Fused sparsity and robust estimation for linear models with unknown variance

Yin Chen 1, 2 Arnak S. Dalalyan 1, 2, 3
1 IMAGINE [Marne-la-Vallée]
LIGM - Laboratoire d'Informatique Gaspard-Monge, CSTB - Centre Scientifique et Technique du Bâtiment, ENPC - École des Ponts ParisTech
Abstract : In this paper, we develop a novel approach to the problem of learning sparse representations in the context of fused sparsity and unknown noise level. We propose an algorithm, termed Scaled Fused Dantzig Selector (SFDS), that accomplishes the aforementioned learning task by means of a second-order cone program. A special emphasize is put on the particular instance of fused sparsity corresponding to the learning in presence of outliers. We establish finite sample risk bounds and carry out an experimental evaluation on both synthetic and real data.
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Yin Chen, Arnak S. Dalalyan. Fused sparsity and robust estimation for linear models with unknown variance. Neural Information Processing Systems (NIPS 2012), Dec 2012, United States. pp.1-16. ⟨hal-00742601⟩

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