Scalable Non-Gaussian Variational Inference for Spatial Fields Using Sparse Autoregressive Normalizing Flows

Abstract: We introduce a novel framework for scalable and flexible variational inference targeting the non-Gaussian posterior of a latent continuous function or field. For both the prior and variational family, we consider sparse autoregressive structures corresponding to nearest-neighbor directed acyclic graphs. Within the variational family, conditional distributions are modeled with highly flexible normalizing flows. We provide an algorithm for doubly stochastic variational optimization, achieving polylogarithmic time complexity per iteration. Empirical evaluations show that our method offers improved accuracy compared to existing techniques.