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Sparse Prediction with the $k$-Support Norm


We derive a novel norm that corresponds to the tightest convex relaxation of sparsity combined with an $\ell_2$ penalty. We show that this new {\em $k$-support norm} provides a tighter relaxation than the elastic net and is thus a good replacement for the Lasso or the elastic net in sparse prediction problems. Through the study of the $k$-support norm, we also bound the looseness of the elastic net, thus shedding new light on it and providing justification for its use.

Dates and versions

hal-00855999 , version 1 (30-08-2013)



Andreas Argyriou, Rina Foygel, Nathan Srebro. Sparse Prediction with the $k$-Support Norm. 2012. ⟨hal-00855999⟩
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