Iterative Refinement of Approximate Posterior for Training Directed Belief Networks

Deep directed graphical models, while a potentially powerful class of generative representations, are challenging to train due to difficult inference. Recent advances in variational inference that make use of an inference or recognition network have advanced well beyond traditional variational inference and Markov chain Monte Carlo methods. While these techniques offer higher flexibility as well as simpler and faster inference, they are still limited by approximate posterior inference and require variance reduction techniques. Less focus has been given to improving or refining the approximate posterior beyond what is provided by variational inference. We show that iterative refinement of the approximate posterior can provide notable gains in maximizing the lower bound of the log likelihood, either by applying gradient descent or by using adaptive importance sampling during the E-step of a variational expectation-maximization algorithm. We show our approach competes with state of the art in both continuous and binary latent variables.