Sparse density estimation with l1 penalties
COLT'07 Proceedings of the 20th annual conference on Learning theory
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We consider the problem of reconstruction of a sparse vector observed against a background of white Gaussian noise. The sparsity is assumed to be unknown. Two approaches to statistical estimation in this case are discussed, namely, the model selection method and threshold estimators. We propose a method of selecting a threshold estimator based on the principle of empirical complexity minimization with minimal conservative penalization.