# On Statistical Optimality of Variational Bayes

arXiv: https://arxiv.org/abs/1712.08983 · HTML: https://mlsanity.com/paper/1712.08983/

## Key facts

- Cited by 21 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Dec 2017.

## Built on by (most cited first, 21 of 21)

- [Personalized Federated Learning via Variational Bayesian Inference](https://mlsanity.com/paper/2206.07977/) (2022)
- [Mean-field Variational Inference via Wasserstein Gradient Flow](https://mlsanity.com/paper/2207.08074/) (2022)
- [On the Convergence of Coordinate Ascent Variational Inference](https://mlsanity.com/paper/2306.01122/) (2023)
- [Layer Adaptive Node Selection in Bayesian Neural Networks: Statistical Guarantees and Implementation Details](https://mlsanity.com/paper/2108.11000/) (2021)
- [FedHB: Hierarchical Bayesian Federated Learning](https://mlsanity.com/paper/2305.04979/) (2023)
- [Statistical and Computational Trade-offs in Variational Inference: A Case Study in Inferential Model Selection](https://mlsanity.com/paper/2207.11208/) (2022)
- [Federated Learning via Variational Bayesian Inference: Personalization, Sparsity and Clustering](https://mlsanity.com/paper/2303.04345/) (2023)
- [Machine Learning and the Future of Bayesian Computation](https://mlsanity.com/paper/2304.11251/) (2023)
- [Structured Optimal Variational Inference for Dynamic Latent Space Models](https://mlsanity.com/paper/2209.15117/) (2022)
- [Bayesian Personalized Federated Learning with Shared and Personalized Uncertainty Representations](https://mlsanity.com/paper/2309.15499/) (2023)
- [Personalized Federated Learning via Amortized Bayesian Meta-Learning](https://mlsanity.com/paper/2307.02222/) (2023)
- [Pointwise uncertainty quantification for sparse variational Gaussian process regression with a Brownian motion prior](https://mlsanity.com/paper/2310.00097/) (2023)
- [Maximum a Posteriori Inference for Factor Graphs via Benders' Decomposition](https://mlsanity.com/paper/2410.19131/) (2024)
- [Bayesian Coreset Optimization for Personalized Federated Learning](https://mlsanity.com/paper/2511.01800/) (2025)
- [Stability of Sequential and Parallel Coordinate Ascent Variational Inference](https://mlsanity.com/paper/2603.20929/) (2026)
- [Symmetry Guarantees Statistic Recovery in Variational Inference](https://mlsanity.com/paper/2604.18310/) (2026)
- [Even More Guarantees for Variational Inference in the Presence of Symmetries](https://mlsanity.com/paper/2604.21407/) (2026)
- [Exclusive Topic Modeling](https://mlsanity.com/paper/2102.03525/) (2021)
- [A Hierarchical Bayesian Model for Deep Few-Shot Meta Learning](https://mlsanity.com/paper/2306.09702/) (2023)
- [Mode Collapse of Mean-Field Variational Inference](https://mlsanity.com/paper/2510.17063/) (2025)
- [Variational bagging: a robust approach for Bayesian uncertainty quantification](https://mlsanity.com/paper/2511.20594/) (2025)

## Abstract (arXiv)

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.