The paper proposes an interesting strategy for active learning in which the model must be learned from little or no data. This is a useful problem to study in practice (which the authors provide examples). As reviewers 2 and 4 note, I recommend polishing the related work particularly in the connections for the BELGAM model. Even the original DLGM paper of Rezende et al. (2014) use priors for the network parameters; but they do MAP estimation.