Variational Bernstein-von Mises theorem with increasing parameter dimension

2025/08/04 by Jiawei Yan, Peirong Xu, Yan, Jiawei +3
Computer Science · Mathematics · #Bayesian Methods and Mixture Models #Statistical Methods and Bayesian Inference #Statistical Methods and Inference

paper · pdf · doi:10.48550/arxiv.2508.02585

Abstract

Variational Bayes (VB) provides a computationally efficient alternative to Markov Chain Monte Carlo, especially for high-dimensional and large-scale inference. However, existing theory on VB primarily focuses on fixed-dimensional settings or specific models. To address this limitation, this paper develops a finite-sample theory for VB in a broad class of parametric models with latent variables. We establish theoretical properties of the VB posterior, including a non-asymptotic variational Bernstein--von Mises theorem. Furthermore, we derive consistency and asymptotic normality of the VB estimator. An application to multivariate Gaussian mixture models is presented for illustration.

Citations

• VaiPhy: a Variational Inference Based Algorithm for Phylogeny
• Variational Inference in high-dimensional linear regression
• Spike and slab variational Bayes for high dimensional logistic regression
• Statistical Inference in Mean-Field Variational Bayes
• Variational Bayes under Model Misspecification
• On Statistical Optimality of Variational Bayes
• Convergence Rates of Variational Posterior Distributions
• Advances in Variational Inference
• Gaussian Approximations for Probability Measures on R^d
• Variational Inference: A Review for Statisticians
• Bernstein - von Mises Theorem for growing parameter dimension

Related

• Variational Bayes under Model Misspecification
• Robust and Scalable Variational Bayes
• Improved dimension dependence in the Bernstein von Mises Theorem via a new Laplace approximation bound
• Statistical Inference in Mean-Field Variational Bayes
• The Bernstein-von Mises theorem for Semiparametric Mixtures