Ellipsoid approximation using random vectors

S. Mendelson; A. Pajor

doi:10.1007/11503415_29

Ellipsoid approximation using random vectors

S. Mendelson^*, A. Pajor

^*Corresponding author for this work

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

5 Citations (Scopus)

Abstract

We analyze the behavior of a random matrix with independent rows, each distributed according to the same probability measure on ℝⁿ or on l₂- We investigate the spectrum of such a matrix and the way the ellipsoid generated by it approximates the covariance structure of the underlying measure. As an application, we provide estimates on the deviation of the spectrum of Gram matrices from the spectrum of the integral operator.

Original language	English
Title of host publication	Learning Theory - 18th Annual Conference on Learning Theory, COLT 2005, Proceedings
Publisher	Springer Verlag
Pages	429-443
Number of pages	15
ISBN (Print)	3540265562, 9783540265566
DOIs	https://doi.org/10.1007/11503415_29
Publication status	Published - 2005
Event	18th Annual Conference on Learning Theory, COLT 2005 - Learning Theory - Bertinoro, Italy Duration: 27 Jun 2005 → 30 Jun 2005

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	3559 LNAI
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	18th Annual Conference on Learning Theory, COLT 2005 - Learning Theory
Country/Territory	Italy
City	Bertinoro
Period	27/06/05 → 30/06/05

Access to Document

10.1007/11503415_29

Cite this

Mendelson, S., & Pajor, A. (2005). Ellipsoid approximation using random vectors. In Learning Theory - 18th Annual Conference on Learning Theory, COLT 2005, Proceedings (pp. 429-443). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 3559 LNAI). Springer Verlag. https://doi.org/10.1007/11503415_29

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title = "Ellipsoid approximation using random vectors",

abstract = "We analyze the behavior of a random matrix with independent rows, each distributed according to the same probability measure on ℝn or on l2- We investigate the spectrum of such a matrix and the way the ellipsoid generated by it approximates the covariance structure of the underlying measure. As an application, we provide estimates on the deviation of the spectrum of Gram matrices from the spectrum of the integral operator.",

author = "S. Mendelson and A. Pajor",

year = "2005",

doi = "10.1007/11503415_29",

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series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

publisher = "Springer Verlag",

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booktitle = "Learning Theory - 18th Annual Conference on Learning Theory, COLT 2005, Proceedings",

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note = "18th Annual Conference on Learning Theory, COLT 2005 - Learning Theory ; Conference date: 27-06-2005 Through 30-06-2005",

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Mendelson, S & Pajor, A 2005, Ellipsoid approximation using random vectors. in Learning Theory - 18th Annual Conference on Learning Theory, COLT 2005, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 3559 LNAI, Springer Verlag, pp. 429-443, 18th Annual Conference on Learning Theory, COLT 2005 - Learning Theory, Bertinoro, Italy, 27/06/05. https://doi.org/10.1007/11503415_29

Ellipsoid approximation using random vectors. / Mendelson, S.; Pajor, A.
Learning Theory - 18th Annual Conference on Learning Theory, COLT 2005, Proceedings. Springer Verlag, 2005. p. 429-443 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 3559 LNAI).

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

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AB - We analyze the behavior of a random matrix with independent rows, each distributed according to the same probability measure on ℝn or on l2- We investigate the spectrum of such a matrix and the way the ellipsoid generated by it approximates the covariance structure of the underlying measure. As an application, we provide estimates on the deviation of the spectrum of Gram matrices from the spectrum of the integral operator.

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M3 - Conference contribution

AN - SCOPUS:26944458088

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T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

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ER -

Ellipsoid approximation using random vectors

Abstract

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