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Region-free Safe Screening Tests for l1-penalized Convex Problems

Abstract : We address the problem of safe screening for l1-penalized convex regression/classification problems, i.e., the identification of zero coordinates of the solutions. Unlike previous contributions of the literature, we propose a screening methodology which does not require the knowledge of a so-called "safe region". Our approach does not rely on any other assumption than convexity (in particular, no strong-convexity hypothesis is needed) and therefore applies to a wide family of convex problems. When the Fenchel conjugate of the data-fidelity term is strongly convex, we show that the popular "GAP sphere test" proposed by Fercoq et al. can be recovered as a particular case of our methodology (up to a minor modification). We illustrate numerically the performance of our procedure on the "sparse support vector machine classification" problem.
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Contributor : Clément Elvira Connect in order to contact the contributor
Submitted on : Friday, October 7, 2022 - 3:30:09 PM
Last modification on : Tuesday, October 25, 2022 - 4:20:26 PM



  • HAL Id : hal-03806099, version 1


Cédric Herzet, Clément Elvira, Hong-Phuong Dang. Region-free Safe Screening Tests for l1-penalized Convex Problems. Eusipco 2022 - 30th European Signal Processing Conference, Aug 2022, Belgrade, Serbia. pp.1-5. ⟨hal-03806099⟩



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