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On l1 Mean and Variance Filtering
KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.ORCID iD: 0000-0002-1927-1690
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)
2011 (English)In: Proceedings of the 45th Annual Asilomar Conference on Signals, Systems, and Computers 2011, IEEE , 2011, 1913-1916 p.Conference paper, Published paper (Refereed)
Abstract [en]

This paper addresses the problem of segmenting a time-series with respect to changes in the mean value or in the variance. The first case is when the time data is modeled as a sequence of independent and normal distributed random variables with unknown, possibly changing, mean value but fixed variance. The main assumption is that the mean value is piecewise constant in time, and the task is to estimate the change times and the mean values within the segments. The second case is when the mean value is constant, but the variance can change. The assumption is that the variance is piecewise constant in time, and we want to estimate change times and the variance values within the segments. To find solutions to these problems, we will study an l_1 regularized maximum likelihood method, related to the fused lasso method and l_1 trend filtering, where the parameters to be estimated are free to vary at each sample. To penalize variations in the estimated parameters, the $l_1$-norm of the time difference of the parameters is used as a regularization term. This idea is closely related to total variation denoising. The main contribution is that a convex formulation of this variance estimation problem, where the parametrization is based on the inverse of the variance, can be formulated as a certain $l_1$ mean estimation problem. This implies that results and methods for mean estimation can be applied to the challenging problem of variance segmentation/estimation

Place, publisher, year, edition, pages
IEEE , 2011. 1913-1916 p.
Series
Conference Record of the Asilomar Conference on Signals, Systems and Computers, ISSN 1058-6393
Keyword [en]
De-noising; Distributed random variables; Estimated parameter; Estimation problem; Fixed variance; Lasso method; Maximum likelihood methods; Mean values; Parametrizations; Piecewise constant; Time-differences; Total variation; Variance estimation
National Category
Control Engineering
Identifiers
URN: urn:nbn:se:kth:diva-55870Scopus ID: 2-s2.0-84861311315ISBN: 9781467303231 (print)OAI: oai:DiVA.org:kth-55870DiVA: diva2:471963
Conference
The 45th Annual Asilomar Conference on Signals, Systems, and Computers, November 6-9, 2011, Pacific Grove, California, USA
Funder
Swedish Research Council
Note

QC 20140908

Available from: 2012-01-31 Created: 2012-01-03 Last updated: 2017-03-28Bibliographically approved

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IR-EE-RT 2011:101(147 kB)139 downloads
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Type fulltextMimetype application/pdf

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