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A Primer on PAC-Bayesian Learning

arXiv 1901.05353 ↗First posted 16 Jan 2019stat.ML cs.LGcited by 132

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Abstract (arXiv)

Generalised Bayesian learning algorithms are increasingly popular in machine learning, due to their PAC generalisation properties and flexibility. The present paper aims at providing a self-contained survey on the resulting PAC-Bayes framework and some of its main theoretical and algorithmic developments.

Key facts. Cited by 132 papers in the map (data through 14 Oct 2026). First posted on arXiv 16 Jan 2019.

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2021: 17; 2022: 33; 2023: 36; 2024: 17; 2025: 16; 2026: 13.

132 papers.

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  1. 2021User-friendly introduction to PAC-Bayes boundscited by 239
  2. 2021Subgroup Generalization and Fairness of Graph Neural Networkscited by 69
  3. 2025Deep Learning is Not So Mysterious or Differentcited by 56
  4. 2022Investigating the Impact of Model Misspecification in Neural Simulation-based Inferencecited by 45
  5. 2021Tighter expected generalization error bounds via Wasserstein distancecited by 43
  6. 2023Generalization in Graph Neural Networks: Improved PAC-Bayesian Bounds on Graph Diffusioncited by 40
  7. 2022Robust Fine-Tuning of Deep Neural Networks with Hessian-based Generalization Guaranteescited by 34
  8. 2023MMD-FUSE: Learning and Combining Kernels for Two-Sample Testing Without Data Splittingcited by 33
  9. 2023A Rigorous Link between Deep Ensembles and (Variational) Bayesian Methodscited by 32
  10. 2022A New Family of Generalization Bounds Using Samplewise Evaluated CMIcited by 28
  11. 2022Sim-to-Lab-to-Real: Safe Reinforcement Learning with Shielding and Generalization Guaranteescited by 27
  12. 2023A unified recipe for deriving (time-uniform) PAC-Bayes boundscited by 25
38 more
  1. 2022PAC-Bayes Generalisation Bounds for Heavy-Tailed Losses through Supermartingalescited by 24
  2. 2021Meta-Learning Reliable Priors in the Function Spacecited by 23
  3. 2022Non-Vacuous Generalisation Bounds for Shallow Neural Networkscited by 22
  4. 2022Online PAC-Bayes Learningcited by 22
  5. 2023Coherent Soft Imitation Learningcited by 22
  6. 2021Learning PAC-Bayes Priors for Probabilistic Neural Networkscited by 21
  7. 2022On PAC-Bayesian reconstruction guarantees for VAEscited by 20
  8. 2021On Margins and Derandomisation in PAC-Bayescited by 19
  9. 2022Integral Probability Metrics PAC-Bayes Boundscited by 19
  10. 2022Few-Shot Calibration of Set Predictors via Meta-Learned Cross-Validation-Based Conformal Predictioncited by 17
  11. 2021Learning Stochastic Majority Votes by Minimizing a PAC-Bayes Generalization Boundcited by 16
  12. 2023Statistical Guarantees for Variational Autoencoders using PAC-Bayesian Theorycited by 16
  13. 2023Exponential Smoothing for Off-Policy Learningcited by 15
  14. 2022PAC-Bayesian Domain Adaptation Bounds for Multiclass Learnerscited by 13
  15. 2022Bayesian Continual Learning via Spiking Neural Networkscited by 13
  16. 2022Empirical Risk Minimization with Relative Entropy Regularizationcited by 13
  17. 2023PAC-Bayesian Generalization Bounds for Adversarial Generative Modelscited by 13
  18. 2024A PAC-Bayesian Link Between Generalisation and Flat Minimacited by 13
  19. 2023Learning via Wasserstein-Based High Probability Generalisation Boundscited by 12
  20. 2023Transformers in Reinforcement Learning: A Surveycited by 12
  21. 2023Improved Algorithms for Stochastic Linear Bandits Using Tail Bounds for Martingale Mixturescited by 12
  22. 2022Adversarial robustness of sparse local Lipschitz predictorscited by 11
  23. 2022Scalable PAC-Bayesian Meta-Learning via the PAC-Optimal Hyper-Posterior: From Theory to Practicecited by 11
  24. 2023Quantum Conformal Prediction for Reliable Uncertainty Quantification in Quantum Machine Learningcited by 11
  25. 2024More Flexible PAC-Bayesian Meta-Learning by Learning Learning Algorithmscited by 11
  26. 2021Wide stochastic networks: Gaussian limit and PAC-Bayesian trainingcited by 10
  27. 2021Progress in Self-Certified Neural Networkscited by 10
  28. 2022Chained Generalisation Boundscited by 10
  29. 2022Inferring Smooth Control: Monte Carlo Posterior Policy Iteration with Gaussian Processescited by 10
  30. 2023A path-norm toolkit for modern networks: consequences, promises and challengescited by 10
  31. 2022Generalisation under gradient descent via deterministic PAC-Bayescited by 9
  32. 2022Tighter PAC-Bayes Generalisation Bounds by Leveraging Example Difficultycited by 9
  33. 2023Data-dependent Generalization Bounds via Variable-Size Compressibilitycited by 9
  34. 2024PAC-Bayes-Chernoff bounds for unbounded lossescited by 9
  35. 2024Generalization bounds for mixing processes via delayed online-to-PAC conversionscited by 9
  36. 2022Empirical Risk Minimization with Relative Entropy Regularization: Optimality and Sensitivity Analysiscited by 8
  37. 2023Bayes meets Bernstein at the Meta Level: an Analysis of Fast Rates in Meta-Learning with PAC-Bayescited by 8
  38. 2023Sparsity-aware generalization theory for deep neural networkscited by 8

50 most cited of 132 All 132 (JSON)