Sparse Density Estimation with L1 Penalties
Abstract
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.
Cite
Text
Bunea et al. "Sparse Density Estimation with L1 Penalties." Annual Conference on Computational Learning Theory, 2007. doi:10.1007/978-3-540-72927-3_38Markdown
[Bunea et al. "Sparse Density Estimation with L1 Penalties." Annual Conference on Computational Learning Theory, 2007.](https://mlanthology.org/colt/2007/bunea2007colt-sparse/) doi:10.1007/978-3-540-72927-3_38BibTeX
@inproceedings{bunea2007colt-sparse,
title = {{Sparse Density Estimation with L1 Penalties}},
author = {Bunea, Florentina and Tsybakov, Alexandre B. and Wegkamp, Marten H.},
booktitle = {Annual Conference on Computational Learning Theory},
year = {2007},
pages = {530-543},
doi = {10.1007/978-3-540-72927-3_38},
url = {https://mlanthology.org/colt/2007/bunea2007colt-sparse/}
}