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Error bounds for Bregman denoising and structured natural parameter estimation

Jalali, Amin and Saunderson, James and Fazel, Maryam and Hassibi, Babak (2017) Error bounds for Bregman denoising and structured natural parameter estimation. In: 2017 IEEE International Symposium on Information Theory (ISIT). IEEEE , Piscataway, NJ, pp. 2273-2277. ISBN 978-1-5090-4096-4. https://resolver.caltech.edu/CaltechAUTHORS:20170816-174255469

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Abstract

We analyze an estimator based on the Bregman divergence for recovery of structured models from additive noise. The estimator can be seen as a regularized maximum likelihood estimator for an exponential family where the natural parameter is assumed to be structured. For all such Bregman denoising estimators, we provide an error bound for a natural associated error measure. Our error bound makes it possible to analyze a wide range of estimators, such as those in proximal denoising and inverse covariance matrix estimation, in a unified manner. In the case of proximal denoising, we exactly recover the existing tight normalized mean squared error bounds. In sparse precision matrix estimation, our bounds provide optimal scaling with interpretable constants in terms of the associated error measure.


Item Type:Book Section
Related URLs:
URLURL TypeDescription
https://doi.org/10.1109/ISIT.2017.8006934DOIArticle
http://ieeexplore.ieee.org/document/8006934/PublisherArticle
Additional Information:© 2017 IEEE. This work was supported in part by the NSF grant CCF-1409836 and ONR grant N00014-16-1-2789.
Funders:
Funding AgencyGrant Number
NSFCCF-1409836
Office of Naval Research (ONR)N00014-16-1-2789
Record Number:CaltechAUTHORS:20170816-174255469
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20170816-174255469
Official Citation:A. Jalali, J. Saunderson, M. Fazel and B. Hassibi, "Error bounds for Bregman denoising and structured natural parameter estimation," 2017 IEEE International Symposium on Information Theory (ISIT), Aachen, Germany, 2017, pp. 2273-2277. doi: 10.1109/ISIT.2017.8006934
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:80543
Collection:CaltechAUTHORS
Deposited By: Kristin Buxton
Deposited On:17 Aug 2017 19:55
Last Modified:03 Oct 2019 18:32

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