Fast and accurate variational inference for models with many latent variables

Abstract

Models with a large number of latent variables are often used to utilize the information in big or complex data, but can be difficult to estimate. Variational inference methods provide an attractive solution. These methods use an approximation to the posterior density, yet for large latent variable models existing choices can be inaccurate or slow to calibrate. Here, we propose a family of tractable variational approximations that are more accurate and faster to calibrate for this case. It combines a parsimonious approximation for the parameter posterior with the exact conditional posterior of the latent variables. We derive a simplified expression for the re-parameterization gradient of the..