Sparse density estimation with ℓ1 penalties

Florentina Bunea; Alexandre B. Tsybakov; Marten H. Wegkamp

doi:10.1007/978-3-540-72927-3_38

Sparse density estimation with ℓ₁ penalties

Florentina Bunea
, Alexandre B. Tsybakov
, Marten H. Wegkamp

Florida State University

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

Abstract

This paper studies oracle properties of ℓ₁-penalized estimators of a probability density. We show that the penalized least squares estimator satisfies sparsity oracle inequalities, i.e., bounds in terms of the number of non-zero components of the oracle vector. The results are valid even when the dimension of the model is (much) larger than the sample size. They are applied to estimation in sparse high-dimensional mixture models, to nonparametric adaptive density estimation and to the problem of aggregation of density estimators.

Original language	English
Title of host publication	Learning Theory - 20th Annual Conference on Learning Theory, COLT 2007, Proceedings
Publisher	Springer Verlag
Pages	530-543
Number of pages	14
ISBN (Print)	9783540729259
DOIs	https://doi.org/10.1007/978-3-540-72927-3_38
Publication status	Published - 1 Jan 2007
Event	20th Annual Conference on Learning Theory, COLT 2007 - San Diego, CA, United States Duration: 13 Jun 2007 → 15 Jun 2007

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	4539 LNAI
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	20th Annual Conference on Learning Theory, COLT 2007
Country/Territory	United States
City	San Diego, CA
Period	13/06/07 → 15/06/07

Access to Document

10.1007/978-3-540-72927-3_38

Cite this

Bunea, F., Tsybakov, A. B., & Wegkamp, M. H. (2007). Sparse density estimation with ℓ₁ penalties. In Learning Theory - 20th Annual Conference on Learning Theory, COLT 2007, Proceedings (pp. 530-543). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 4539 LNAI). Springer Verlag. https://doi.org/10.1007/978-3-540-72927-3_38

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title = "Sparse density estimation with ℓ1 penalties",

abstract = "This paper studies oracle properties of ℓ1-penalized estimators of a probability density. We show that the penalized least squares estimator satisfies sparsity oracle inequalities, i.e., bounds in terms of the number of non-zero components of the oracle vector. The results are valid even when the dimension of the model is (much) larger than the sample size. They are applied to estimation in sparse high-dimensional mixture models, to nonparametric adaptive density estimation and to the problem of aggregation of density estimators.",

author = "Florentina Bunea and Tsybakov, \{Alexandre B.\} and Wegkamp, \{Marten H.\}",

year = "2007",

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Bunea, F, Tsybakov, AB & Wegkamp, MH 2007, Sparse density estimation with ℓ₁ penalties. in Learning Theory - 20th Annual Conference on Learning Theory, COLT 2007, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 4539 LNAI, Springer Verlag, pp. 530-543, 20th Annual Conference on Learning Theory, COLT 2007, San Diego, CA, United States, 13/06/07. https://doi.org/10.1007/978-3-540-72927-3_38

Sparse density estimation with ℓ₁ penalties. / Bunea, Florentina; Tsybakov, Alexandre B.; Wegkamp, Marten H.
Learning Theory - 20th Annual Conference on Learning Theory, COLT 2007, Proceedings. Springer Verlag, 2007. p. 530-543 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 4539 LNAI).

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

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N2 - This paper studies oracle properties of ℓ1-penalized estimators of a probability density. We show that the penalized least squares estimator satisfies sparsity oracle inequalities, i.e., bounds in terms of the number of non-zero components of the oracle vector. The results are valid even when the dimension of the model is (much) larger than the sample size. They are applied to estimation in sparse high-dimensional mixture models, to nonparametric adaptive density estimation and to the problem of aggregation of density estimators.

AB - This paper studies oracle properties of ℓ1-penalized estimators of a probability density. We show that the penalized least squares estimator satisfies sparsity oracle inequalities, i.e., bounds in terms of the number of non-zero components of the oracle vector. The results are valid even when the dimension of the model is (much) larger than the sample size. They are applied to estimation in sparse high-dimensional mixture models, to nonparametric adaptive density estimation and to the problem of aggregation of density estimators.

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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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Bunea F, Tsybakov AB, Wegkamp MH. Sparse density estimation with ℓ₁ penalties. In Learning Theory - 20th Annual Conference on Learning Theory, COLT 2007, Proceedings. Springer Verlag. 2007. p. 530-543. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-540-72927-3_38