PriorVAE: encoding spatial priors with variational autoencoders for small-area estimation.
File(s)
Published version
Author(s)
Type
Journal Article
Abstract
Gaussian processes (GPs), implemented through multivariate Gaussian distributions for a finite collection of data, are the most popular approach in small-area spatial statistical modelling. In this context, they are used to encode correlation structures over space and can generalize well in interpolation tasks. Despite their flexibility, off-the-shelf GPs present serious computational challenges which limit their scalability and practical usefulness in applied settings. Here, we propose a novel, deep generative modelling approach to tackle this challenge, termed PriorVAE: for a particular spatial setting, we approximate a class of GP priors through prior sampling and subsequent fitting of a variational autoencoder (VAE). Given a trained VAE, the resultant decoder allows spatial inference to become incredibly efficient due to the low dimensional, independently distributed latent Gaussian space representation of the VAE. Once trained, inference using the VAE decoder replaces the GP within a Bayesian sampling framework. This approach provides tractable and easy-to-implement means of approximately encoding spatial priors and facilitates efficient statistical inference. We demonstrate the utility of our VAE two-stage approach on Bayesian, small-area estimation tasks.
Date Issued
2022-06-08
Date Acceptance
2022-05-12
Citation
Journal of the Royal Society Interface, 2022, 19 (191), pp.1-11
ISSN
1742-5662
Publisher
The Royal Society
Start Page
1
End Page
11
Journal / Book Title
Journal of the Royal Society Interface
Volume
19
Issue
191
Copyright Statement
© 2022 The Authors. Published by the Royal Society under the terms of the Creative Commons AttributionLicense http://creativecommons.org/licenses/by/4.0/, which permits unrestricted use, provided the originalauthor and source are credited.
License URL
Identifier
https://www.ncbi.nlm.nih.gov/pubmed/35673858
Subjects
Bayesian inference
Gaussian process prior
small-area estimation
spatial modelling
variational autoencoder
Publication Status
Published
Coverage Spatial
England
Date Publish Online
2022-06-08