Combinatorial Penalties: Which structures are preserved by convex relaxations?
Machine Learning
2018-03-08 v2 Machine Learning
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.
Cite
@article{arxiv.1710.06273,
title = {Combinatorial Penalties: Which structures are preserved by convex relaxations?},
author = {Marwa El Halabi and Francis Bach and Volkan Cevher},
journal= {arXiv preprint arXiv:1710.06273},
year = {2018}
}