Partial correlation graphical LASSO

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• dc.contributor.author Carter, Jack Storror
• dc.contributor.author Rossell Ribera, David
• dc.contributor.author Smith, Jim Q.
• dc.date.accessioned 2025-04-17T06:17:01Z
• dc.date.available 2025-04-17T06:17:01Z
• dc.date.issued 2023
• dc.description.abstract 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.
• dc.description.sponsorship 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 2021
• dc.format.mimetype application/pdf
• dc.identifier.citation Carter JS, Rossell D, Smith JQ. Partial correlation graphical LASSO. Scandinavian Journal of Statistics. 2023;51(1):32-63. DOI: 10.1111/sjos.12675
• dc.identifier.doi http://dx.doi.org/10.1111/sjos.12675
• dc.identifier.issn 0303-6898
• dc.identifier.uri http://hdl.handle.net/10230/70162
• dc.language.iso eng
• dc.publisher Wiley
• dc.relation.ispartof Scandinavian Journal of Statistics. 2023;51(1):32-63
• dc.relation.projectID info:eu-repo/grantAgreement/ES/3PE/CNS2022-135963
• dc.rights This 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.
• dc.rights.accessRights info:eu-repo/semantics/openAccess
• dc.rights.uri https://creativecommons.org/licenses/by/4.0/
• dc.subject.keyword Covariance matrix estimation
• dc.subject.keyword Gaussian graphical model
• dc.subject.keyword Gaphical LASSO
• dc.subject.keyword Partial correlation
• dc.subject.keyword Penalized likelihood
• dc.subject.keyword Precision matrix
• dc.title Partial correlation graphical LASSO
• dc.type info:eu-repo/semantics/article
• dc.type.version info:eu-repo/semantics/publishedVersion