mlsanityData to 7 Oct 2026

Concentration of tempered posteriors and of their variational approximations

arXiv 1706.09293 ↗First posted 28 Jun 2017math.ST cs.LG stat.THcited by 66

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Abstract (arXiv)

While Bayesian methods are extremely popular in statistics and machine learning, their application to massive datasets is often challenging, when possible at all. Indeed, the classical MCMC algorithms are prohibitively slow when both the model dimension and the sample size are large. Variational Bayesian methods aim at approximating the posterior by a distribution in a tractable family. Thus, MCMC are replaced by an optimization algorithm which is orders of magnitude faster. VB methods have been applied in such computationally demanding applications as including collaborative filtering, image and video processing, NLP and text processing... However, despite very nice results in practice, the theoretical properties of these approximations are usually not known. In this paper, we propose a general approach to prove the concentration of variational approximations of fractional posteriors. We apply our theory to two examples: matrix completion, and Gaussian VB.

Key facts. Cited by 66 papers in the map (data through 7 Oct 2026). First posted on arXiv 28 Jun 2017.

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Citing papers per year: 2021: 10; 2022: 8; 2023: 15; 2024: 13; 2025: 11; 2026: 9.

66 papers.

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  1. 2021User-friendly introduction to PAC-Bayes boundscited by 234
  2. 2022Variational inference via Wasserstein gradient flowscited by 84
  3. 2022Personalized Federated Learning via Variational Bayesian Inferencecited by 68
  4. 2021Detecting Model Misspecification in Amortized Bayesian Inference with Neural Networkscited by 48
  5. 2023Forward-backward Gaussian variational inference via JKO in the Bures-Wasserstein Spacecited by 36
  6. 2023Provable convergence guarantees for black-box variational inferencecited by 29
  7. 2023On the Convergence of Black-Box Variational Inferencecited by 22
  8. 2024Outlier-robust Kalman Filtering through Generalised Bayescited by 21
  9. 2022Mean-field Variational Inference via Wasserstein Gradient Flowcited by 19
  10. 2023On the Convergence of Coordinate Ascent Variational Inferencecited by 18
  11. 2021On the Robustness to Misspecification of α-Posteriors and Their Variational Approximationscited by 15
  12. 2021Local convexity of the TAP free energy and AMP convergence for Z2-synchronizationcited by 15
38 more
  1. 2023Towards Understanding the Dynamics of Gaussian-Stein Variational Gradient Descentcited by 13
  2. 2021A practical tutorial on Variational Bayescited by 10
  3. 2021Variational Inference in high-dimensional linear regressioncited by 10
  4. 2023Linear Convergence of Black-Box Variational Inference: Should We Stick the Landing?cited by 10
  5. 2024Posterior and variational inference for deep neural networks with heavy-tailed weightscited by 9
  6. 2024Variational Inference in Location-Scale Families: Exact Recovery of the Mean and Correlation Matrixcited by 9
  7. 2021The computational asymptotics of Gaussian variational inference and the Laplace approximationcited by 8
  8. 2022Tackling covariate shift with node-based Bayesian neural networkscited by 8
  9. 2024Detecting Model Misspecification in Amortized Bayesian Inference with Neural Networks: An Extended Investigationcited by 8
  10. 2024Concentration of a sparse Bayesian model with Horseshoe prior in estimating high-dimensional precision matrixcited by 8
  11. 2022Statistical and Computational Trade-offs in Variational Inference: A Case Study in Inferential Model Selectioncited by 7
  12. 2024Concentration properties of fractional posterior in 1-bit matrix completioncited by 7
  13. 2021Monotonic Alpha-divergence Minimisation for Variational Inferencecited by 5
  14. 2022Meta-Uncertainty in Bayesian Model Comparisoncited by 5
  15. 2023Semiparametric inference using fractional posteriorscited by 4
  16. 2023Particle Mean Field Variational Bayescited by 4
  17. 2023Machine Learning and the Future of Bayesian Computationcited by 4
  18. 2023FedBIAD: Communication-Efficient and Accuracy-Guaranteed Federated Learning with Bayesian Inference-Based Adaptive Dropoutcited by 4
  19. 2023Bayesian Model Selection via Mean-Field Variational Approximationcited by 4
  20. 2025High-dimensional Bayesian Tobit regression for censored response with Horseshoe priorcited by 4
  21. 2022AdaAnn: Adaptive Annealing Scheduler for Probability Density Approximationcited by 3
  22. 2025Generalized Guarantees for Variational Inference in the Presence of Even and Elliptical Symmetrycited by 3
  23. 2026Position: agentic AI orchestration should be Bayes-consistentcited by 3
  24. 2022Structured Optimal Variational Inference for Dynamic Latent Space Modelscited by 2
  25. 2023Variational Gaussian Processes For Linear Inverse Problemscited by 2
  26. 2024General bounds on the quality of Bayesian coresetscited by 2
  27. 2025STITCH-OPE: Trajectory Stitching with Guided Diffusion for Off-Policy Evaluationcited by 2
  28. 2025Handling bounded response in high dimensions: a Horseshoe prior Bayesian Beta regression approachcited by 2
  29. 2023Pointwise uncertainty quantification for sparse variational Gaussian process regression with a Brownian motion priorcited by 1
  30. 2024Adaptive posterior concentration rates for sparse high-dimensional linear regression with random design and unknown error variancecited by 1
  31. 2024Temperature Optimization for Bayesian Deep Learningcited by 1
  32. 2024Convergence of Statistical Estimators via Mutual Information Boundscited by 1
  33. 2025Robust and Scalable Variational Bayescited by 1
  34. 2025Nearly Dimension-Independent Convergence of Mean-Field Black-Box Variational Inferencecited by 1
  35. 2026Stability of Sequential and Parallel Coordinate Ascent Variational Inferencecited by 1
  36. 2026Convergence of projected stochastic natural gradient variational inference for various step size and sample or batch size schedulescited by 1
  37. 2026Symmetry Guarantees Statistic Recovery in Variational Inferencecited by 1
  38. 2021Simulation comparisons between Bayesian and de-biased estimators in low-rank matrix completioncited by 0

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