Diffusion Probabilistic Models and Predictive Stacking in Bayesian Geostatistics



In this talk, I will discuss two different topics. The past decade has witnessed the success of generative modeling (e.g. GANs, VAEs,…) in creating high quality samples in a wide variety of data modalities. The first part of this talk is concerned with the recently developed diffusion models, the key idea of which is to reverse a certain stochastic dynamics. I will first take a continuous-time perspective, and examine the performance of different SDE schemes including VE (variance exploding) and VP (variance preserving). The discretization is more subtle, and our idea is to “contract” the reversed dynamics leading to possible new diffusion model designs. I will also highlight the difference between the ideal continuous time framework, and more realistic discrete modeling.

In the second part (if time permits), I will talk about predictive stacking in Bayesian geostatistics. The approach builds an augmented Bayesian linear regression framework that subsumes the realisations of the spatial random field and delivers tractable posterior inference, and then combines such inference by stacking individual models that is computationally efficient without the need of iterative algorithms such as MCMC and can exploit the benefits of parallel computations.


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