Elizaveta Semenova

Deep generative modelling aiding spatial statistics

Recent advances have demonstrated the use of deep generative models, like variational autoencoders (VAEs), to encode Gaussian Process (GP) priors or their finite realizations. These learned generators can replace original priors within Markov Chain Monte Carlo (MCMC) as a drop-in replacement, enabling efficient inference. However, this approach loses information about the original priors' hyperparameters, rendering hyperparameter inference impossible and the learned priors less distinct. To address this issue, a new method called PriorCVAE can be used. It conditions the VAE on stochastic process hyperparameters, allowing joint encoding and inference of hyperparameters and GP realizations. Importantly, PriorCVAE is model-agnostic, making it applicable to various domains, including encoding solutions of ordinary differential equations (ODEs). This method offers a practical tool for approximate inference with promising applications in spatial and spatiotemporal contexts.

In the talk, I will begin with an overview of spatial statistics and then introduce the PriorVAE method for encoding prior realizations. By discussing the advantages and limitations of PriorVAE, I will introduce PriorCVAE, demonstrate its applications, and explore potential future research directions.