Richer variational families (semi-implicit VI) for NNGP-based spatial variational inference

Develop and analyze semi-implicit variational inference variational families for the variational distribution in Nearest Neighbor Gaussian Process (NNGP)-based Bayesian spatial linear mixed effects models, in order to better capture complex posterior dependencies between regression coefficients and spatial random effects while retaining computational scalability.

Background

The paper introduces spVarBayes, a suite of variational Bayes methods for large spatial data using NNGP priors, including spVB-MFA, spVB-MFA-LR, spVB-NNGP, and a joint version capturing dependence between fixed and random effects. While these methods significantly improve accuracy and speed over existing VI approaches and compare favorably to MCMC baselines, the authors note limitations of block-independence and Gaussian variational families in capturing complex posterior dependencies.

To address these limitations, the authors identify open directions that would enhance flexibility and accuracy, specifically richer variational families such as semi-implicit variational inference, which are designed to better represent intricate dependency structures in posterior distributions beyond standard Gaussian approximations.