Sparse Prediction with the $k$-Support Norm

Andreas Argyriou (1, 2) , Rina Foygel (3) , Nathan Srebro (4)

1 CVN - Centre de vision numérique
2 GALEN - Organ Modeling through Extraction, Representation and Understanding of Medical Image Content
3 Department of Statistics [Stanford]
4 Toyota Technological Institute

We derive a novel norm that corresponds to the tightest convex relaxation of sparsity combined with an L_2 penalty. We show that this new k-support norm provides a tighter relaxation than the elastic net and can thus be advantageous in sparse prediction problems. We also bound the looseness of the elastic net, thus shedding new light on it and providing justification for its use.

Domaines: Imagerie médicale

Andreas Argyriou, Rina Foygel, Nathan Srebro. Sparse Prediction with the $k$-Support Norm. Neural Information Processing Systems, Dec 2012, Lake Tahoe, United States. pp.1466-1474. ⟨hal-00858954⟩