Reviews: Hierarchical Implicit Models and Likelihood-Free Variational Inference

The paper defines a class of probability models -- hierarchical implicit models -- consisting of observations with associated'local' latent variables that are conditionally independent given a set of'global' latent variables, and in which the observation likelihood is not assumed to be tractable. It describes an approach for KL-based variational inference in such'likelihood-free' models, using a GAN-style discriminator to estimate the log ratio between a'variational joint' q(x, z), constructed using the empirical distribution on observations, and the true model joint density. This approach has the side benefit of supporting implicit variational models ('variational programs'). Proof-of-concept applications are demonstrated to ecological simulation, a Bayesian GAN, and sequence modeling with a stochastic RNN. The exposition is very clear, well cited, and the technical machinery is carefully explained.