Variance Reduction and Quasi-Newton for Particle-Based Variational Inference

Particle-based Variational Inference methods (ParVIs), like Stein Variational Gradient Descent, are nonparametric variational inference methods that optimize a set of particles to best approximate a target distribution. ParVIs have been proposed as efficient approximate inference algorithms and as potential alternatives to MCMC methods. However, to our knowledge, the quality of the posterior approximation of particles from ParVIs has not been examined before for challenging, large-scale Bayesian inference problems. In this paper, we find that existing ParVI approaches converge insufficiently fast under sample quality metrics, and we propose a novel variance reduction and quasi-Newton preconditioning framework for all ParVIs, by leveraging the Riemannian structure of the Wasserstein space and advanced Riemannian optimization algorithms. Experimental results demonstrate the accelerated convergence of ParVIs for accurate posterior inference in large-scale and ill-conditioned problems.