  In many real-world problems, there is a limited set of training data, but an
abundance of unlabeled data. We propose a new method, Generative Posterior
Networks (GPNs), that uses unlabeled data to estimate epistemic uncertainty in
high-dimensional problems. A GPN is a generative model that, given a prior
distribution over functions, approximates the posterior distribution directly
by regularizing the network towards samples from the prior. We prove
theoretically that our method indeed approximates the Bayesian posterior and
show empirically that it improves epistemic uncertainty estimation and
scalability over competing methods.
