Error bounds for Bregman denoising and structured natural parameter estimation

Amin Jalali, James Saunderson, Maryam Fazel, Babak Hassibi

Research output: Chapter in Book/Report/Conference proceedingConference PaperResearchpeer-review

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.

Original languageEnglish
Title of host publication2017 IEEE International Symposium on Information Theory (ISIT 2017)
EditorsMartin Bossert, Stephen Hanly, Stephan ten Brink, Sennur Ulukus
Place of PublicationPiscataway NJ USA
PublisherIEEE, Institute of Electrical and Electronics Engineers
Pages2273-2277
Number of pages5
ISBN (Electronic)9781509040964
ISBN (Print)9781509040971
DOIs
Publication statusPublished - 2017
EventIEEE International Symposium on Information Theory 2017 - Aachen, Germany
Duration: 25 Jun 201730 Jun 2017

Conference

ConferenceIEEE International Symposium on Information Theory 2017
Abbreviated titleISIT 2017
CountryGermany
CityAachen
Period25/06/1730/06/17

Cite this

Jalali, A., Saunderson, J., Fazel, M., & Hassibi, B. (2017). Error bounds for Bregman denoising and structured natural parameter estimation. In M. Bossert, S. Hanly, S. ten Brink, & S. Ulukus (Eds.), 2017 IEEE International Symposium on Information Theory (ISIT 2017) (pp. 2273-2277). IEEE, Institute of Electrical and Electronics Engineers. https://doi.org/10.1109/ISIT.2017.8006934