Variational Bayesian Framework for Joint Posterior-Predictive Inference

A new variational Bayesian framework directly targets the posterior-predictive distribution, jointly learning approximations of both the posterior and predictive distribution. This approach introduces a variational upper bound on Kullback-Leibler divergence with moment-based regularization. The method is trained in an amortized manner, aiming to reduce computational demands of traditional two-stage procedures, especially for high-fidelity models like those governed by partial differential equations.