Sparse density estimation with l1 penalties

被引：25

作者：

Bunea, Florentina ^{[1
]}

Tsybakov, Alexandre B. ^{[2
]}

Wegkamp, Marten H. ^{[1
]}

机构：

[1] Florida State Univ, Tallahassee, FL 32306 USA

[2] Univ Paris 04, Lab Probabil Modeles Aeatoires, Paris, France

来源：

LEARNING THEORY, PROCEEDINGS | 2007年 / 4539卷

关键词：

D O I：

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

中图分类号：

TP18 [人工智能理论];

学科分类号：

081104 ; 0812 ; 0835 ; 1405 ;

摘要：

This paper studies oracle properties of l(1)-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.

引用

页码：530 / +

页数：3

共 30 条

[1] Adapting to unknown sparsity by controlling the false discovery rate
Abramovich, Felix
Benjamini, Yoav
Donoho, David L.
Johnstone, Iain M.
[J]. ANNALS OF STATISTICS, 2006, 34 (02) : 584 - 653
[2] [Anonymous], RES PAPERS PROBABILI
[3] Risk bounds for model selection via penalization
Barron, A
Birgé, L
Massart, P
[J]. PROBABILITY THEORY AND RELATED FIELDS, 1999, 113 (03) : 301 - 413
[4] BUNEA F, 2006, UNPUB SPARSITY ORACL
[5] BUNEA F, 2005, IN PRESS ANN STAT
[6] Aggregation and sparsity via l1 penalized least squares
Bunea, Florentina
Tsybakov, Alexandre B.
Wegkamp, Marten H.
[J]. LEARNING THEORY, PROCEEDINGS, 2006, 4005 : 379 - 391
[7] Chen SSB, 2001, SIAM REV, V43, P129, DOI [10.1137/S003614450037906X, 10.1137/S1064827596304010]
[8] DEVROYE L, 2000, COMBINATORIAL METHOD
[9] DE-NOISING BY SOFT-THRESHOLDING
DONOHO, DL
[J]. IEEE TRANSACTIONS ON INFORMATION THEORY, 1995, 41 (03) : 613 - 627
[10] Uncertainty principles and ideal atomic decomposition
Donoho, DL
Huo, XM
[J]. IEEE TRANSACTIONS ON INFORMATION THEORY, 2001, 47 (07) : 2845 - 2862

← 1 2 3 →