Extension of replica analysis to MAP estimation with applications to compressed sensing
Author(s)Rangan, Sundeep; Fletcher, Alyson K.; Goyal, Vivek K.
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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.
DepartmentMassachusetts Institute of Technology. Research Laboratory of Electronics
2010 IEEE International Symposium on Information Theory Proceedings (ISIT)
Institute of Electrical and Electronics Engineers (IEEE)
Rangan, Sundeep, Alyson K. Fletcher, and Vivek K Goyal. “Extension of Replica Analysis to MAP Estimation with Applications to Compressed Sensing.” IEEE, 2010. 1543–1547. © Copyright 2010 IEEE
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