Title: On Statistical Optimality of Variational Bayes,
Abstract: The article addresses a long-standing open problem on the justification of
using variational Bayes methods for parameter estimation. We provide general
conditions for obtaining optimal risk bounds for point estimates acquired from
mean-field variational Bayesian inference. The conditions pertain to the
existence of certain test functions for the distance metric on the parameter
space and minimal assumptions on the prior. A general recipe for verification
of the conditions is outlined which is broadly applicable to existing Bayesian
models with or without latent variables. As illustrations, specific
applications to Latent Dirichlet Allocation and Gaussian mixture models are
discussed.