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dc.contributor.author
Stucky, Benjamin
dc.contributor.author
van de Geer, Sara
dc.date.accessioned
2018-01-05T07:52:05Z
dc.date.available
2017-10-19T02:04:52Z
dc.date.available
2017-11-24T17:16:59Z
dc.date.available
2017-12-22T13:04:35Z
dc.date.available
2018-01-04T15:44:49Z
dc.date.available
2018-01-05T07:52:05Z
dc.date.issued
2017
dc.identifier.issn
1532-4435
dc.identifier.issn
1533-7928
dc.identifier.uri
http://hdl.handle.net/20.500.11850/197668
dc.identifier.doi
10.3929/ethz-b-000197668
dc.description.abstract
We study a set of regularization methods for high-dimensional linear regression models. These penalized estimators have the square root of the residual sum of squared errors as loss function, and any weakly decomposable norm as penalty function. This fit measure is chosen because of its property that the estimator does not depend on the unknown standard deviation of the noise. On the other hand, a generalized weakly decomposable norm penalty is very useful in being able to deal with different underlying sparsity structures. We can choose a different sparsity inducing norm depending on how we want to interpret the unknown parameter vector β β . Structured sparsity norms, as defined in Micchelli et al. (2010), are special cases of weakly decomposable norms, therefore we also include the square root LASSO (Belloni et al., 2011), the group square root LASSO (Bunea et al., 2014) and a new method called the square root SLOPE (in a similar fashion to the SLOPE from Bogdan et al. 2015). For this collection of estimators our results provide sharp oracle inequalities with the Karush-Kuhn-Tucker conditions. We discuss some examples of estimators. Based on a simulation we illustrate some advantages of the square root SLOPE.
en_US
dc.language.iso
en
en_US
dc.publisher
MIT Press
en_US
dc.rights.uri
http://creativecommons.org/licenses/by/4.0/
dc.subject
Square root LASSO
en_US
dc.subject
Structured sparsity
en_US
dc.subject
Karush-Kuhn-Tucker
en_US
dc.subject
Sharp oracale inequality
en_US
dc.subject
Weak decomposability
en_US
dc.title
Sharp oracle inequalities for square root regularization
en_US
dc.type
Journal Article
dc.rights.license
Creative Commons Attribution 4.0 International
ethz.journal.title
Journal of Machine Learning Research
ethz.journal.volume
18
en_US
ethz.journal.issue
67
en_US
ethz.journal.abbreviated
J. mach. learn. res.
ethz.pages.start
1
en_US
ethz.pages.end
29
en_US
ethz.version.deposit
publishedVersion
en_US
ethz.grant
Inference in high-dimensional statistics
en_US
ethz.identifier.wos
ethz.identifier.scopus
ethz.publication.place
Cambridge, MA
en_US
ethz.publication.status
published
en_US
ethz.leitzahl
ETH Zürich::00002 - ETH Zürich::00012 - Lehre und Forschung::00007 - Departemente::02000 - Dep. Mathematik / Dep. of Mathematics::02537 - Seminar für Statistik (SfS) / Seminar for Statistics (SfS)::03717 - van de Geer, Sara / van de Geer, Sara
en_US
ethz.leitzahl.certified
ETH Zürich::00002 - ETH Zürich::00012 - Lehre und Forschung::00007 - Departemente::02000 - Dep. Mathematik / Dep. of Mathematics::02537 - Seminar für Statistik (SfS) / Seminar for Statistics (SfS)::03717 - van de Geer, Sara / van de Geer, Sara
ethz.identifier.url
http://www.jmlr.org/papers/v18/15-482.html
ethz.grant.agreementno
149145
ethz.grant.fundername
SNF
ethz.grant.funderDoi
10.13039/501100001711
ethz.grant.program
Projektförderung in Mathematik, Natur- und Ingenieurwissenschaften (Abteilung II)
ethz.date.deposited
2017-10-19T02:04:53Z
ethz.source
SCOPUS
ethz.eth
yes
en_US
ethz.availability
Open access
en_US
ethz.rosetta.installDate
2017-12-22T13:04:38Z
ethz.rosetta.lastUpdated
2018-11-06T06:17:08Z
ethz.rosetta.versionExported
true
ethz.COinS
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