PriorVAE: Encoding spatial priors with VAEs for small-area estimation

TL;DR

PriorVAE introduces a deep generative model using VAEs to efficiently approximate Gaussian process priors, significantly improving scalability and inference speed in small-area spatial statistical modeling.

Contribution

It presents a novel method to encode spatial priors with VAEs, replacing GPs for scalable and efficient small-area estimation.

Findings

VAE-based approach achieves faster inference.

Maintains comparable accuracy to traditional GPs.

Enables practical application in large-scale spatial modeling.

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 generalise 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.