Learning Model Reparametrizations: Implicit Variational Inference by Fitting MCMC distributions

We introduce a new algorithm for approximate inference that combines reparametrization, Markov chain Monte Carlo and variational methods. We construct a very flexible implicit variational distribution synthesized by an arbitrary Markov chain Monte Carlo operation and a deterministic transformation that can be optimized using the reparametrization trick. Unlike current methods for implicit variational inference, our method avoids the computation of log density ratios and therefore it is easily applicable to arbitrary continuous and differentiable models. We demonstrate the proposed algorithm for fitting banana-shaped distributions and for training variational autoencoders.