Improving Variational Approximations

Nick Foti, Ryan Adams, and I just put a paper on the arxiv about improving variational approximations (short version accepted early to AABI2016). We focused on one problematic aspect of variational inference in practice -- that once the optimization problem is solved, the approximation is set and there isn't a straightforward way to improve it, even when we can afford some extra compute time. Markov chain Monte Carlo methods have a simple solution -- run the chain for more steps and the posterior approximation will get better and better. When that pre-specified class of distributions (the variational family) doesn't include the neighborhood around the target distribution, the resulting VI solution will still be sub-optimal, in that there will be a non-zero KL-divergence between the approximation and the target. This will result in biased posterior estimates.