A Dynamic Screening Principle for the Lasso

Antoine Bonnefoy 1 Valentin Emiya 1 Liva Ralaivola 1 Rémi Gribonval 2
1 QARMA - éQuipe AppRentissage et MultimediA [Marseille]
LIF - Laboratoire d'informatique Fondamentale de Marseille
2 PANAMA - Parcimonie et Nouveaux Algorithmes pour le Signal et la Modélisation Audio
Inria Rennes – Bretagne Atlantique , IRISA-D5 - SIGNAUX ET IMAGES NUMÉRIQUES, ROBOTIQUE
Abstract : The Lasso is an optimization problem devoted to finding a sparse representation of some signal with respect to a predefined dictionary. An original and computationally-efficient method is proposed here to solve this problem, based on a dynamic screening principle. It makes it possible to accelerate a large class of optimization algorithms by iteratively reducing the size of the dictionary during the optimization process, discarding elements that are provably known not to belong to the solution of the Lasso. The iterative reduction of the dictionary is what we call dynamic screening. As this screening step is inexpensive, the computational cost of the algorithm using our dynamic screening strategy is lower than that of the base algorithm. Numerical experiments on synthetic and real data support the relevance of this approach.
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Antoine Bonnefoy, Valentin Emiya, Liva Ralaivola, Rémi Gribonval. A Dynamic Screening Principle for the Lasso. European Signal Processing Conference EUSIPCO 2014, Sep 2014, Lisboa, Portugal. pp.1-5. ⟨hal-00880787v4⟩

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