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. © Springer-Verlag Berlin Heidelberg 2007.
CITATION STYLE
Bunea, F., Tsybakov, A. B., & Wegkamp, M. H. (2007). Sparse density estimation with ℓ1 penalties. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 4539 LNAI, pp. 530–543). Springer Verlag. https://doi.org/10.1007/978-3-540-72927-3_38
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