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2010

Collaborative Hierarchical Sparse Modeling

Sprechmann, Pablo, Ramirez, Ignacio, Sapiro, Guillermo et al.

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Understand

Sparse modeling is a powerful framework for data analysis and processing.

Traditionally, encoding in this framework is done by solving an l_1-regularized linear regression problem, usually called Lasso.
In this work we first combine the sparsity-inducing property of the Lasso model, at the individual feature level, with the block-sparsity property of the group Lasso model, where sparse groups of features are jointly encoded, obtaining a sparsity pattern hierarchically structured.
This results in the hierarchical Lasso, which shows important practical modeling advantages.

Collaborative Hierarchical Sparse Modeling · Around

Built on

Parallel and Distributed Comptutation: Numerical Methods
D. Bertsekas and J. Tsitsiklis, · 1989
Earlier work this paper cites.
“Regression shrinkage and selection via the LASSO,”
R. Tibshirani, · 1996
Earlier work this paper cites.
“Simultaneous variable selection,”
B. Turlach, W. Venables, and S. Wright, · 2004
Earlier work this paper cites.
“Image decomposition via the combination of sparse representations and a variational approach,”
Original
J. Starck, M. Elad, and D. Donoho, · 2004
Earlier work this paper cites.

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Cited in the paper.

Then

“Sparse reconstruction by separable approximation,”
J. Wright, R. Nowak, and M. Figueiredo, · 2009
Later among the works it cites.
“A note on the group lasso and a sparse group lasso,”
J. Friedman, T. Hastie, and R. Tibshirani, · 2010
Closest in time.
“Classification and clustering via dictionary learning with structured incoherence and shared features,”
I. Ramirez, P. Sprechmann, and G. Sapiro, · 2010
Closest in time.

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