Regularized spectrum estimation in spaces induced by stable spline kernels

G. Bottegal; G. Pillonetto

doi:10.1109/ACC.2012.6315037

Regularized spectrum estimation in spaces induced by stable spline kernels

G. Bottegal
, G. Pillonetto

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

Abstract

We introduce a new kernel-based nonparametric approach to estimate the second-order statistics of scalar and stationary stochastic processes. The correlations functions are assumed to be summable and are modeled as realizations of zero-mean Gaussian processes using the recently introduced Stable Spline kernel. In this way, information on the decay to zero of the functions to reconstruct is included in the estimation process. The overall complexity of the proposed algorithm scales linearly with the number of available samples of the processes. Numerical experiments show that the method compares favorably with respect to classical nonparametric spectral analysis approaches with an oracle-type choice of the parameters.

Original language	English
Title of host publication	2012 American Control Conference (ACC), 27-29 June 2012, Montreal, Canada
Place of Publication	Piscataway
Publisher	Institute of Electrical and Electronics Engineers
Pages	2695-2700
Number of pages	6
ISBN (Electronic)	978-1-4577-1096-4
ISBN (Print)	978-1-4577-1095-7
DOIs	https://doi.org/10.1109/ACC.2012.6315037
Publication status	Published - 2012
Externally published	Yes
Event	2012 American Control Conference, ACC 2012 - Fairmont Queen Elizabeth, Montreal, Canada Duration: 27 Jun 2012 → 29 Jun 2012 http://acc2012.a2c2.org/ http://acc2012.a2c2.org/index.php

Conference

Conference	2012 American Control Conference, ACC 2012
Abbreviated title	ACC 2012
Country/Territory	Canada
City	Montreal
Period	27/06/12 → 29/06/12
Internet address	http://acc2012.a2c2.org/ http://acc2012.a2c2.org/index.php

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10.1109/ACC.2012.6315037

Cite this

@inproceedings{a63b9b3ffcfe4d45b060aa6838cf1e56,

title = "Regularized spectrum estimation in spaces induced by stable spline kernels",

abstract = "We introduce a new kernel-based nonparametric approach to estimate the second-order statistics of scalar and stationary stochastic processes. The correlations functions are assumed to be summable and are modeled as realizations of zero-mean Gaussian processes using the recently introduced Stable Spline kernel. In this way, information on the decay to zero of the functions to reconstruct is included in the estimation process. The overall complexity of the proposed algorithm scales linearly with the number of available samples of the processes. Numerical experiments show that the method compares favorably with respect to classical nonparametric spectral analysis approaches with an oracle-type choice of the parameters.",

author = "G. Bottegal and G. Pillonetto",

year = "2012",

doi = "10.1109/ACC.2012.6315037",

language = "English",

isbn = "978-1-4577-1095-7",

pages = "2695--2700",

booktitle = "2012 American Control Conference (ACC), 27-29 June 2012, Montreal, Canada",

publisher = "Institute of Electrical and Electronics Engineers",

address = "United States",

note = "2012 American Control Conference, ACC 2012, ACC 2012 ; Conference date: 27-06-2012 Through 29-06-2012",

url = "http://acc2012.a2c2.org/, http://acc2012.a2c2.org/index.php",

}

Bottegal, G & Pillonetto, G 2012, Regularized spectrum estimation in spaces induced by stable spline kernels. in 2012 American Control Conference (ACC), 27-29 June 2012, Montreal, Canada. Institute of Electrical and Electronics Engineers, Piscataway, pp. 2695-2700, 2012 American Control Conference, ACC 2012, Montreal, Quebec, Canada, 27/06/12. https://doi.org/10.1109/ACC.2012.6315037

Regularized spectrum estimation in spaces induced by stable spline kernels. / Bottegal, G.; Pillonetto, G.
2012 American Control Conference (ACC), 27-29 June 2012, Montreal, Canada. Piscataway: Institute of Electrical and Electronics Engineers, 2012. p. 2695-2700.

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

TY - GEN

T1 - Regularized spectrum estimation in spaces induced by stable spline kernels

AU - Bottegal, G.

AU - Pillonetto, G.

PY - 2012

Y1 - 2012

N2 - We introduce a new kernel-based nonparametric approach to estimate the second-order statistics of scalar and stationary stochastic processes. The correlations functions are assumed to be summable and are modeled as realizations of zero-mean Gaussian processes using the recently introduced Stable Spline kernel. In this way, information on the decay to zero of the functions to reconstruct is included in the estimation process. The overall complexity of the proposed algorithm scales linearly with the number of available samples of the processes. Numerical experiments show that the method compares favorably with respect to classical nonparametric spectral analysis approaches with an oracle-type choice of the parameters.

AB - We introduce a new kernel-based nonparametric approach to estimate the second-order statistics of scalar and stationary stochastic processes. The correlations functions are assumed to be summable and are modeled as realizations of zero-mean Gaussian processes using the recently introduced Stable Spline kernel. In this way, information on the decay to zero of the functions to reconstruct is included in the estimation process. The overall complexity of the proposed algorithm scales linearly with the number of available samples of the processes. Numerical experiments show that the method compares favorably with respect to classical nonparametric spectral analysis approaches with an oracle-type choice of the parameters.

U2 - 10.1109/ACC.2012.6315037

DO - 10.1109/ACC.2012.6315037

M3 - Conference contribution

SN - 978-1-4577-1095-7

SP - 2695

EP - 2700

BT - 2012 American Control Conference (ACC), 27-29 June 2012, Montreal, Canada

PB - Institute of Electrical and Electronics Engineers

CY - Piscataway

T2 - 2012 American Control Conference, ACC 2012

Y2 - 27 June 2012 through 29 June 2012

ER -

Regularized spectrum estimation in spaces induced by stable spline kernels

Abstract

Conference

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