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 UNSPECIFIED Computational, Information-Theoretic Learning with StatisticsLearning/Statistics & OptimisationTheory & Algorithms 3860 Alexandre Tsybakov 25 February 2008