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Sparse Estimation by Exponential Weighting

Author(s): Rigollet, Philippe; Tsybakov, Alexandre B.

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Abstract: Consider a regression model with fixed design and Gaussian noise where the regression function can potentially be well approximated by a function that admits a sparse representation in a given dictionary. This paper resorts to exponential weights to exploit this underlying sparsity by implementing the principle of sparsity pattern aggregation. This model selection take on sparse estimation allows us to derive sparsity oracle inequalities in several popular frameworks, including ordinary sparsity, fused sparsity and group sparsity. One striking aspect of these theoretical results is that they hold under no condition in the dictionary. Moreover, we describe an efficient implementation of the sparsity pattern aggregation principle that compares favorably to state-of-the-art procedures on some basic numerical examples.
Publication Date: Nov-2012
Citation: Rigollet, Philippe, Tsybakov, Alexandre B. (2012). Sparse Estimation by Exponential Weighting. Statistical Science, 27 (4), 558 - 575. doi:10.1214/12-STS393
DOI: doi:10.1214/12-STS393
ISSN: 0883-4237
Pages: 558 - 575
Type of Material: Journal Article
Journal/Proceeding Title: Statistical Science
Version: Author's manuscript

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