Combinatorial Penalties: Which structures are preserved by convex relaxations?

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.


Published in:
Proceedings of the 21st International Conference on Artificial Intelligence and Statistics
Presented at:
21st International Conference on Artificial Intelligence and Statistics (AISTATS), Lanzarotte, Spain , April 9-11, 2017
Year:
2017
Laboratories:




 Record created 2017-08-31, last modified 2018-02-08

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