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

^*Corresponding author for this work

Not published at Aalto University

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

1 Citation (Scopus)

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).

Original language	English
Title of host publication	2011 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2011 - Proceedings
Pages	4156-4159
Number of pages	4
DOIs	https://doi.org/10.1109/ICASSP.2011.5947268
Publication status	Published - 2011
MoE publication type	A4 Conference publication
Event	IEEE International Conference on Acoustics, Speech, and Signal Processing - Prague, Czech Republic Duration: 22 May 2011 → 27 May 2011 Conference number: 36

Publication series

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

Conference

Conference	IEEE International Conference on Acoustics, Speech, and Signal Processing
Abbreviated title	ICASSP
Country/Territory	Czech Republic
City	Prague
Period	22/05/2011 → 27/05/2011

Keywords

reproducing kernel Hilbert space
RKHS
sparse covariance estimation
Sparsity
variance bound

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10.1109/ICASSP.2011.5947268

Cite this

Jung, A., Schmutzhard, S., Hlawatsch, F., & Hero, A. O. (2011). Performance bounds for sparse parametric covariance estimation in Gaussian models. In 2011 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2011 - Proceedings (pp. 4156-4159). Article 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. pp. 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. in 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, pp. 4156-4159, IEEE International Conference on Acoustics, Speech, and Signal Processing, Prague, Czech Republic, 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. p. 4156-4159 5947268 (ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings).

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

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. In 2011 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2011 - Proceedings. 2011. p. 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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