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LARS: efficient algorithm to solve lasso
elastic net: in case of collinear dictionary atoms, it will pick collinear atoms together, or drop them together.
group lasso: in the extreme case, it behavors like lasso, however in a group manner, i.e. a group is either picked or dropped, and sparsity is obtained at the group level, but within each group, sparsity can't be guarantteed.
sparse group lasso: sparsity is gotten at both group level and within each group.
A note on the group lasso and a sparse group lassoadaptive lasso:
Packages:
(1) LARS: l1-magic http://statweb.stanford.edu/~candes/l1magic/
(2) CRAN - Package glmnet, Package 'glmnet'
(3) SPAMS: http://spams-devel.gforge.inria.fr/
(4) SLEP: http://www.public.asu.edu/~jye02/Software/SLEP/
(5) SIRS: http://www-bcf.usc.edu/~jinchilv/publications/software/
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