The Generalized Reparameterization Gradient
The reparameterization gradient has become a widely used method to obtain Monte Carlo gradients to optimize the variational objective. However, this technique does not easily apply to commonly used distributions such as beta or gamma without further approximations, and most practical applications of the reparameterization gradient fit Gaussian distributions. In this paper, we introduce the generalized reparameterization gradient, a method that extends the reparameterization gradient to a wider class of variational distributions. Generalized reparameterizations use invertible transformations of the latent variables which lead to transformed distributions that weakly depend on the variational parameters. This results in new Monte Carlo gradients that combine reparameterization gradients and score function gradients. We demonstrate our approach on variational inference for two complex probabilistic models. The generalized reparameterization is effective: even a single sample from the variational distribution is enough to obtain a low-variance gradient.
This works studies stochastic variational inference for approximate posterior inference. The authors propose a unified framework for black-box variational inference based on the log-derivative trick (or score function method) and the reparametrization trick. More specifically, they generalise the latter to non-Gaussian posteriors and discuss three other popular cases (Gamma, Beta and log-normal). The report good experimental results. 
This paper was a pleasure to read. It was very well-written and provided an excellent and comprehensive synthesis of recent advances that make stochastic variational inference more generic.  The proposed formulation unifies black-box variational inference based on the score function and the reparametrization trick (used in the variational auto-encoder). The authors introduce the so-called generalized reparameterization gradient, a method that extends the reparameterization gradient to a wider class of variational distributions by allowing for weak dependency. The main idea is to define an invertible transformation of the latent variables such that the distribution of the transformed variables is only weakly governed by the variational parameters. This essentially means that at least the first moments of the auxiliary variable do not depend on the original variational parameters. While being presented as general, it is still required in practice to identify an appropriate transformation. Also, the considered cases are in the same class as the one covered by ADVI, but results are encouraging. The general reformulation is also a step forward in the direction of handling non-conjugate cases.  Could the authors discuss the choice of the denominator in the case of the beta into more detail? From the appendix, it was not clear to me why these choices are working well.  While the authors indicate that it is sufficient to consider only one sample, could they comment on how the results improve as a function of the number of samples?