Learning Stochastic Majority Votes by Minimizing a PAC-Bayes Generalization Bound
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Abstract (arXiv)
We investigate a stochastic counterpart of majority votes over finite ensembles of classifiers, and study its generalization properties. While our approach holds for arbitrary distributions, we instantiate it with Dirichlet distributions: this allows for a closed-form and differentiable expression for the expected risk, which then turns the generalization bound into a tractable training objective. The resulting stochastic majority vote learning algorithm achieves state-of-the-art accuracy and benefits from (non-vacuous) tight generalization bounds, in a series of numerical experiments when compared to competing algorithms which also minimize PAC-Bayes objectives -- both with uninformed (data-independent) and informed (data-dependent) priors.
Key facts. Cited by 16 papers in the map (data through 7 Oct 2026). Builds on 19 of its 45 references that are in the map. First posted on arXiv 23 Jun 2021.
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19 of 45 references.
References · 19
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- 2019PyTorch: An Imperative Style, High-Performance Deep Learning Librarycited by 20,160
- 2017Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithmscited by 4,283
- 2017Computing Nonvacuous Generalization Bounds for Deep (Stochastic) Neural Networks with Many More Parameters than Training Datacited by 527
- 2019A Primer on PAC-Bayesian Learningcited by 130
- 2015On the properties of variational approximations of Gibbs posteriorscited by 121
- 2020Tighter risk certificates for neural networkscited by 112
- 2018Implicit Reparameterization Gradientscited by 84
- 2020On the role of data in PAC-Bayes boundscited by 64
- 2020PAC-Bayes Analysis Beyond the Usual Boundscited by 63
- 2016A Strongly Quasiconvex PAC-Bayesian Boundcited by 54
- 2015Risk Bounds for the Majority Vote: From a PAC-Bayesian Analysis to a Learning Algorithmcited by 50
7 more
- 2018Pathwise Derivatives Beyond the Reparameterization Trickcited by 36
- 2019PAC-Bayes Un-Expected Bernstein Inequalitycited by 36
- 2020Second Order PAC-Bayesian Bounds for the Weighted Majority Votecited by 34
- 2018Learning Gaussian Processes by Minimizing PAC-Bayesian Generalization Boundscited by 24
- 2021A General Framework for the Practical Disintegration of PAC-Bayesian Boundscited by 21
- 2018On PAC-Bayesian Bounds for Random Forestscited by 10
- 2021Self-Bounding Majority Vote Learning Algorithms by the Direct Minimization of a Tight PAC-Bayesian C-Boundcited by 8
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Citing papers per year: 2021: 1; 2022: 6; 2023: 4; 2024: 3; 2025: 1; 2026: 1.
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- 2023MMD-FUSE: Learning and Combining Kernels for Two-Sample Testing Without Data Splittingcited by 33
- 2022Non-Vacuous Generalisation Bounds for Shallow Neural Networkscited by 22
- 2021On Margins and Derandomisation in PAC-Bayescited by 19
- 2023Learning via Wasserstein-Based High Probability Generalisation Boundscited by 11
- 2022Generalisation under gradient descent via deterministic PAC-Bayescited by 9
- 2022Tighter PAC-Bayes Generalisation Bounds by Leveraging Example Difficultycited by 9
- 2024Uniform Generalization Bounds on Data-Dependent Hypothesis Sets via PAC-Bayesian Theory on Random Setscited by 9
- 2022Shedding a PAC-Bayesian Light on Adaptive Sliced-Wasserstein Distancescited by 7
- 2022On Margins and Generalisation for Voting Classifierscited by 7
- 2022Generalization Bounds for Gradient Methods via Discrete and Continuous Priorcited by 5
- 2025A Framework for Bounding Deterministic Risk with PAC-Bayes: Applications to Majority Votescited by 3
- 2023Federated Learning with Nonvacuous Generalisation Boundscited by 2
4 more
- 2024Learning via Surrogate PAC-Bayescited by 1
- 2024Multi-View Majority Vote Learning Algorithms: Direct Minimization of PAC-Bayesian Boundscited by 1
- 2023Bounding the Worst-class Error: A Boosting Approachcited by 0
- 2026PAC-Bayesian Generalization Guarantees for Fairness on Stochastic and Deterministic Classifierscited by 0
- 2026PAC-Bayesian Generalization Guarantees for Fairness on Stochastic and Deterministic Classifiers12 Feb 2026
- 2025A Framework for Bounding Deterministic Risk with PAC-Bayes: Applications to Majority Votes29 Oct 2025
- 2024Multi-View Majority Vote Learning Algorithms: Direct Minimization of PAC-Bayesian Bounds9 Nov 2024
- 2024Learning via Surrogate PAC-Bayes14 Oct 2024
- 2024Uniform Generalization Bounds on Data-Dependent Hypothesis Sets via PAC-Bayesian Theory on Random Sets26 Apr 2024
- 2023Bounding the Worst-class Error: A Boosting Approach20 Oct 2023
- 2023Federated Learning with Nonvacuous Generalisation Bounds17 Oct 2023
- 2023MMD-FUSE: Learning and Combining Kernels for Two-Sample Testing Without Data Splitting14 Jun 2023
- 2023Learning via Wasserstein-Based High Probability Generalisation Bounds7 Jun 2023
- 2022Tighter PAC-Bayes Generalisation Bounds by Leveraging Example Difficulty20 Oct 2022
- 2022Generalisation under gradient descent via deterministic PAC-Bayes6 Sep 2022
- 2022On Margins and Generalisation for Voting Classifiers9 Jun 2022
4 more
- 2022Shedding a PAC-Bayesian Light on Adaptive Sliced-Wasserstein Distances7 Jun 2022
- 2022Generalization Bounds for Gradient Methods via Discrete and Continuous Prior27 May 2022
- 2022Non-Vacuous Generalisation Bounds for Shallow Neural Networks3 Feb 2022
- 2021On Margins and Derandomisation in PAC-Bayes8 Jul 2021
- 2023MMD-FUSE: Learning and Combining Kernels for Two-Sample Testing Without Data Splittingcited by 33
- 2022Non-Vacuous Generalisation Bounds for Shallow Neural Networkscited by 22
- 2021On Margins and Derandomisation in PAC-Bayescited by 19
- 2023Learning via Wasserstein-Based High Probability Generalisation Boundscited by 11
- 2022Generalisation under gradient descent via deterministic PAC-Bayescited by 9
- 2022Tighter PAC-Bayes Generalisation Bounds by Leveraging Example Difficultycited by 9
- 2024Uniform Generalization Bounds on Data-Dependent Hypothesis Sets via PAC-Bayesian Theory on Random Setscited by 9
- 2022Shedding a PAC-Bayesian Light on Adaptive Sliced-Wasserstein Distancescited by 7
- 2022On Margins and Generalisation for Voting Classifierscited by 7
- 2022Generalization Bounds for Gradient Methods via Discrete and Continuous Priorcited by 5
- 2025A Framework for Bounding Deterministic Risk with PAC-Bayes: Applications to Majority Votescited by 3
- 2023Federated Learning with Nonvacuous Generalisation Boundscited by 2
12 most cited of 16 All 16 (JSON)
- 2026PAC-Bayesian Generalization Guarantees for Fairness on Stochastic and Deterministic Classifiers12 Feb 2026
- 2025A Framework for Bounding Deterministic Risk with PAC-Bayes: Applications to Majority Votes29 Oct 2025
- 2024Multi-View Majority Vote Learning Algorithms: Direct Minimization of PAC-Bayesian Bounds9 Nov 2024
- 2024Learning via Surrogate PAC-Bayes14 Oct 2024
- 2024Uniform Generalization Bounds on Data-Dependent Hypothesis Sets via PAC-Bayesian Theory on Random Sets26 Apr 2024
- 2023Bounding the Worst-class Error: A Boosting Approach20 Oct 2023
- 2023Federated Learning with Nonvacuous Generalisation Bounds17 Oct 2023
- 2023MMD-FUSE: Learning and Combining Kernels for Two-Sample Testing Without Data Splitting14 Jun 2023
- 2023Learning via Wasserstein-Based High Probability Generalisation Bounds7 Jun 2023
- 2022Tighter PAC-Bayes Generalisation Bounds by Leveraging Example Difficulty20 Oct 2022
- 2022Generalisation under gradient descent via deterministic PAC-Bayes6 Sep 2022
- 2022On Margins and Generalisation for Voting Classifiers9 Jun 2022
12 newest of 16 All 16 (JSON)