Robust least squares methods under bounded data uncertainties

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dc.citation.epage92en_US
dc.citation.spage82en_US
dc.citation.volumeNumber36en_US
dc.contributor.authorVanli, N. D.en_US
dc.contributor.authorDonmez, M. A.en_US
dc.contributor.authorKozat, S. S.en_US
dc.date.accessioned2016-02-08T10:15:57Z
dc.date.available2016-02-08T10:15:57Z
dc.date.issued2015en_US
dc.departmentDepartment of Electrical and Electronics Engineeringen_US
dc.description.abstractWe study the problem of estimating an unknown deterministic signal that is observed through an unknown deterministic data matrix under additive noise. In particular, we present a minimax optimization framework to the least squares problems, where the estimator has imperfect data matrix and output vector information. We define the performance of an estimator relative to the performance of the optimal least squares (LS) estimator tuned to the underlying unknown data matrix and output vector, which is defined as the regret of the estimator. We then introduce an efficient robust LS estimation approach that minimizes this regret for the worst possible data matrix and output vector, where we refrain from any structural assumptions on the data. We demonstrate that minimizing this worst-case regret can be cast as a semi-definite programming (SDP) problem. We then consider the regularized and structured LS problems and present novel robust estimation methods by demonstrating that these problems can also be cast as SDP problems. We illustrate the merits of the proposed algorithms with respect to the well-known alternatives in the literature through our simulations.en_US
dc.description.provenanceMade available in DSpace on 2016-02-08T10:15:57Z (GMT). No. of bitstreams: 1 bilkent-research-paper.pdf: 70227 bytes, checksum: 26e812c6f5156f83f0e77b261a471b5a (MD5) Previous issue date: 2015en
dc.identifier.doi10.1016/j.dsp.2014.10.004en_US
dc.identifier.issn1051-2004
dc.identifier.urihttp://hdl.handle.net/11693/23580
dc.language.isoEnglishen_US
dc.publisherAcademic Pressen_US
dc.relation.isversionofhttp://dx.doi.org/10.1016/j.dsp.2014.10.004en_US
dc.source.titleDigital Signal Processingen_US
dc.subjectData estimationen_US
dc.subjectLeast squaresen_US
dc.subjectAdditive noiseen_US
dc.subjectEstimationen_US
dc.subjectMatrix algebraen_US
dc.subjectOptimizationen_US
dc.subjectMinimaxen_US
dc.subjectRegreten_US
dc.subjectRobusten_US
dc.subjectLeast squares approximationsen_US
dc.titleRobust least squares methods under bounded data uncertaintiesen_US
dc.typeArticleen_US

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