Extension of replica analysis to MAP estimation with applications to compressed sensing

Sundeep Rangan; Alyson K. Fletcher; Vivek K. Goyal

doi:10.1109/ISIT.2010.5513520

Extension of replica analysis to MAP estimation with applications to compressed sensing

Sundeep Rangan, Alyson K. Fletcher, Vivek K. Goyal

Electrical and Computer Engineering

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Abstract

The replica method is a non-rigorous but widely-accepted technique from statistical physics used in the asymptotic analysis of large, random, nonlinear problems. This paper applies the replica method to analyze non-Gaussian maximum a posteriori (MAP) estimation. The main result is a counterpart to Guo and Verdú's replica analysis of minimum mean-squared error estimation. The replica MAP analysis can be readily applied to many estimators used in compressed sensing, including basis pursuit, lasso, linear estimation with thresholding, and zero norm-regularized estimation. Among other benefits, the replica method provides a computationally-tractable method for exactly computing various performance metrics including mean-squared error and sparsity pattern recovery probability.

Original language	English (US)
Title of host publication	2010 IEEE International Symposium on Information Theory, ISIT 2010 - Proceedings
Pages	1543-1547
Number of pages	5
DOIs	https://doi.org/10.1109/ISIT.2010.5513520
State	Published - 2010
Event	2010 IEEE International Symposium on Information Theory, ISIT 2010 - Austin, TX, United States Duration: Jun 13 2010 → Jun 18 2010

Publication series

Name	IEEE International Symposium on Information Theory - Proceedings
ISSN (Print)	2157-8103

Other

Other	2010 IEEE International Symposium on Information Theory, ISIT 2010
Country/Territory	United States
City	Austin, TX
Period	6/13/10 → 6/18/10

ASJC Scopus subject areas

Theoretical Computer Science
Information Systems
Modeling and Simulation
Applied Mathematics

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10.1109/ISIT.2010.5513520

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Extension of replica analysis to MAP estimation with applications to compressed sensing. / Rangan, Sundeep; Fletcher, Alyson K.; Goyal, Vivek K.
2010 IEEE International Symposium on Information Theory, ISIT 2010 - Proceedings. 2010. p. 1543-1547 5513520 (IEEE International Symposium on Information Theory - Proceedings).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Rangan, S, Fletcher, AK & Goyal, VK 2010, Extension of replica analysis to MAP estimation with applications to compressed sensing. in 2010 IEEE International Symposium on Information Theory, ISIT 2010 - Proceedings., 5513520, IEEE International Symposium on Information Theory - Proceedings, pp. 1543-1547, 2010 IEEE International Symposium on Information Theory, ISIT 2010, Austin, TX, United States, 6/13/10. https://doi.org/10.1109/ISIT.2010.5513520

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abstract = "The replica method is a non-rigorous but widely-accepted technique from statistical physics used in the asymptotic analysis of large, random, nonlinear problems. This paper applies the replica method to analyze non-Gaussian maximum a posteriori (MAP) estimation. The main result is a counterpart to Guo and Verd{\'u}'s replica analysis of minimum mean-squared error estimation. The replica MAP analysis can be readily applied to many estimators used in compressed sensing, including basis pursuit, lasso, linear estimation with thresholding, and zero norm-regularized estimation. Among other benefits, the replica method provides a computationally-tractable method for exactly computing various performance metrics including mean-squared error and sparsity pattern recovery probability.",

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year = "2010",

doi = "10.1109/ISIT.2010.5513520",

language = "English (US)",

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N2 - The replica method is a non-rigorous but widely-accepted technique from statistical physics used in the asymptotic analysis of large, random, nonlinear problems. This paper applies the replica method to analyze non-Gaussian maximum a posteriori (MAP) estimation. The main result is a counterpart to Guo and Verdú's replica analysis of minimum mean-squared error estimation. The replica MAP analysis can be readily applied to many estimators used in compressed sensing, including basis pursuit, lasso, linear estimation with thresholding, and zero norm-regularized estimation. Among other benefits, the replica method provides a computationally-tractable method for exactly computing various performance metrics including mean-squared error and sparsity pattern recovery probability.

AB - The replica method is a non-rigorous but widely-accepted technique from statistical physics used in the asymptotic analysis of large, random, nonlinear problems. This paper applies the replica method to analyze non-Gaussian maximum a posteriori (MAP) estimation. The main result is a counterpart to Guo and Verdú's replica analysis of minimum mean-squared error estimation. The replica MAP analysis can be readily applied to many estimators used in compressed sensing, including basis pursuit, lasso, linear estimation with thresholding, and zero norm-regularized estimation. Among other benefits, the replica method provides a computationally-tractable method for exactly computing various performance metrics including mean-squared error and sparsity pattern recovery probability.

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BT - 2010 IEEE International Symposium on Information Theory, ISIT 2010 - Proceedings

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Extension of replica analysis to MAP estimation with applications to compressed sensing

Abstract

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