Approximate Laplace approximations for scalable model selection

Mostra el registre complet Registre parcial de l'ítem

• dc.contributor.author Rossell Ribera, David
• dc.contributor.author Abril Pla, Oriol
• dc.contributor.author Bhattacharya, Anirban
• dc.date.accessioned 2022-05-24T11:21:51Z
• dc.date.available 2022-05-24T11:21:51Z
• dc.date.issued 2021
• dc.description Includes supplementary materials for the online appendix.
• dc.description.abstract We propose the approximate Laplace approximation (ALA) to evaluate integrated likelihoods, a bottleneck in Bayesian model selection. The Laplace approximation (LA) is a popular tool that speeds up such computation and equips strong model selection properties. However, when the sample size is large or one considers many models the cost of the required optimizations becomes impractical. ALA reduces the cost to that of solving a least-squares problem for each model. Further, it enables efficient computation across models such as sharing pre-computed sufficient statistics and certain operations in matrix decompositions. We prove that in generalized (possibly non-linear) models ALA achieves a strong form of model selection consistency for a suitably-defined optimal model, at the same functional rates as exact computation. We consider fixed- and high-dimensional problems, group and hierarchical constraints, and the possibility that all models are misspecified. We also obtain ALA rates for Gaussian regression under non-local priors, an important example where the LA can be costly and does not consistently estimate the integrated likelihood. Our examples include non-linear regression, logistic, Poisson and survival models. We implement the methodology in the R package mombf.
• dc.description.sponsorship Spanish Government grants Europa Excelencia, Grant/Award Number: EUR2020-112096, RYC-2015-18544 and PGC2018-101643-B-I00; NIH, Grant/Award Number: R01 CA158113DMS-01.
• dc.format.mimetype application/pdf
• dc.identifier.citation Rosell D, Abril O, Bhattacharya A. Approximate Laplace approximations for scalable model selection. J R Stat Soc Series B. 2021 Sep;83(4):853-79. DOI: 10.1111/rssb.12466
• dc.identifier.doi http://dx.doi.org/10.1111/rssb.12466
• dc.identifier.issn 1369-7412
• dc.identifier.uri http://hdl.handle.net/10230/53231
• dc.language.iso eng
• dc.publisher Wiley
• dc.relation.ispartof Journal of the Royal Statistical Society: Series B. 2021 Sep;83(4):853-79
• dc.relation.projectID info:eu-repo/grantAgreement/ES/2PE/PGC2018-101643-B-I00
• dc.relation.projectID info:eu-repo/grantAgreement/ES/2PE/EUR2020-112096
• dc.rights © 2021 The Authors. Journal of the Royal Statistical Society: Series B (Statistical Methodology) published by John Wiley & Sons Ltd on behalf of Royal Statistical Society. This is an open access article under the terms of the Creative Commons Attribution-NonCommercial-NoDerivs License (http://creativecommons.org/licenses/by-nc-nd/4.0/), which permits use and distribution in any medium, provided the original work is properly cited, the use is non-commercial and no modifications or adaptations are made.
• dc.rights.accessRights info:eu-repo/semantics/openAccess
• dc.rights.uri http://creativecommons.org/licenses/by-nc-nd/4.0/
• dc.subject.keyword Approximate inference
• dc.subject.keyword Hierarchical constraints
• dc.subject.keyword Group constraints
• dc.subject.keyword Model misspecification
• dc.subject.keyword Model selection
• dc.subject.keyword Non- local priors
• dc.subject.keyword Non- parametric regression
• dc.title Approximate Laplace approximations for scalable model selection
• dc.type info:eu-repo/semantics/article
• dc.type.version info:eu-repo/semantics/publishedVersion