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Structured Sparsity through Convex Optimization (2012)
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| Citations: | 47 - 6 self |
BibTeX
@MISC{Bach12structuredsparsity,
author = {Francis Bach and Rodolphe Jenatton and Julien Mairal and Guillaume Obozinski},
title = {Structured Sparsity through Convex Optimization},
year = {2012}
}
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Abstract
Sparse estimation methods are aimed at using or obtaining parsimonious representations of data or models. While naturally cast as a combinatorial optimization problem, variable or feature selection admits a convex relaxation through the regularization by the ℓ1-norm. In this paper, we consider situations where we are not only interested in sparsity, but where some structural prior knowledge is available as well. We show that the ℓ1-norm can then be extended to structured norms built on either disjoint or overlapping groups of variables, leading to a flexible framework that can deal with various structures. We present applications to unsupervised learning, for structured sparse principal component analysis and hierarchical dictionary learning, and to supervised learning in the context of nonlinear variable selection.
Keyphrases
convex optimization present application hierarchical dictionary learning unsupervised learning flexible framework structured sparse principal component analysis sparse estimation method structural prior knowledge key word various structure feature selection nonlinear variable selection convex relaxation combinatorial optimization problem parsimonious representation
