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February 2018 Consistent parameter estimation for LASSO and approximate message passing
Ali Mousavi, Arian Maleki, Richard G. Baraniuk
Ann. Statist. 46(1): 119-148 (February 2018). DOI: 10.1214/17-AOS1544


This paper studies the optimal tuning of the regularization parameter in LASSO or the threshold parameters in approximate message passing (AMP). Considering a model in which the design matrix and noise are zero-mean i.i.d. Gaussian, we propose a data-driven approach for estimating the regularization parameter of LASSO and the threshold parameters in AMP. Our estimates are consistent, that is, they converge to their asymptotically optimal values in probability as $n$, the number of observations, and $p$, the ambient dimension of the sparse vector, grow to infinity, while $n/p$ converges to a fixed number $\delta$. As a byproduct of our analysis, we will shed light on the asymptotic properties of the solution paths of LASSO and AMP.


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Ali Mousavi. Arian Maleki. Richard G. Baraniuk. "Consistent parameter estimation for LASSO and approximate message passing." Ann. Statist. 46 (1) 119 - 148, February 2018.


Received: 1 November 2015; Revised: 1 January 2017; Published: February 2018
First available in Project Euclid: 22 February 2018

zbMATH: 06865107
MathSciNet: MR3766948
Digital Object Identifier: 10.1214/17-AOS1544

Primary: 62G05 , 62J05

Keywords: approximate message passing , estimation , Lasso , Sparsity

Rights: Copyright © 2018 Institute of Mathematical Statistics


Vol.46 • No. 1 • February 2018
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