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The Ethereal
Combinatorial Penalties: Which structures are preserved by convex relaxations?
October 17, 2017 ยท Declared Dead ยท ๐ International Conference on Artificial Intelligence and Statistics
"No code URL or promise found in abstract"
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Authors
Marwa El Halabi, Francis Bach, Volkan Cevher
arXiv ID
1710.06273
Category
cs.LG: Machine Learning
Cross-listed
stat.ML
Citations
17
Venue
International Conference on Artificial Intelligence and Statistics
Last Checked
5 months ago
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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