Performance bounds for sparse parametric covariance estimation in Gaussian models

Alexander Jung; Sebastian Schmutzhard; Franz Hlawatsch; Alfred O. Hero

doi:10.1109/ICASSP.2011.5947268

Performance bounds for sparse parametric covariance estimation in Gaussian models

Alexander Jung^*
, Sebastian Schmutzhard
, Franz Hlawatsch
, Alfred O. Hero

^*Tämän työn vastaava kirjoittaja

Ei julkaistu Aalto-yliopiston affiliaatiolla

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

1 Sitaatiot (Scopus)

Abstrakti

We consider estimation of a sparse parameter vector that determines the covariance matrix of a Gaussian random vector via a sparse expansion into known "basis matrices." Using the theory of reproducing kernel Hilbert spaces, we derive lower bounds on the variance of estimators with a given mean function. This includes unbiased estimation as a special case. We also present a numerical comparison of our lower bounds with the variance of two standard estimators (hard-thresholding estimator and maximum likelihood estimator).

Alkuperäiskieli	Englanti
Otsikko	2011 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2011 - Proceedings
Sivut	4156-4159
Sivumäärä	4
DOI - pysyväislinkit	https://doi.org/10.1109/ICASSP.2011.5947268
Tila	Julkaistu - 2011
OKM-julkaisutyyppi	A4 Artikkeli konferenssijulkaisussa
Tapahtuma	IEEE International Conference on Acoustics, Speech, and Signal Processing - Prague, Tshekki Kesto: 22 toukok. 2011 → 27 toukok. 2011 Konferenssinumero: 36

Julkaisusarja

Nimi	ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings
ISSN (painettu)	1520-6149

Conference

Conference	IEEE International Conference on Acoustics, Speech, and Signal Processing
Lyhennettä	ICASSP
Maa/Alue	Tshekki
Kaupunki	Prague
Ajanjakso	22/05/2011 → 27/05/2011

Pääsy asiakirjaan

10.1109/ICASSP.2011.5947268

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Linkki julkaisuun Scopuksessa

Siteeraa tätä

Jung, A., Schmutzhard, S., Hlawatsch, F., & Hero, A. O. (2011). Performance bounds for sparse parametric covariance estimation in Gaussian models. teoksessa 2011 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2011 - Proceedings (Sivut 4156-4159). Artikkeli 5947268 (ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings). https://doi.org/10.1109/ICASSP.2011.5947268

Jung, Alexander ; Schmutzhard, Sebastian ; Hlawatsch, Franz et al. / Performance bounds for sparse parametric covariance estimation in Gaussian models. 2011 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2011 - Proceedings. 2011. Sivut 4156-4159 (ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings).

@inproceedings{df849bf83ba34d25b39954a986cde4f1,

title = "Performance bounds for sparse parametric covariance estimation in Gaussian models",

abstract = "We consider estimation of a sparse parameter vector that determines the covariance matrix of a Gaussian random vector via a sparse expansion into known {"}basis matrices.{"} Using the theory of reproducing kernel Hilbert spaces, we derive lower bounds on the variance of estimators with a given mean function. This includes unbiased estimation as a special case. We also present a numerical comparison of our lower bounds with the variance of two standard estimators (hard-thresholding estimator and maximum likelihood estimator).",

keywords = "reproducing kernel Hilbert space, RKHS, sparse covariance estimation, Sparsity, variance bound",

author = "Alexander Jung and Sebastian Schmutzhard and Franz Hlawatsch and Hero, \{Alfred O.\}",

year = "2011",

doi = "10.1109/ICASSP.2011.5947268",

language = "English",

isbn = "9781457705397",

series = "ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings",

pages = "4156--4159",

booktitle = "2011 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2011 - Proceedings",

note = "IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP ; Conference date: 22-05-2011 Through 27-05-2011",

}

Jung, A, Schmutzhard, S, Hlawatsch, F & Hero, AO 2011, Performance bounds for sparse parametric covariance estimation in Gaussian models. julkaisussa 2011 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2011 - Proceedings., 5947268, ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings, Sivut 4156-4159, IEEE International Conference on Acoustics, Speech, and Signal Processing, Prague, Tshekki, 22/05/2011. https://doi.org/10.1109/ICASSP.2011.5947268

Performance bounds for sparse parametric covariance estimation in Gaussian models. / Jung, Alexander; Schmutzhard, Sebastian; Hlawatsch, Franz et al.
2011 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2011 - Proceedings. 2011. s. 4156-4159 5947268 (ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings).

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

TY - GEN

T1 - Performance bounds for sparse parametric covariance estimation in Gaussian models

AU - Jung, Alexander

AU - Schmutzhard, Sebastian

AU - Hlawatsch, Franz

AU - Hero, Alfred O.

N1 - Conference code: 36

PY - 2011

Y1 - 2011

N2 - We consider estimation of a sparse parameter vector that determines the covariance matrix of a Gaussian random vector via a sparse expansion into known "basis matrices." Using the theory of reproducing kernel Hilbert spaces, we derive lower bounds on the variance of estimators with a given mean function. This includes unbiased estimation as a special case. We also present a numerical comparison of our lower bounds with the variance of two standard estimators (hard-thresholding estimator and maximum likelihood estimator).

AB - We consider estimation of a sparse parameter vector that determines the covariance matrix of a Gaussian random vector via a sparse expansion into known "basis matrices." Using the theory of reproducing kernel Hilbert spaces, we derive lower bounds on the variance of estimators with a given mean function. This includes unbiased estimation as a special case. We also present a numerical comparison of our lower bounds with the variance of two standard estimators (hard-thresholding estimator and maximum likelihood estimator).

KW - reproducing kernel Hilbert space

KW - RKHS

KW - sparse covariance estimation

KW - Sparsity

KW - variance bound

UR - https://www.scopus.com/pages/publications/80051649970

U2 - 10.1109/ICASSP.2011.5947268

DO - 10.1109/ICASSP.2011.5947268

M3 - Conference article in proceedings

AN - SCOPUS:80051649970

SN - 9781457705397

T3 - ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings

SP - 4156

EP - 4159

BT - 2011 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2011 - Proceedings

T2 - IEEE International Conference on Acoustics, Speech, and Signal Processing

Y2 - 22 May 2011 through 27 May 2011

ER -

Jung A, Schmutzhard S, Hlawatsch F, Hero AO. Performance bounds for sparse parametric covariance estimation in Gaussian models. julkaisussa 2011 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2011 - Proceedings. 2011. s. 4156-4159. 5947268. (ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings). doi: 10.1109/ICASSP.2011.5947268

Performance bounds for sparse parametric covariance estimation in Gaussian models

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Julkaisusarja

Conference

Pääsy asiakirjaan

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