Encoding spatiotemporal priors with VAEs for small-area estimation

• URL: http://arxiv.org/abs/2110.10422v1
• Date: Wed, 20 Oct 2021 08:14:15 GMT
• Title: Encoding spatiotemporal priors with VAEs for small-area estimation
• Authors: Elizaveta Semenova, Yidan Xu, Adam Howes, Theo Rashid, Samir Bhatt, Swapnil Mishra, Seth Flaxman
• Abstract summary: We propose a deep generative modelling approach to tackle a noveltemporal setting. We approximate a class of prior samplings through prior fitting of a variational autoencoder (VAE) VAE allows inference to become incredibly efficient due to independently distributed latent latent Gaussian space representation. We demonstrate the utility of our VAE two stage approach on Bayesian, small-area estimation tasks.
• Score: 2.4783465852664324
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Gaussian processes (GPs), implemented through multivariate Gaussian distributions for a finite collection of data, are the most popular approach in small-area spatiotemporal statistical modelling. In this context they are used to encode correlation structures over space and time 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: for a particular spatiotemporal 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 spatiotemporal 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 spatiotemporal priors and facilitates efficient statistical inference. We demonstrate the utility of our VAE two stage approach on Bayesian, small-area estimation tasks.

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