surfaces. We solve the generalised Fourier transform with such a model, and present a family of non-stationary and non-monotonic kernels that can learn input-dependent and potentially long-range, non-monotonic covariances between inputs. We derive efficient inference using model whitening and marginalized posterior, and show with case studies that these kernels are necessary when modelling even rather simple time series, image or geospatial data with non-stationary characteristics.",

author = "Sami Remes and Markus Heinonen and Samuel Kaski",

note = "Odottele, ett{\"a} julkaisu tulee ulos kes{\"a}ll{\"a} ja lis{\"a}{\"a} ISBN. Asiasta sovittu Samuel Kasken ja Markus Heinosen kanssa tammikuussa.; NIPS Symposium on Interpretable Machine Learning ; Conference date: 04-12-2017 Through 09-12-2017",

year = "2017",

language = "English",

series = "Advances in Neural Information Processing Systems",

publisher = "Curran Associates, Inc.",

pages = "4645--4654",

booktitle = "Advances in Neural Information Processing Systems 30",

}

Remes, S, Heinonen, M & Kaski, S 2017, Non-Stationary Spectral Kernels. in Advances in Neural Information Processing Systems 30: Proceedings of NIPS2017. Advances in Neural Information Processing Systems, vol. 30, Curran Associates, Inc., pp. 4645-4654, NIPS Symposium on Interpretable Machine Learning, Los Angeles, United States, 04/12/2017. <https://arxiv.org/abs/1705.08736>

Non-Stationary Spectral Kernels. / Remes, Sami; Heinonen, Markus ; Kaski, Samuel.

Advances in Neural Information Processing Systems 30: Proceedings of NIPS2017. Curran Associates, Inc., 2017. p. 4645-4654 (Advances in Neural Information Processing Systems; Vol. 30).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Scientific › peer-review

TY - GEN

T1 - Non-Stationary Spectral Kernels

AU - Remes, Sami

AU - Heinonen, Markus

AU - Kaski, Samuel

N1 - Conference code: 31

PY - 2017

Y1 - 2017

N2 - We propose non-stationary spectral kernels for Gaussian process regression. We propose to model the spectral density of a non-stationary kernel function as a mixture of input-dependent Gaussian process frequency density surfaces. We solve the generalised Fourier transform with such a model, and present a family of non-stationary and non-monotonic kernels that can learn input-dependent and potentially long-range, non-monotonic covariances between inputs. We derive efficient inference using model whitening and marginalized posterior, and show with case studies that these kernels are necessary when modelling even rather simple time series, image or geospatial data with non-stationary characteristics.

AB - We propose non-stationary spectral kernels for Gaussian process regression. We propose to model the spectral density of a non-stationary kernel function as a mixture of input-dependent Gaussian process frequency density surfaces. We solve the generalised Fourier transform with such a model, and present a family of non-stationary and non-monotonic kernels that can learn input-dependent and potentially long-range, non-monotonic covariances between inputs. We derive efficient inference using model whitening and marginalized posterior, and show with case studies that these kernels are necessary when modelling even rather simple time series, image or geospatial data with non-stationary characteristics.

UR - https://arxiv.org/abs/1705.08736

UR - http://papers.nips.cc/paper/7050-non-stationary-spectral-kernels.pdf

M3 - Conference contribution

T3 - Advances in Neural Information Processing Systems

SP - 4645

EP - 4654

BT - Advances in Neural Information Processing Systems 30

PB - Curran Associates, Inc.

T2 - NIPS Symposium on Interpretable Machine Learning

Y2 - 4 December 2017 through 9 December 2017

ER -