Partial correlation graphical LASSO

Standard likelihood penalties to learn Gaussian graphical models are based on regularizing the off-diagonal entries of the precision matrix. Such methods, and their Bayesian counterparts, are not invariant to scalar multiplication of the variables, unless one standardizes the observed data to unit s...

Descripción completa

Detalles Bibliográficos
Autores: Carter, Jack Storror, Rossell Ribera, David, Smith, Jim Q.
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2023
País:España
Institución:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
Repositorio:Recercat. Dipósit de la Recerca de Catalunya
OAI Identifier:oai:recercat.cat:10230/70162
Acceso en línea:http://hdl.handle.net/10230/70162
http://dx.doi.org/10.1111/sjos.12675
Access Level:acceso abierto
Palabra clave:Covariance matrix estimation
Gaussian graphical model
Gaphical LASSO
Partial correlation
Penalized likelihood
Precision matrix
id ES_f79e5f0a6b9931196db3ad3bdfc4e39f
oai_identifier_str oai:recercat.cat:10230/70162
network_acronym_str ES
network_name_str España
repository_id_str
spelling Partial correlation graphical LASSOCarter, Jack StorrorRossell Ribera, DavidSmith, Jim Q.Covariance matrix estimationGaussian graphical modelGaphical LASSOPartial correlationPenalized likelihoodPrecision matrixStandard likelihood penalties to learn Gaussian graphical models are based on regularizing the off-diagonal entries of the precision matrix. Such methods, and their Bayesian counterparts, are not invariant to scalar multiplication of the variables, unless one standardizes the observed data to unit sample variances. We show that such standardization can have a strong effect on inference and introduce a new family of penalties based on partial correlations. We show that the latter, as well as the maximum likelihood, L0 and logarithmic penalties are scale invariant. We illustrate the use of one such penalty, the partial correlation graphical LASSO, which sets an L1 penalty on partial correlations. The associated optimization problem is no longer convex, but is conditionally convex. We show via simulated examples and in two real datasets that, besides being scale invariant, there can be important gains in terms of inference.Agencia Estatal de Investigación, Grant/Award Number: CNS2022-135963; Bando Per L’incentivazione Della Progettazione Europea 2020, Grant/Award Number:100021-2020-Er-Incent_Eu_Riccomagno; Engineering and Physical Sciences Research Council, Grant/AwardNumbers: EP/K039628/1, EP/L016710/1,EP/N510129/1; Europa Excelencia, Grant/Award Number: EUR2020-112096; Fundación BBVA, Ayudas a Proyectos de Investigación Científica en Matemáticas 2021Wiley202520252023info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfapplication/pdfhttp://hdl.handle.net/10230/70162http://dx.doi.org/10.1111/sjos.12675reponame:Recercat. Dipósit de la Recerca de Catalunyainstname:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)InglésScandinavian Journal of Statistics. 2023;51(1):32-63info:eu-repo/grantAgreement/ES/3PE/CNS2022-135963This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited. © 2023 The Authors.http://creativecommons.org/licenses/by/4.0/info:eu-repo/semantics/openAccessoai:recercat.cat:10230/701622026-05-29T05:05:01Z
dc.title.none.fl_str_mv Partial correlation graphical LASSO
title Partial correlation graphical LASSO
spellingShingle Partial correlation graphical LASSO
Carter, Jack Storror
Covariance matrix estimation
Gaussian graphical model
Gaphical LASSO
Partial correlation
Penalized likelihood
Precision matrix
title_short Partial correlation graphical LASSO
title_full Partial correlation graphical LASSO
title_fullStr Partial correlation graphical LASSO
title_full_unstemmed Partial correlation graphical LASSO
title_sort Partial correlation graphical LASSO
dc.creator.none.fl_str_mv Carter, Jack Storror
Rossell Ribera, David
Smith, Jim Q.
author Carter, Jack Storror
author_facet Carter, Jack Storror
Rossell Ribera, David
Smith, Jim Q.
author_role author
author2 Rossell Ribera, David
Smith, Jim Q.
author2_role author
author
dc.subject.none.fl_str_mv Covariance matrix estimation
Gaussian graphical model
Gaphical LASSO
Partial correlation
Penalized likelihood
Precision matrix
topic Covariance matrix estimation
Gaussian graphical model
Gaphical LASSO
Partial correlation
Penalized likelihood
Precision matrix
description Standard likelihood penalties to learn Gaussian graphical models are based on regularizing the off-diagonal entries of the precision matrix. Such methods, and their Bayesian counterparts, are not invariant to scalar multiplication of the variables, unless one standardizes the observed data to unit sample variances. We show that such standardization can have a strong effect on inference and introduce a new family of penalties based on partial correlations. We show that the latter, as well as the maximum likelihood, L0 and logarithmic penalties are scale invariant. We illustrate the use of one such penalty, the partial correlation graphical LASSO, which sets an L1 penalty on partial correlations. The associated optimization problem is no longer convex, but is conditionally convex. We show via simulated examples and in two real datasets that, besides being scale invariant, there can be important gains in terms of inference.
publishDate 2023
dc.date.none.fl_str_mv 2023
2025
2025
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/10230/70162
http://dx.doi.org/10.1111/sjos.12675
url http://hdl.handle.net/10230/70162
http://dx.doi.org/10.1111/sjos.12675
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Scandinavian Journal of Statistics. 2023;51(1):32-63
info:eu-repo/grantAgreement/ES/3PE/CNS2022-135963
dc.rights.none.fl_str_mv http://creativecommons.org/licenses/by/4.0/
info:eu-repo/semantics/openAccess
rights_invalid_str_mv http://creativecommons.org/licenses/by/4.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Wiley
publisher.none.fl_str_mv Wiley
dc.source.none.fl_str_mv reponame:Recercat. Dipósit de la Recerca de Catalunya
instname:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
instname_str Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
reponame_str Recercat. Dipósit de la Recerca de Catalunya
collection Recercat. Dipósit de la Recerca de Catalunya
repository.name.fl_str_mv
repository.mail.fl_str_mv
_version_ 1869424899350593536
score 15,81155

Similares en LA Referencia