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Effective condition number bounds for convex regularization
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Amelunxen, Dennis, Lotz, Martin and Walvin, Jake (2020) Effective condition number bounds for convex regularization. IEEE Transactions on Information Theory, 66 (4). 2501 -2516. doi:10.1109/TIT.2020.2965720
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WRAP-effective-condition-number-convex-regularization-Lotz-2019.pdf - Accepted Version - Requires a PDF viewer. Download (886Kb) | Preview |
Official URL: https://doi.org/10.1109/TIT.2020.2965720
Abstract
We derive bounds relating Renegar's condition number to quantities that govern the statistical performance of convex regularization in settings that include the ℓ 1 -analysis setting. Using results from conic integral geometry, we show that the bounds can be made to depend only on a random projection, or restriction, of the analysis operator to a lower dimensional space, and can still be effective if these operators are ill-conditioned. As an application, we get new bounds for the undersampling phase transition of composite convex regularizers. Key tools in the analysis are Slepian's inequality and the kinematic formula from integral geometry.
| Item Type: | Journal Article | ||||||||
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| Subjects: | Q Science > QA Mathematics | ||||||||
| Divisions: | Faculty of Science > Mathematics | ||||||||
| Library of Congress Subject Headings (LCSH): | Convex sets, Integral geometry, Mathematical optimization | ||||||||
| Journal or Publication Title: | IEEE Transactions on Information Theory | ||||||||
| Publisher: | IEEE | ||||||||
| ISSN: | 0018-9448 | ||||||||
| Official Date: | April 2020 | ||||||||
| Dates: |
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| Volume: | 66 | ||||||||
| Number: | 4 | ||||||||
| Page Range: | 2501 -2516 | ||||||||
| DOI: | 10.1109/TIT.2020.2965720 | ||||||||
| Status: | Peer Reviewed | ||||||||
| Publication Status: | Published | ||||||||
| Publisher Statement: | © 2019 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works. | ||||||||
| Access rights to Published version: | Restricted or Subscription Access | ||||||||
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