We derive streamlined mean field variational Bayes algorithms for fitting linear mixed models with crossed random effects. In the most general situation, where the dimensions of the crossed groups are arbitrarily large, streamlining is hindered by lack of sparseness in the underlying least squares system. Because of this fact we also consider a hierarchy of relaxations of the mean field product restriction. The least stringent product restriction delivers a high degree of inferential accuracy. However, this accuracy must be mitigated against its higher storage and computing demands. Faster sparse storage and computing alternatives are also provided, but come with the price of diminished inferential accuracy. This article provides full algorithmic details of three variational inference strategies, presents detailed empirical results on their pros and cons and, thus, guides the users on their choice of variational inference approach depending on the problem size and computing resources. Supplementary materials for this article are available online.

Streamlined Variational Inference for Linear Mixed Models with Crossed Random Effects

Di Credico, Gioia;
2023-01-01

Abstract

We derive streamlined mean field variational Bayes algorithms for fitting linear mixed models with crossed random effects. In the most general situation, where the dimensions of the crossed groups are arbitrarily large, streamlining is hindered by lack of sparseness in the underlying least squares system. Because of this fact we also consider a hierarchy of relaxations of the mean field product restriction. The least stringent product restriction delivers a high degree of inferential accuracy. However, this accuracy must be mitigated against its higher storage and computing demands. Faster sparse storage and computing alternatives are also provided, but come with the price of diminished inferential accuracy. This article provides full algorithmic details of three variational inference strategies, presents detailed empirical results on their pros and cons and, thus, guides the users on their choice of variational inference approach depending on the problem size and computing resources. Supplementary materials for this article are available online.
File in questo prodotto:
File Dimensione Formato  
Di Credico Streamlined.pdf

Accesso chiuso

Descrizione: articolo
Tipologia: Documento in Versione Editoriale
Licenza: Copyright Editore
Dimensione 7.4 MB
Formato Adobe PDF
7.4 MB Adobe PDF   Visualizza/Apri   Richiedi una copia
Di+Credico+Streamlined-Post_print.pdf

Open Access dal 02/09/2023

Tipologia: Bozza finale post-referaggio (post-print)
Licenza: Digital Rights Management non definito
Dimensione 7.78 MB
Formato Adobe PDF
7.78 MB Adobe PDF Visualizza/Apri
Pubblicazioni consigliate

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11368/3028999
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 0
  • ???jsp.display-item.citation.isi??? 1
social impact