A1 Journal article (refereed)
Fast and universal estimation of latent variable models using extended variational approximations (2023)
Korhonen, P., Hui, F. K. C., Niku, J., & Taskinen, S. (2023). Fast and universal estimation of latent variable models using extended variational approximations. Statistics and Computing, 33, Article 26. https://doi.org/10.1007/s11222-022-10189-w
JYU authors or editors
Publication details
All authors or editors: Korhonen, Pekka; Hui, Francis K. C.; Niku, Jenni; Taskinen, Sara
Journal or series: Statistics and Computing
ISSN: 0960-3174
eISSN: 1573-1375
Publication year: 2023
Publication date: 24/12/2022
Volume: 33
Article number: 26
Publisher: Springer
Publication country: United States
Publication language: English
DOI: https://doi.org/10.1007/s11222-022-10189-w
Publication open access: Openly available
Publication channel open access: Partially open access channel
Publication is parallel published (JYX): https://jyx.jyu.fi/handle/123456789/84733
Abstract
Generalized linear latent variable models (GLLVMs) are a class of methods for analyzing multi-response data which has gained considerable popularity in recent years, e.g., in the analysis of multivariate abundance data in ecology. One of the main features of GLLVMs is their capacity to handle a variety of responses types, such as (overdispersed) counts, binomial and (semi-)continuous responses, and proportions data. On the other hand, the inclusion of unobserved latent variables poses a major computational challenge, as the resulting marginal likelihood function involves an intractable integral for non-normally distributed responses. This has spurred research into a number of approximation methods to overcome this integral, with a recent and particularly computationally scalable one being that of variational approximations (VA). However, research into the use of VA for GLLVMs has been hampered by the fact that fully closed-form variational lower bounds have only been obtained for certain combinations of response distributions and link functions. In this article, we propose an extended variational approximations (EVA) approach which widens the set of VA-applicable GLLVMs dramatically. EVA draws inspiration from the underlying idea behind the Laplace approximation: by replacing the complete-data likelihood function with its second order Taylor approximation about the mean of the variational distribution, we can obtain a fully closed-form approximation to the marginal likelihood of the GLLVM for any response type and link function. Through simulation studies and an application to a species community of testate amoebae, we demonstrate how EVA results in a “universal” approach to fitting GLLVMs, which remains competitive in terms of estimation and inferential performance relative to both standard VA (where any intractable integrals are either overcome through reparametrization or quadrature) and a Laplace approximation approach, while being computationally more scalable than both methods in practice.
Keywords: variables; estimating (statistical methods)
Free keywords: generalized linear latent variable models; laplace approximation; multi-response data; multivariate abundance data; ordination; variational approximations
Contributing organizations
Ministry reporting: Yes
Reporting Year: 2022
JUFO rating: 2