Abstract
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.
Research of F. Bunea and M. Wegkamp is supported in part by NSF grant DMS 0406049.
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Bunea, F., Tsybakov, A.B., Wegkamp, M.H. (2007). Sparse Density Estimation with ℓ1 Penalties. In: Bshouty, N.H., Gentile, C. (eds) Learning Theory. COLT 2007. Lecture Notes in Computer Science(), vol 4539. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-72927-3_38
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DOI: https://doi.org/10.1007/978-3-540-72927-3_38
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