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Recent advances have shown that GP priors, or their finite realisations, canbe encoded using deep generative models such as variational autoencoders(VAEs). These learned generators can serve as drop-in replacements for theoriginal priors during MCMC inference. While this approach enables efficientinference, it loses information about the hyperparameters of the originalmodels, and consequently makes inference over hyperparameters impossible andthe learned priors indistinct. To overcome this limitation, we condition theVAE on stochastic process hyperparameters. This allows the joint encoding ofhyperparameters with GP realizations and their subsequent estimation duringinference. Further, we demonstrate that our proposed method, PriorCVAE, isagnostic to the nature of the models which it approximates, and can be used,for instance, to encode solutions of ODEs. It provides a practical tool forapproximate inference and shows potential in real-life spatial andspatiotemporal applications.

PriorCVAE: scalable MCMC parameter inference with Bayesian deep generative modelling