mlsanityData to 7 Oct 2026

Second Order PAC-Bayesian Bounds for the Weighted Majority Vote

arXiv 2007.13532 ↗First posted 1 Jul 2020cs.LG stat.MLcited by 34

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Abstract (arXiv)

We present a novel analysis of the expected risk of weighted majority vote in multiclass classification. The analysis takes correlation of predictions by ensemble members into account and provides a bound that is amenable to efficient minimization, which yields improved weighting for the majority vote. We also provide a specialized version of our bound for binary classification, which allows to exploit additional unlabeled data for tighter risk estimation. In experiments, we apply the bound to improve weighting of trees in random forests and show that, in contrast to the commonly used first order bound, minimization of the new bound typically does not lead to degradation of the test error of the ensemble.

Key facts. Cited by 34 papers in the map (data through 7 Oct 2026). First posted on arXiv 1 Jul 2020.

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Citing papers per year: 2021: 10; 2022: 6; 2023: 8; 2024: 4; 2025: 2; 2026: 4.

34 papers.

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  1. 2023MMD-FUSE: Learning and Combining Kernels for Two-Sample Testing Without Data Splittingcited by 33
  2. 2021Diversity and Generalization in Neural Network Ensemblescited by 32
  3. 2021How Tight Can PAC-Bayes be in the Small Data Regime?cited by 24
  4. 2023Joint Training of Deep Ensembles Fails Due to Learner Collusioncited by 23
  5. 2022Non-Vacuous Generalisation Bounds for Shallow Neural Networkscited by 22
  6. 2023When are ensembles really effective?cited by 21
  7. 2021On Margins and Derandomisation in PAC-Bayescited by 19
  8. 2021Learning Stochastic Majority Votes by Minimizing a PAC-Bayes Generalization Boundcited by 16
  9. 2021A PAC-Bayes Analysis of Adversarial Robustnesscited by 13
  10. 2021Chebyshev-Cantelli PAC-Bayes-Bennett Inequality for the Weighted Majority Votecited by 13
  11. 2022Split-kl and PAC-Bayes-split-kl Inequalities for Ternary Random Variablescited by 11
  12. 2022Tighter PAC-Bayes Generalisation Bounds by Leveraging Example Difficultycited by 9
22 more
  1. 2024PAC-Bayes-Chernoff bounds for unbounded lossescited by 9
  2. 2021Self-Bounding Majority Vote Learning Algorithms by the Direct Minimization of a Tight PAC-Bayesian C-Boundcited by 8
  3. 2022On Margins and Generalisation for Voting Classifierscited by 7
  4. 2021Loss function based second-order Jensen inequality and its application to particle variational inferencecited by 3
  5. 2021Multi-class Probabilistic Bounds for Self-learningcited by 3
  6. 2022Confident Sinkhorn Allocation for Pseudo-Labelingcited by 3
  7. 2023Improving Fairness with Ensemble Combination: Margin-Dependent Boundscited by 3
  8. 2023PAC-Bayesian Soft Actor-Critic Learningcited by 3
  9. 2025A Framework for Bounding Deterministic Risk with PAC-Bayes: Applications to Majority Votescited by 3
  10. 2021Kernel Interpolation as a Bayes Point Machinecited by 1
  11. 2023Responsible AI (RAI) Games and Ensemblescited by 1
  12. 2024Multi-View Majority Vote Learning Algorithms: Direct Minimization of PAC-Bayesian Boundscited by 1
  13. 2026Smoothness-Based Derandomization of PAC-Bayes Boundscited by 1
  14. 2022Excess risk analysis for epistemic uncertainty with application to variational inferencecited by 0
  15. 2023EnSolver: Uncertainty-Aware Ensemble CAPTCHA Solvers with Theoretical Guaranteescited by 0
  16. 2023Something for (almost) nothing: Improving deep ensemble calibration using unlabeled datacited by 0
  17. 2024On Uniform, Bayesian, and PAC-Bayesian Deep Ensemblescited by 0
  18. 2024How many classifiers do we need?cited by 0
  19. 2025The Majority Vote Paradigm Shift: When Popular Meets Optimalcited by 0
  20. 2026PAC-Bayesian Generalization Guarantees for Fairness on Stochastic and Deterministic Classifierscited by 0
  21. 2026On the disintegration of the stochastic majority vote: From PAC-Bayesian bounds to a self-bounding algorithmcited by 0
  22. 2026CORE-STACK+: Meta-Learning for Deep Stacked Generalizationcited by 0