mlsanityData to 7 Oct 2026

Convergence Rates of Variational Posterior Distributions

arXiv 1712.02519 ↗First posted 7 Dec 2017math.ST stat.ML stat.THcited by 45

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Abstract (arXiv)

We study convergence rates of variational posterior distributions for nonparametric and high-dimensional inference. We formulate general conditions on prior, likelihood, and variational class that characterize the convergence rates. Under similar "prior mass and testing" conditions considered in the literature, the rate is found to be the sum of two terms. The first term stands for the convergence rate of the true posterior distribution, and the second term is contributed by the variational approximation error. For a class of priors that admit the structure of a mixture of product measures, we propose a novel prior mass condition, under which the variational approximation error of the mean-field class is dominated by convergence rate of the true posterior. We demonstrate the applicability of our general results for various models, prior distributions and variational classes by deriving convergence rates of the corresponding variational posteriors.

Key facts. Cited by 45 papers in the map (data through 7 Oct 2026). First posted on arXiv 7 Dec 2017.

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Citing papers per year: 2021: 9; 2022: 5; 2023: 9; 2024: 7; 2025: 9; 2026: 6.

45 papers.

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  1. 2021User-friendly introduction to PAC-Bayes boundscited by 234
  2. 2021Detecting Model Misspecification in Amortized Bayesian Inference with Neural Networkscited by 48
  3. 2022Mean-field Variational Inference via Wasserstein Gradient Flowcited by 19
  4. 2023On the Convergence of Coordinate Ascent Variational Inferencecited by 18
  5. 2021Local convexity of the TAP free energy and AMP convergence for Z2-synchronizationcited by 15
  6. 2021A practical tutorial on Variational Bayescited by 10
  7. 2024Posterior and variational inference for deep neural networks with heavy-tailed weightscited by 9
  8. 2024Variational Inference in Location-Scale Families: Exact Recovery of the Mean and Correlation Matrixcited by 9
  9. 2021The computational asymptotics of Gaussian variational inference and the Laplace approximationcited by 8
  10. 2024Detecting Model Misspecification in Amortized Bayesian Inference with Neural Networks: An Extended Investigationcited by 8
  11. 2022Statistical and Computational Trade-offs in Variational Inference: A Case Study in Inferential Model Selectioncited by 7
  12. 2022Meta-Uncertainty in Bayesian Model Comparisoncited by 5
33 more
  1. 2023Particle Mean Field Variational Bayescited by 4
  2. 2023Machine Learning and the Future of Bayesian Computationcited by 4
  3. 2023A Mean Field Approach to Empirical Bayes Estimation in High-dimensional Linear Regressioncited by 4
  4. 2023Bayesian Model Selection via Mean-Field Variational Approximationcited by 4
  5. 2021Spike and slab Bayesian sparse principal component analysiscited by 3
  6. 2021A fast asynchronous MCMC sampler for sparse Bayesian inferencecited by 3
  7. 2024Nonparametric Automatic Differentiation Variational Inference with Spline Approximationcited by 3
  8. 2024A Particle Algorithm for Mean-Field Variational Inferencecited by 3
  9. 2025Generalized Guarantees for Variational Inference in the Presence of Even and Elliptical Symmetrycited by 3
  10. 2022Structured Optimal Variational Inference for Dynamic Latent Space Modelscited by 2
  11. 2023Variational Gaussian Processes For Linear Inverse Problemscited by 2
  12. 2025Adaptive sparse variational approximations for Gaussian process regressioncited by 2
  13. 2021Bayesian Joint Chance Constrained Optimization: Approximations and Statistical Consistencycited by 1
  14. 2023Pointwise uncertainty quantification for sparse variational Gaussian process regression with a Brownian motion priorcited by 1
  15. 2024Convergence of Statistical Estimators via Mutual Information Boundscited by 1
  16. 2025Globally Convergent Variational Inferencecited by 1
  17. 2025Robust and Scalable Variational Bayescited by 1
  18. 2025Nearly Dimension-Independent Convergence of Mean-Field Black-Box Variational Inferencecited by 1
  19. 2025Rotated Mean-Field Variational Inference and Iterative Gaussianizationcited by 1
  20. 2026Symmetry Guarantees Statistic Recovery in Variational Inferencecited by 1
  21. 2026Even More Guarantees for Variational Inference in the Presence of Symmetriescited by 1
  22. 2021Exclusive Topic Modelingcited by 0
  23. 2022Scalable and adaptive variational Bayes methods for Hawkes processescited by 0
  24. 2023Variational Inference: Posterior Threshold Improves Network Clustering Accuracy in Sparse Regimescited by 0
  25. 2023The surrogate Gibbs-posterior of a corrected stochastic MALA: Towards uncertainty quantification for neural networkscited by 0
  26. 2024Variational Bayesian Bow tie Neural Networks with Shrinkagecited by 0
  27. 2025Variational empirical Bayes variable selection in high-dimensional logistic regressioncited by 0
  28. 2025Variational bagging: a robust approach for Bayesian uncertainty quantificationcited by 0
  29. 2025Robust Variational Bayes by Min-Max Median Aggregationcited by 0
  30. 2026Functional Bias and Tangent-Space Geometry in Variational Inferencecited by 0
  31. 2026Variational predictive resamplingcited by 0
  32. 2026Fast rates in Bayesian online learning with approximate posteriorscited by 0
  33. 2026Posterior Tempering Explains Variance Inflation in Linear and Generalized Linear Thompson Samplingcited by 0