On the use of gradient information in Gaussian process quadratures

Jakub Pruher; Simo Särkkä

doi:10.1109/MLSP.2016.7738903

On the use of gradient information in Gaussian process quadratures

University of West Bohemia

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

6 Sitaatiot (Scopus)

Abstrakti

Gaussian process quadrature is a promising alternative Bayesian approach to numerical integration, which offers attractive advantages over its well-known classical counterparts. We show how Gaussian process quadrature can naturally incorporate gradient information about the integrand. These results are applied for the design of transformation of means and covariances of Gaussian random variables. We theoretically analyze connections between our proposed moment transform and the linearization transform based on Taylor series. Numerical experiments on common sensor network nonlinearities show that adding gradient information improves the resulting estimates.

Alkuperäiskieli	Englanti
Otsikko	Proceedings of the 26th IEEE International Workshop on Machine Learning for Signal Processing, MLSP 2016
Toimittajat	Francesco 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.2016.7738903
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.2016.7738903

Muut tiedostot ja linkit

Link to publication in Scopus

Siteeraa tätä

Pruher, J., & Särkkä, S. (2016). On the use of gradient information in Gaussian process quadratures. teoksessa F. A. N. Palmieri, A. Uncini, K. Diamantaras, & J. Larsen (Toimittajat), Proceedings of the 26th IEEE International Workshop on Machine Learning for Signal Processing, MLSP 2016 (Vuosikerta 2016-November). Artikkeli 7738903 (IEEE International Workshop on Machine Learning for Signal Processing). IEEE. https://doi.org/10.1109/MLSP.2016.7738903

Pruher, Jakub ; Särkkä, Simo. / On the use of gradient information in Gaussian process quadratures. Proceedings of the 26th IEEE International Workshop on Machine Learning for Signal Processing, MLSP 2016. Toimittaja / Francesco A.N. Palmieri ; Aurelio Uncini ; Kostas Diamantaras ; Jan Larsen. Vuosikerta 2016-November IEEE, 2016. (IEEE International Workshop on Machine Learning for Signal Processing).

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title = "On the use of gradient information in Gaussian process quadratures",

abstract = "Gaussian process quadrature is a promising alternative Bayesian approach to numerical integration, which offers attractive advantages over its well-known classical counterparts. We show how Gaussian process quadrature can naturally incorporate gradient information about the integrand. These results are applied for the design of transformation of means and covariances of Gaussian random variables. We theoretically analyze connections between our proposed moment transform and the linearization transform based on Taylor series. Numerical experiments on common sensor network nonlinearities show that adding gradient information improves the resulting estimates.",

keywords = "Bayesian quadrature, derivative, Gaussian process quadrature, gradient, moment transformation",

author = "Jakub Pruher and Simo S{\"a}rkk{\"a}",

year = "2016",

month = nov,

day = "8",

doi = "10.1109/MLSP.2016.7738903",

language = "English",

volume = "2016-November",

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

publisher = "IEEE",

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

booktitle = "Proceedings of the 26th 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",

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Pruher, J & Särkkä, S 2016, On the use of gradient information in Gaussian process quadratures. julkaisussa FAN Palmieri, A Uncini, K Diamantaras & J Larsen (toim), Proceedings of the 26th IEEE International Workshop on Machine Learning for Signal Processing, MLSP 2016. Vuosikerta 2016-November, 7738903, 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.2016.7738903

On the use of gradient information in Gaussian process quadratures. / Pruher, Jakub; Särkkä, Simo.
Proceedings of the 26th IEEE International Workshop on Machine Learning for Signal Processing, MLSP 2016. toim. / Francesco A.N. Palmieri; Aurelio Uncini; Kostas Diamantaras; Jan Larsen. Vuosikerta 2016-November IEEE, 2016. 7738903 (IEEE International Workshop on Machine Learning for Signal Processing).

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

TY - GEN

T1 - On the use of gradient information in Gaussian process quadratures

AU - Pruher, Jakub

AU - Särkkä, Simo

N1 - Conference code: 26

PY - 2016/11/8

Y1 - 2016/11/8

N2 - Gaussian process quadrature is a promising alternative Bayesian approach to numerical integration, which offers attractive advantages over its well-known classical counterparts. We show how Gaussian process quadrature can naturally incorporate gradient information about the integrand. These results are applied for the design of transformation of means and covariances of Gaussian random variables. We theoretically analyze connections between our proposed moment transform and the linearization transform based on Taylor series. Numerical experiments on common sensor network nonlinearities show that adding gradient information improves the resulting estimates.

AB - Gaussian process quadrature is a promising alternative Bayesian approach to numerical integration, which offers attractive advantages over its well-known classical counterparts. We show how Gaussian process quadrature can naturally incorporate gradient information about the integrand. These results are applied for the design of transformation of means and covariances of Gaussian random variables. We theoretically analyze connections between our proposed moment transform and the linearization transform based on Taylor series. Numerical experiments on common sensor network nonlinearities show that adding gradient information improves the resulting estimates.

KW - Bayesian quadrature

KW - derivative

KW - Gaussian process quadrature

KW - gradient

KW - moment transformation

UR - http://www.scopus.com/inward/record.url?scp=85002188812&partnerID=8YFLogxK

U2 - 10.1109/MLSP.2016.7738903

DO - 10.1109/MLSP.2016.7738903

M3 - Conference article in proceedings

AN - SCOPUS:85002188812

VL - 2016-November

T3 - IEEE International Workshop on Machine Learning for Signal Processing

BT - Proceedings of the 26th IEEE International Workshop on Machine Learning for Signal Processing, MLSP 2016

A2 - Palmieri, Francesco 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 -

Pruher J, Särkkä S. On the use of gradient information in Gaussian process quadratures. julkaisussa Palmieri FAN, Uncini A, Diamantaras K, Larsen J, toimittajat, Proceedings of the 26th IEEE International Workshop on Machine Learning for Signal Processing, MLSP 2016. Vuosikerta 2016-November. IEEE. 2016. 7738903. (IEEE International Workshop on Machine Learning for Signal Processing). doi: 10.1109/MLSP.2016.7738903

On the use of gradient information in Gaussian process quadratures

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Julkaisusarja

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