On Statistical Optimality of Variational Bayes
This addresses a foundational issue in Bayesian inference, offering theoretical justification for variational methods used in machine learning.
The paper tackles the open problem of justifying variational Bayes for parameter estimation by providing general conditions for optimal risk bounds, with applications to Latent Dirichlet Allocation and Gaussian mixture models.
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.