Combinatorial Penalties: Which structures are preserved by convex relaxations?

Marwa El Halabi 1 Francis Bach 2 Volkan Cevher 1
2 SIERRA - Statistical Machine Learning and Parsimony
DI-ENS - Département d'informatique de l'École normale supérieure, CNRS - Centre National de la Recherche Scientifique, Inria de Paris
Abstract : We consider the homogeneous and the non-homogeneous convex relaxations for combinatorial penalty functions defined on support sets. Our study identifies key differences in the tightness of the resulting relaxations through the notion of the lower combinatorial envelope of a set-function along with new necessary conditions for support identification. We then propose a general adaptive estimator for convex monotone regularizers, and derive new sufficient conditions for support recovery in the asymptotic setting.
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Communication dans un congrès
AISTATS 2018 - 22nd International Conference on Artificial Intelligence and Statistics, Apr 2018, Canary Islands, Spain. 〈10.06273〉
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https://hal.archives-ouvertes.fr/hal-01652151
Contributeur : Francis Bach <>
Soumis le : jeudi 30 novembre 2017 - 07:57:32
Dernière modification le : lundi 28 janvier 2019 - 09:03:45

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Marwa El Halabi, Francis Bach, Volkan Cevher. Combinatorial Penalties: Which structures are preserved by convex relaxations?. AISTATS 2018 - 22nd International Conference on Artificial Intelligence and Statistics, Apr 2018, Canary Islands, Spain. 〈10.06273〉. 〈hal-01652151〉

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