Approximate state-space Gaussian processes via spectral transformation

Toni Karvonen; Simo Särkkä

doi:10.1109/MLSP.2016.7738812

Approximate state-space Gaussian processes via spectral transformation

Tutkimustuotos: Artikkeli kirjassa/konferenssijulkaisussa › Conference article in proceedings › Scientific › vertaisarvioitu

8 Sitaatiot (Scopus)

295 Lataukset (Pure)

Abstrakti

State-space representations of Gaussian process regression use Kalman filtering and smoothing theory to downscale the computational complexity of the regression in the number of data points from cubic to linear. As their exact implementation requires the covariance function to possess rational spectral density, rational approximations to the spectral density must be often used. In this article we introduce new spectral transformation based methods for this purpose: a spectral composition method and a spectral preconditioning method. We study convergence of the approximations theoretically and run numerical experiments to attest their accuracy for different densities, in particular the fractional Matern.

Alkuperäiskieli	Englanti
Otsikko	Proceedings of the 2016 IEEE International Workshop on Machine Learning for Signal Processing, MLSP 2016
Toimittajat	Fransesco A.N. Palmieri, Aurelio Uncini, Kostas Diamantaras, Jan Larsen
Kustantaja	IEEE
Vuosikerta	2016-November
ISBN (elektroninen)	9781509007462
DOI - pysyväislinkit	https://doi.org/10.1109/MLSP.2016.7738812
Tila	Julkaistu - 8 marrask. 2016
OKM-julkaisutyyppi	A4 Artikkeli konferenssijulkaisussa
Tapahtuma	IEEE International Workshop on Machine Learning for Signal Processing - Salerno, Italia Kesto: 13 syysk. 2016 → 16 syysk. 2016 Konferenssinumero: 26 http://mlsp2016.conwiz.dk/home.htm

Julkaisusarja

Nimi	IEEE International Workshop on Machine Learning for Signal Processing
Kustantaja	IEEE COMPUTER SOCIETY PRESS
ISSN (painettu)	2161-0363
ISSN (elektroninen)	2161-0371

Workshop

Workshop	IEEE International Workshop on Machine Learning for Signal Processing
Lyhennettä	MLSP
Maa/Alue	Italia
Kaupunki	Salerno
Ajanjakso	13/09/2016 → 16/09/2016
www-osoite	http://mlsp2016.conwiz.dk/home.htm

Pääsy asiakirjaan

10.1109/MLSP.2016.7738812

karvonen_sarkka_MLSP_2016_7738812Accepted author manuscript, 368 KB

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Link to publication in Scopus

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Karvonen, T., & Särkkä, S. (2016). Approximate state-space Gaussian processes via spectral transformation. teoksessa F. A. N. Palmieri, A. Uncini, K. Diamantaras, & J. Larsen (Toimittajat), Proceedings of the 2016 IEEE International Workshop on Machine Learning for Signal Processing, MLSP 2016 (Vuosikerta 2016-November). Artikkeli 7738812 (IEEE International Workshop on Machine Learning for Signal Processing). IEEE. https://doi.org/10.1109/MLSP.2016.7738812

Karvonen, Toni ; Särkkä, Simo. / Approximate state-space Gaussian processes via spectral transformation. Proceedings of the 2016 IEEE International Workshop on Machine Learning for Signal Processing, MLSP 2016. Toimittaja / Fransesco A.N. Palmieri ; Aurelio Uncini ; Kostas Diamantaras ; Jan Larsen. Vuosikerta 2016-November IEEE, 2016. (IEEE International Workshop on Machine Learning for Signal Processing).

@inproceedings{b6f103f9f3ce45edbdb2bb013a22288f,

title = "Approximate state-space Gaussian processes via spectral transformation",

abstract = "State-space representations of Gaussian process regression use Kalman filtering and smoothing theory to downscale the computational complexity of the regression in the number of data points from cubic to linear. As their exact implementation requires the covariance function to possess rational spectral density, rational approximations to the spectral density must be often used. In this article we introduce new spectral transformation based methods for this purpose: a spectral composition method and a spectral preconditioning method. We study convergence of the approximations theoretically and run numerical experiments to attest their accuracy for different densities, in particular the fractional Matern.",

keywords = "composite approximation, fractional Mat{\'e}rn, Gaussian process regression, spectral preconditioning, state-space approximation",

author = "Toni Karvonen and Simo S{\"a}rkk{\"a}",

year = "2016",

month = nov,

day = "8",

doi = "10.1109/MLSP.2016.7738812",

language = "English",

volume = "2016-November",

series = "IEEE International Workshop on Machine Learning for Signal Processing",

publisher = "IEEE",

editor = "Palmieri, {Fransesco A.N.} and Aurelio Uncini and Kostas Diamantaras and Larsen, {Jan }",

booktitle = "Proceedings of the 2016 IEEE International Workshop on Machine Learning for Signal Processing, MLSP 2016",

address = "United States",

note = "IEEE International Workshop on Machine Learning for Signal Processing, MLSP ; Conference date: 13-09-2016 Through 16-09-2016",

url = "http://mlsp2016.conwiz.dk/home.htm",

}

Karvonen, T & Särkkä, S 2016, Approximate state-space Gaussian processes via spectral transformation. julkaisussa FAN Palmieri, A Uncini, K Diamantaras & J Larsen (toim), Proceedings of the 2016 IEEE International Workshop on Machine Learning for Signal Processing, MLSP 2016. Vuosikerta 2016-November, 7738812, IEEE International Workshop on Machine Learning for Signal Processing, IEEE, IEEE International Workshop on Machine Learning for Signal Processing, Salerno, Italia, 13/09/2016. https://doi.org/10.1109/MLSP.2016.7738812

Approximate state-space Gaussian processes via spectral transformation. / Karvonen, Toni; Särkkä, Simo.
Proceedings of the 2016 IEEE International Workshop on Machine Learning for Signal Processing, MLSP 2016. toim. / Fransesco A.N. Palmieri; Aurelio Uncini; Kostas Diamantaras; Jan Larsen. Vuosikerta 2016-November IEEE, 2016. 7738812 (IEEE International Workshop on Machine Learning for Signal Processing).

Tutkimustuotos: Artikkeli kirjassa/konferenssijulkaisussa › Conference article in proceedings › Scientific › vertaisarvioitu

TY - GEN

T1 - Approximate state-space Gaussian processes via spectral transformation

AU - Karvonen, Toni

AU - Särkkä, Simo

N1 - Conference code: 26

PY - 2016/11/8

Y1 - 2016/11/8

N2 - State-space representations of Gaussian process regression use Kalman filtering and smoothing theory to downscale the computational complexity of the regression in the number of data points from cubic to linear. As their exact implementation requires the covariance function to possess rational spectral density, rational approximations to the spectral density must be often used. In this article we introduce new spectral transformation based methods for this purpose: a spectral composition method and a spectral preconditioning method. We study convergence of the approximations theoretically and run numerical experiments to attest their accuracy for different densities, in particular the fractional Matern.

AB - State-space representations of Gaussian process regression use Kalman filtering and smoothing theory to downscale the computational complexity of the regression in the number of data points from cubic to linear. As their exact implementation requires the covariance function to possess rational spectral density, rational approximations to the spectral density must be often used. In this article we introduce new spectral transformation based methods for this purpose: a spectral composition method and a spectral preconditioning method. We study convergence of the approximations theoretically and run numerical experiments to attest their accuracy for different densities, in particular the fractional Matern.

KW - composite approximation

KW - fractional Matérn

KW - Gaussian process regression

KW - spectral preconditioning

KW - state-space approximation

UR - http://www.scopus.com/inward/record.url?scp=85002179430&partnerID=8YFLogxK

U2 - 10.1109/MLSP.2016.7738812

DO - 10.1109/MLSP.2016.7738812

M3 - Conference article in proceedings

AN - SCOPUS:85002179430

VL - 2016-November

T3 - IEEE International Workshop on Machine Learning for Signal Processing

BT - Proceedings of the 2016 IEEE International Workshop on Machine Learning for Signal Processing, MLSP 2016

A2 - Palmieri, Fransesco A.N.

A2 - Uncini, Aurelio

A2 - Diamantaras, Kostas

A2 - Larsen, Jan

PB - IEEE

T2 - IEEE International Workshop on Machine Learning for Signal Processing

Y2 - 13 September 2016 through 16 September 2016

ER -

Karvonen T, Särkkä S. Approximate state-space Gaussian processes via spectral transformation. julkaisussa Palmieri FAN, Uncini A, Diamantaras K, Larsen J, toimittajat, Proceedings of the 2016 IEEE International Workshop on Machine Learning for Signal Processing, MLSP 2016. Vuosikerta 2016-November. IEEE. 2016. 7738812. (IEEE International Workshop on Machine Learning for Signal Processing). doi: 10.1109/MLSP.2016.7738812

Approximate state-space Gaussian processes via spectral transformation

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