mlsanityData to 14 Oct 2026

PAC-Bayes bounds for stable algorithms with instance-dependent priors

arXiv 1806.06827 ↗First posted 18 Jun 2018stat.ML cs.LGcited by 21

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Abstract (arXiv)

PAC-Bayes bounds have been proposed to get risk estimates based on a training sample. In this paper the PAC-Bayes approach is combined with stability of the hypothesis learned by a Hilbert space valued algorithm. The PAC-Bayes setting is used with a Gaussian prior centered at the expected output. Thus a novelty of our paper is using priors defined in terms of the data-generating distribution. Our main result estimates the risk of the randomized algorithm in terms of the hypothesis stability coefficients. We also provide a new bound for the SVM classifier, which is compared to other known bounds experimentally. Ours appears to be the first stability-based bound that evaluates to non-trivial values.

Key facts. Cited by 21 papers in the map (data through 14 Oct 2026). First posted on arXiv 18 Jun 2018.

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Citing papers per year: 2021: 6; 2022: 7; 2023: 4; 2024: 3; 2025: 1.

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  1. 2022On Convergence of FedProx: Local Dissimilarity Invariant Bounds, Non-smoothness and Beyondcited by 38
  2. 2021Generalization Bounds for Meta-Learning via PAC-Bayes and Uniform Stabilitycited by 30
  3. 2021PAC-Bayes Information Bottleneckcited by 28
  4. 2022Non-Vacuous Generalisation Bounds for Shallow Neural Networkscited by 22
  5. 2021On Margins and Derandomisation in PAC-Bayescited by 19
  6. 2023Differentially Private Algorithms for the Stochastic Saddle Point Problem with Optimal Rates for the Strong Gapcited by 12
  7. 2021PAC-Bayes Bounds for Meta-learning with Data-Dependent Priorcited by 11
  8. 2022Scalable PAC-Bayesian Meta-Learning via the PAC-Optimal Hyper-Posterior: From Theory to Practicecited by 11
  9. 2022Tighter PAC-Bayes Generalisation Bounds by Leveraging Example Difficultycited by 9
  10. 2022PAC-Bayes Bounds for Bandit Problems: A Survey and Experimental Comparisoncited by 7
  11. 2023Sample-Conditioned Hypothesis Stability Sharpens Information-Theoretic Generalization Boundscited by 6
  12. 2021PAC Bayesian Performance Guarantees for Deep (Stochastic) Networks in Medical Imagingcited by 3
9 more
  1. 2022Controlling Multiple Errors Simultaneously with a PAC-Bayes Boundcited by 3
  2. 2023STEEL: Singularity-aware Reinforcement Learningcited by 3
  3. 2024Leveraging Gradients for Unsupervised Accuracy Estimation under Distribution Shiftcited by 3
  4. 2021Probabilistic fine-tuning of pruning masks and PAC-Bayes self-bounded learningcited by 2
  5. 2023Information-Theoretic Generalization Bounds for Transductive Learning and its Applicationscited by 2
  6. 2024Generalization of Hamiltonian algorithmscited by 2
  7. 2024Stability and Sharper Risk Bounds with Convergence Rate tildeO(1/n2)cited by 2
  8. 2022Higher-Order Generalization Bounds: Learning Deep Probabilistic Programs via PAC-Bayes Objectivescited by 1
  9. 2025Randomized Pairwise Learning with Adaptive Sampling: A PAC-Bayes Analysiscited by 1