# Sparse Prediction with the $k$-Support Norm

Abstract : 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.
Document type :
Preprints, Working Papers, ...
Domain :

https://hal.inria.fr/hal-00855999
Contributor : Puneet Kumar Dokania <>
Submitted on : Friday, August 30, 2013 - 12:02:29 PM
Last modification on : Thursday, February 25, 2021 - 11:28:02 AM

### Identifiers

• HAL Id : hal-00855999, version 1
• ARXIV : 1204.5043

### Citation

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

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