PASCAL - Pattern Analysis, Statistical Modelling and Computational Learning

Sparse density estimation with $\ell_1$ penalties.
Florentina Bunea, Alexandre Tsybakov and Marten Wegkamp
In: COLT 2007, 13-15 Jun 2007, San Diego, USA.

Abstract

This paper studies oracle properties of $\ell_1$-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.

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EPrint Type:Conference or Workshop Item (Paper)
Project Keyword:Project Keyword UNSPECIFIED
Subjects:Computational, Information-Theoretic Learning with Statistics
Learning/Statistics & Optimisation
Theory & Algorithms
ID Code:3860
Deposited By:Alexandre Tsybakov
Deposited On:25 February 2008