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Sparse estimation based on a validation criterion
KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre. (System Identification Group)ORCID iD: 0000-0003-0355-2663
KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre. (System Identification Group)ORCID iD: 0000-0002-9368-3079
2011 (English)In: 2011 50th Conference On Decision And Control And European Control Conference, IEEE , 2011, 2825-2830 p.Conference paper, Published paper (Refereed)
Abstract [en]

A sparse estimator with close ties with the LASSO (least absolute shrinkage and selection operator) is analysed. The basic idea of the estimator is to relax the least-squares cost function to what the least-squares method would achieve on validation data and then use this as a constraint in the minimization of the l(1)-norm of the parameter vector. In a linear regression framework, exact conditions are established for when the estimator is consistent in probability and when it possesses sparseness. By adding a re-estimation step, where least-squares is used to re-estimate the non-zero elements of the parameter vector, the so called Oracle property can be obtained, i.e. the estimator achieves the asymptotic Cramer-Rao lower bound corresponding to when it is known which regressors are active. The method is shown to perform favourably compared to other methods on a simulation example.

Place, publisher, year, edition, pages
IEEE , 2011. 2825-2830 p.
Series
IEEE Conference on Decision and Control. Proceedings, ISSN 0191-2216
Keyword [en]
Least absolute shrinkage and selection operators, Least Square, Least squares methods, Least-squares cost functions, Lower bounds, Parameter vectors, Simulation example, Sparse estimation, Validation criteria, Validation data
National Category
Control Engineering
Research subject
SRA - ICT
Identifiers
URN: urn:nbn:se:kth:diva-72604DOI: 10.1109/CDC.2011.6161189ISI: 000303506203070Scopus ID: 2-s2.0-84860663410ISBN: 978-1-61284-801-3 (print)OAI: oai:DiVA.org:kth-72604DiVA: diva2:488312
Conference
50th IEEE Conference on Decision and Control and European Control Conference (CDC-ECC11). Orlando, FL, USA. December 12-15, 2011
Note

QC 20120329

Available from: 2012-02-01 Created: 2012-01-31 Last updated: 2013-12-13Bibliographically approved

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Rojas, Cristian R.Hjalmarsson, Håkan

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