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Combinatorial Penalties: Structure preserved by convex relaxations
| Content Provider | Semantic Scholar |
|---|---|
| Author | Halabi, Marwa El Bach, Francis Cevher, Volkan |
| Copyright Year | 2017 |
| Abstract | In this paper, we study convex relaxations of combinatorial penalty functions. Specifically, we consider models penalized by the sum of an $\ell_p$-norm and a set function defined over the support of the unknown parameter vector, which encodes prior knowledge on supports. We consider both homogeneous and non-homogeneous convex relaxations, and highlight the difference in the tightness of each relaxation through the notion of the lower combinatorial envelope of a set-function. We characterize necessary conditions under which the support of the unknown parameter vector can be correctly identified. We then propose a general adaptive estimator for convex monotone regularizers based on majorization-minimization, and identify sufficient conditions for support recovery in the asymptotic setting. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | https://infoscience.epfl.ch/record/230392/files/structure-preprint.pdf |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
