<div class="csl-bib-body">
<div class="csl-entry">Graczyk, P., Schneider, U., Skalski, T., & Tardivel, P. (2023). Pattern Recovery in Penalized Estimation and its Geometry. In <i>European Meeting of Statisticians 2023 : Book of Abstracts</i> (pp. 223–223). http://hdl.handle.net/20.500.12708/189992</div>
</div>
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dc.identifier.uri
http://hdl.handle.net/20.500.12708/189992
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dc.description.abstract
For many penalized estimators such as LASSO, SLOPE, OSCAR, PACS, fused, clustered and generalized LASSO, the penalty term is a real-valued polyhedral gauge. We focus on pattern recovery at β with respect to such a penalty term, where β is the unknown parameter of regression coefficients. For LASSO, the pattern of β only depends on the sign of β and sign recovery by LASSO is a well known topic in the literature. We introduce the notion of patterns and pattern recovery in the broad framework of gauge-penalized least-squares estimation and illustrate the patterns different polyhedral gauges. We also provide theoretical guarantees for pattern recovery, in particular the “noiseless recovery condition” is necessary for a probability of recovery larger than 1/2 and can be viewed as a generalization of the LASSO’s irrepresentability condition. This condition may be relaxed using thresholded penalized least squares estimators, a class of estimators generalizing the thresholded LASSO. Indeed, we show that the “accessibility condition”, a weaker condition than the “noiseless recovery condition”, is necessary and asymptotically sufficient for pattern recovery in thresholded penalized estimation. We also provide a geometric interpretation of our approach to pattern recovery and the accessibility condition.
en
dc.language.iso
en
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dc.subject
Penalized Estimation
en
dc.subject
Pattern Recovery
en
dc.title
Pattern Recovery in Penalized Estimation and its Geometry
en
dc.type
Inproceedings
en
dc.type
Konferenzbeitrag
de
dc.contributor.affiliation
University of Angers, France
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dc.contributor.affiliation
Wrocław University of Science and Technology, Poland
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dc.contributor.affiliation
University of Wroclaw and University of Burgundy
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dc.description.startpage
223
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dc.description.endpage
223
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dc.type.category
Abstract Book Contribution
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tuw.booktitle
European Meeting of Statisticians 2023 : Book of Abstracts
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tuw.researchTopic.id
A4
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tuw.researchTopic.id
C4
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tuw.researchTopic.id
A3
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tuw.researchTopic.name
Mathematical Methods in Economics
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tuw.researchTopic.name
Mathematical and Algorithmic Foundations
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tuw.researchTopic.name
Fundamental Mathematics Research
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tuw.researchTopic.value
40
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tuw.researchTopic.value
20
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tuw.researchTopic.value
40
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tuw.publication.orgunit
E105-02 - Forschungsbereich Ökonometrie und Systemtheorie
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dc.description.numberOfPages
1
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tuw.author.orcid
0000-0001-8212-8881
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tuw.author.orcid
0000-0001-5752-572X
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tuw.author.orcid
0000-0002-8496-3909
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tuw.event.name
European Meeting of Statisticians 2023
en
tuw.event.startdate
03-07-2023
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tuw.event.enddate
07-07-2023
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tuw.event.online
On Site
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tuw.event.type
Event for scientific audience
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tuw.event.place
Warsaw
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tuw.event.country
PL
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tuw.event.institution
Bernoulli Society for Mathematical Statistics and Probability
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tuw.event.presenter
Schneider, Ulrike
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wb.sciencebranch
Informatik
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wb.sciencebranch
Mathematik
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wb.sciencebranch.oefos
1020
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wb.sciencebranch.oefos
1010
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wb.sciencebranch.value
20
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wb.sciencebranch.value
80
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item.grantfulltext
restricted
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item.languageiso639-1
en
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item.fulltext
no Fulltext
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item.cerifentitytype
Publications
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item.openairetype
conference paper
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item.openairecristype
http://purl.org/coar/resource_type/c_5794
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crisitem.author.dept
University of Angers, France
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crisitem.author.dept
E105 - Institut für Stochastik und Wirtschaftsmathematik