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dc.contributor.authorMousavi, Ali
Maleki, Arian
Baraniuk, Richard G.
dc.date.accessioned 2018-07-11T19:50:55Z
dc.date.available 2018-07-11T19:50:55Z
dc.date.issued 2018
dc.identifier.citation Mousavi, Ali, Maleki, Arian and Baraniuk, Richard G.. "Consistent parameter estimation for LASSO and approximate message passing." The Annals of Statistics, 46, no. 1 (2018) Institute of Mathematical Statistics: 119-148. https://doi.org/10.1214/17-AOS1544.
dc.identifier.urihttps://hdl.handle.net/1911/102399
dc.description.abstract 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 nn, the number of observations, and pp, the ambient dimension of the sparse vector, grow to infinity, while n/pn/p converges to a fixed number δδ. As a byproduct of our analysis, we will shed light on the asymptotic properties of the solution paths of LASSO and AMP.
dc.language.iso eng
dc.publisher Institute of Mathematical Statistics
dc.rights Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
dc.title Consistent parameter estimation for LASSO and approximate message passing
dc.type Journal article
dc.citation.journalTitle The Annals of Statistics
dc.citation.volumeNumber 46
dc.citation.issueNumber 1
dc.type.dcmi Text
dc.identifier.doihttps://doi.org/10.1214/17-AOS1544
dc.type.publication publisher version
dc.citation.firstpage 119
dc.citation.lastpage 148


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