Adaptive Recovery of Signals by Convex Optimization

Zaid Harchaoui, Anatoli Juditsky, Arkadi Nemirovski, Dmitry Ostrovsky
Proceedings of The 28th Conference on Learning Theory, PMLR 40:929-955, 2015.

Abstract

We present a theoretical framework for adaptive estimation and prediction of signals of unknown structure in the presence of noise. The framework allows to address two intertwined challenges: (i) designing optimal statistical estimators; (ii) designing efficient numerical algorithms. In particular, we establish oracle inequalities for the performance of adaptive procedures, which rely upon convex optimization and thus can be efficiently implemented. As an application of the proposed approach, we consider denoising of harmonic oscillations.

Cite this Paper

BibTeX
@InProceedings{pmlr-v40-Harchaoui15, title = {Adaptive Recovery of Signals by Convex Optimization}, author = {Harchaoui, Zaid and Juditsky, Anatoli and Nemirovski, Arkadi and Ostrovsky, Dmitry}, booktitle = {Proceedings of The 28th Conference on Learning Theory}, pages = {929--955}, year = {2015}, editor = {Grünwald, Peter and Hazan, Elad and Kale, Satyen}, volume = {40}, series = {Proceedings of Machine Learning Research}, address = {Paris, France}, month = {03--06 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v40/Harchaoui15.pdf}, url = {https://proceedings.mlr.press/v40/Harchaoui15.html}, abstract = {We present a theoretical framework for adaptive estimation and prediction of signals of unknown structure in the presence of noise. The framework allows to address two intertwined challenges: (i) designing optimal statistical estimators; (ii) designing efficient numerical algorithms. In particular, we establish oracle inequalities for the performance of adaptive procedures, which rely upon convex optimization and thus can be efficiently implemented. As an application of the proposed approach, we consider denoising of harmonic oscillations.} }
Endnote
%0 Conference Paper %T Adaptive Recovery of Signals by Convex Optimization %A Zaid Harchaoui %A Anatoli Juditsky %A Arkadi Nemirovski %A Dmitry Ostrovsky %B Proceedings of The 28th Conference on Learning Theory %C Proceedings of Machine Learning Research %D 2015 %E Peter Grünwald %E Elad Hazan %E Satyen Kale %F pmlr-v40-Harchaoui15 %I PMLR %P 929--955 %U https://proceedings.mlr.press/v40/Harchaoui15.html %V 40 %X We present a theoretical framework for adaptive estimation and prediction of signals of unknown structure in the presence of noise. The framework allows to address two intertwined challenges: (i) designing optimal statistical estimators; (ii) designing efficient numerical algorithms. In particular, we establish oracle inequalities for the performance of adaptive procedures, which rely upon convex optimization and thus can be efficiently implemented. As an application of the proposed approach, we consider denoising of harmonic oscillations.
RIS
TY - CPAPER TI - Adaptive Recovery of Signals by Convex Optimization AU - Zaid Harchaoui AU - Anatoli Juditsky AU - Arkadi Nemirovski AU - Dmitry Ostrovsky BT - Proceedings of The 28th Conference on Learning Theory DA - 2015/06/26 ED - Peter Grünwald ED - Elad Hazan ED - Satyen Kale ID - pmlr-v40-Harchaoui15 PB - PMLR DP - Proceedings of Machine Learning Research VL - 40 SP - 929 EP - 955 L1 - http://proceedings.mlr.press/v40/Harchaoui15.pdf UR - https://proceedings.mlr.press/v40/Harchaoui15.html AB - We present a theoretical framework for adaptive estimation and prediction of signals of unknown structure in the presence of noise. The framework allows to address two intertwined challenges: (i) designing optimal statistical estimators; (ii) designing efficient numerical algorithms. In particular, we establish oracle inequalities for the performance of adaptive procedures, which rely upon convex optimization and thus can be efficiently implemented. As an application of the proposed approach, we consider denoising of harmonic oscillations. ER -
APA
Harchaoui, Z., Juditsky, A., Nemirovski, A. & Ostrovsky, D.. (2015). Adaptive Recovery of Signals by Convex Optimization. Proceedings of The 28th Conference on Learning Theory, in Proceedings of Machine Learning Research 40:929-955 Available from https://proceedings.mlr.press/v40/Harchaoui15.html.

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