mlsanityData to 14 Oct 2026

On Statistical Optimality of Variational Bayes

arXiv 1712.08983 ↗First posted 25 Dec 2017math.ST stat.ML stat.THcited by 21

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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.

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

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Citing papers per year: 2021: 2; 2022: 4; 2023: 8; 2024: 1; 2025: 3; 2026: 3.

21 papers.

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  1. 2022Personalized Federated Learning via Variational Bayesian Inferencecited by 68
  2. 2022Mean-field Variational Inference via Wasserstein Gradient Flowcited by 19
  3. 2023On the Convergence of Coordinate Ascent Variational Inferencecited by 18
  4. 2021Layer Adaptive Node Selection in Bayesian Neural Networks: Statistical Guarantees and Implementation Detailscited by 14
  5. 2023FedHB: Hierarchical Bayesian Federated Learningcited by 8
  6. 2022Statistical and Computational Trade-offs in Variational Inference: A Case Study in Inferential Model Selectioncited by 7
  7. 2023Federated Learning via Variational Bayesian Inference: Personalization, Sparsity and Clusteringcited by 5
  8. 2023Machine Learning and the Future of Bayesian Computationcited by 4
  9. 2022Structured Optimal Variational Inference for Dynamic Latent Space Modelscited by 2
  10. 2023Bayesian Personalized Federated Learning with Shared and Personalized Uncertainty Representationscited by 2
  11. 2023Personalized Federated Learning via Amortized Bayesian Meta-Learningcited by 1
  12. 2023Pointwise uncertainty quantification for sparse variational Gaussian process regression with a Brownian motion priorcited by 1
9 more
  1. 2024Maximum a Posteriori Inference for Factor Graphs via Benders' Decompositioncited by 1
  2. 2025Bayesian Coreset Optimization for Personalized Federated Learningcited by 1
  3. 2026Stability of Sequential and Parallel Coordinate Ascent Variational Inferencecited by 1
  4. 2026Symmetry Guarantees Statistic Recovery in Variational Inferencecited by 1
  5. 2026Even More Guarantees for Variational Inference in the Presence of Symmetriescited by 1
  6. 2021Exclusive Topic Modelingcited by 0
  7. 2023A Hierarchical Bayesian Model for Deep Few-Shot Meta Learningcited by 0
  8. 2025Mode Collapse of Mean-Field Variational Inferencecited by 0
  9. 2025Variational bagging: a robust approach for Bayesian uncertainty quantificationcited by 0