Open Access
November 2012 Sparse Estimation by Exponential Weighting
Philippe Rigollet, Alexandre B. Tsybakov
Statist. Sci. 27(4): 558-575 (November 2012). DOI: 10.1214/12-STS393


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.


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Philippe Rigollet. Alexandre B. Tsybakov. "Sparse Estimation by Exponential Weighting." Statist. Sci. 27 (4) 558 - 575, November 2012.


Published: November 2012
First available in Project Euclid: 21 December 2012

zbMATH: 1331.62351
MathSciNet: MR3025134
Digital Object Identifier: 10.1214/12-STS393

Keywords: Exponential weights , fused sparsity , group sparsity , high-dimensional regression , Sparse regression , Sparsity , sparsity oracle inequalities , sparsity pattern aggregation , sparsity prior

Rights: Copyright © 2012 Institute of Mathematical Statistics

Vol.27 • No. 4 • November 2012
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