PriorVAE: encoding spatial priors with variational autoencoders for small-area estimation
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 interpol...
| Main Authors: | , , , , , , |
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| Format: | Journal article |
| Language: | English |
| Published: |
Royal Society
2022
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| _version_ | 1797106999887921152 |
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| author | Semenova, ES Xu, Y Howes, A Rashid, T Bhatt, S Mishra, S Flaxman, S |
| author_facet | Semenova, ES Xu, Y Howes, A Rashid, T Bhatt, S Mishra, S Flaxman, S |
| author_sort | Semenova, ES |
| collection | OXFORD |
| description | 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. |
| first_indexed | 2024-03-07T07:10:26Z |
| format | Journal article |
| id | oxford-uuid:3309c032-c573-4b17-8748-9474e4f6087a |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T07:10:26Z |
| publishDate | 2022 |
| publisher | Royal Society |
| record_format | dspace |
| spelling | oxford-uuid:3309c032-c573-4b17-8748-9474e4f6087a2022-06-21T11:06:45ZPriorVAE: encoding spatial priors with variational autoencoders for small-area estimationJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:3309c032-c573-4b17-8748-9474e4f6087aEnglishSymplectic ElementsRoyal Society2022Semenova, ESXu, YHowes, ARashid, TBhatt, SMishra, SFlaxman, SGaussian 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. |
| spellingShingle | Semenova, ES Xu, Y Howes, A Rashid, T Bhatt, S Mishra, S Flaxman, S PriorVAE: encoding spatial priors with variational autoencoders for small-area estimation |
| title | PriorVAE: encoding spatial priors with variational autoencoders for small-area estimation |
| title_full | PriorVAE: encoding spatial priors with variational autoencoders for small-area estimation |
| title_fullStr | PriorVAE: encoding spatial priors with variational autoencoders for small-area estimation |
| title_full_unstemmed | PriorVAE: encoding spatial priors with variational autoencoders for small-area estimation |
| title_short | PriorVAE: encoding spatial priors with variational autoencoders for small-area estimation |
| title_sort | priorvae encoding spatial priors with variational autoencoders for small area estimation |
| work_keys_str_mv | AT semenovaes priorvaeencodingspatialpriorswithvariationalautoencodersforsmallareaestimation AT xuy priorvaeencodingspatialpriorswithvariationalautoencodersforsmallareaestimation AT howesa priorvaeencodingspatialpriorswithvariationalautoencodersforsmallareaestimation AT rashidt priorvaeencodingspatialpriorswithvariationalautoencodersforsmallareaestimation AT bhatts priorvaeencodingspatialpriorswithvariationalautoencodersforsmallareaestimation AT mishras priorvaeencodingspatialpriorswithvariationalautoencodersforsmallareaestimation AT flaxmans priorvaeencodingspatialpriorswithvariationalautoencodersforsmallareaestimation |