Statistical Inference in Mean-Field Variational Bayes

Abstract

We conduct non-asymptotic analysis on the mean-field variational inference for approximating posterior distributions in complex Bayesian models that may involve latent variables. We show that the mean-field approximation to the posterior can be well-approximated relative to the Kullback-Leibler divergence discrepancy measure by a normal distribution whose center is the maximum likelihood estimator (MLE). In particular, our results imply that the center of the mean-field approximation matches the MLE up to higher-order terms and there is essentially no loss of efficiency in using it as a point estimator for the parameter in any regular parametric model with latent variables. We also propose a new class of variational weighted likelihood bootstrap (VWLB) methods for quantifying the uncertainty in the mean-field variational inference. The proposed VWLB can be viewed as a new sampling scheme that produces independent samples for approximating the posterior. Comparing with traditional sampling algorithms such Markov Chain Monte Carlo, VWLB can be implemented in parallel and is free of tuning.

References in corpus (7)

• Variational Autoencoder for Deep Learning of Images, Labels and Captions
• Asymptotic normality of maximum likelihood and its variational approximation for stochastic blockmodels
• Frequentist Consistency of Variational Bayes
• From $\epsilon$-entropy to KL-entropy: Analysis of minimum information complexity density estimation
• Parametric estimation. Finite sample theory
• Asymptotic normality and valid inference for Gaussian variational approximation
• A Variational Algorithm for Bayesian Variable Selection

Cited by in corpus (2)

• Bayesian Model Selection via Mean-Field Variational Approximation
• Variational Inference in high-dimensional linear regression