THE BENEFIT OF GROUP SPARSITY

This paper develops a theory for group Lasso using a concept called strong group sparsity. Our result shows that group Lasso is superior to standard Lasso for strongly group-sparse signals. This provides a convincing theoretical justification for using group sparse regularization when the underlying...

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Bibliographic Details
Published in:The Annals of statistics 2010-08, Vol.38 (4), p.1978-2004
Main Authors: Huang, Junzhou, Zhang, Tong
Format: Article
Language:English
Subjects:
62G05
62J05
Approximation
Eigenvalues
Error rates
Estimators
Exact sciences and technology
General topics
group Lasso
Group performance
Group size
group sparsity
Group structure
Group theory
Group theory and generalizations
Groups
L_1 regularization
Lasso
Mathematical analysis
Mathematical vectors
Mathematics
Numerical analysis
Numerical analysis in abstract spaces
Numerical analysis. Scientific computation
Numerical linear algebra
parameter estimation
Probability and statistics
regression
Sample size
Sciences and techniques of general use
Signal noise
Sparsity
Statistics
Studies
variable selection
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Description
Summary:This paper develops a theory for group Lasso using a concept called strong group sparsity. Our result shows that group Lasso is superior to standard Lasso for strongly group-sparse signals. This provides a convincing theoretical justification for using group sparse regularization when the underlying group structure is consistent with the data. Moreover, the theory predicts some limitations of the group Lasso formulation that are confirmed by simulation studies.
ISSN:0090-5364
2168-8966
DOI:10.1214/09-AOS778