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

Résultats de recherche: Le chapitre dans un livre, un rapport, une anthologie ou une collection › Contribution à une conférence › Revue par des pairs

36 Citations (Scopus)

Résumé

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.

langue originale	Anglais
titre	Learning Theory - 20th Annual Conference on Learning Theory, COLT 2007, Proceedings
Editeur	Springer Verlag
Pages	530-543
Nombre de pages	14
ISBN (imprimé)	9783540729259
Les DOIs	https://doi.org/10.1007/978-3-540-72927-3_38
état	Publié - 1 janv. 2007
Evénement	20th Annual Conference on Learning Theory, COLT 2007 - San Diego, CA, États-Unis Durée: 13 juin 2007 → 15 juin 2007

Série de publications

Nom	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	4539 LNAI
ISSN (imprimé)	0302-9743
ISSN (Electronique)	1611-3349

Une conférence

Une conférence	20th Annual Conference on Learning Theory, COLT 2007
Pays/Territoire	États-Unis
La ville	San Diego, CA
période	13/06/07 → 15/06/07

Accès au document

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

Contient cette citation

Bunea, F., Tsybakov, A. B., & Wegkamp, M. H. (2007). Sparse density estimation with l₁ penalties. Dans Learning Theory - 20th Annual Conference on Learning Theory, COLT 2007, Proceedings (p. 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

@inproceedings{ed81b01c6e8a417f99714307c936ea22,

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",

month = jan,

day = "1",

doi = "10.1007/978-3-540-72927-3\_38",

language = "English",

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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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note = "20th Annual Conference on Learning Theory, COLT 2007 ; Conference date: 13-06-2007 Through 15-06-2007",

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Bunea, F, Tsybakov, AB & Wegkamp, MH 2007, Sparse density estimation with l₁ penalties. Dans 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, p. 530-543, 20th Annual Conference on Learning Theory, COLT 2007, San Diego, CA, États-Unis, 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).

Résultats de recherche: Le chapitre dans un livre, un rapport, une anthologie ou une collection › Contribution à une conférence › Revue par des pairs

TY - GEN

T1 - Sparse density estimation with l1 penalties

AU - Bunea, Florentina

AU - Tsybakov, Alexandre B.

AU - Wegkamp, Marten H.

PY - 2007/1/1

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

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SN - 9783540729259

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

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BT - Learning Theory - 20th Annual Conference on Learning Theory, COLT 2007, Proceedings

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Bunea F, Tsybakov AB, Wegkamp MH. Sparse density estimation with l₁ penalties. Dans 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