mlsanityData to 7 Oct 2026

Learning Gaussian Processes by Minimizing PAC-Bayesian Generalization Bounds

arXiv 1810.12263 ↗First posted 29 Oct 2018stat.ML cs.LGcited by 24

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Abstract (arXiv)

Gaussian Processes (GPs) are a generic modelling tool for supervised learning. While they have been successfully applied on large datasets, their use in safety-critical applications is hindered by the lack of good performance guarantees. To this end, we propose a method to learn GPs and their sparse approximations by directly optimizing a PAC-Bayesian bound on their generalization performance, instead of maximizing the marginal likelihood. Besides its theoretical appeal, we find in our evaluation that our learning method is robust and yields significantly better generalization guarantees than other common GP approaches on several regression benchmark datasets.

Key facts. Cited by 24 papers in the map (data through 7 Oct 2026). First posted on arXiv 29 Oct 2018.

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Citing papers per year: 2021: 9; 2022: 3; 2023: 2; 2024: 6; 2025: 3; 2026: 1.

24 papers.

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  1. 2021Personalized Federated Learning with Gaussian Processescited by 76
  2. 2021How to Certify Machine Learning Based Safety-critical Systems? A Systematic Literature Reviewcited by 36
  3. 2023More PAC-Bayes bounds: From bounded losses, to losses with general tail behaviors, to anytime validitycited by 17
  4. 2021Learning Stochastic Majority Votes by Minimizing a PAC-Bayes Generalization Boundcited by 16
  5. 2021A PAC-Bayes Analysis of Adversarial Robustnesscited by 13
  6. 2021Chebyshev-Cantelli PAC-Bayes-Bennett Inequality for the Weighted Majority Votecited by 13
  7. 2022Scalable PAC-Bayesian Meta-Learning via the PAC-Optimal Hyper-Posterior: From Theory to Practicecited by 11
  8. 2024PAC-Bayes-Chernoff bounds for unbounded lossescited by 9
  9. 2021Self-Bounding Majority Vote Learning Algorithms by the Direct Minimization of a Tight PAC-Bayesian C-Boundcited by 8
  10. 2022PAC-Bayes Bounds for Bandit Problems: A Survey and Experimental Comparisoncited by 7
  11. 2024Leveraging PAC-Bayes Theory and Gibbs Distributions for Generalization Bounds with Complexity Measurescited by 7
  12. 2021On out-of-distribution detection with Bayesian neural networkscited by 6
12 more
  1. 2024Data-Driven Performance Guarantees for Classical and Learned Optimizerscited by 5
  2. 2024Deep Exploration with PAC-Bayescited by 4
  3. 2025Streaming Generated Gaussian Process Experts for Online Learning and Control: Extended Versioncited by 4
  4. 2021PAC Bayesian Performance Guarantees for Deep (Stochastic) Networks in Medical Imagingcited by 3
  5. 2023PAC-Bayesian Soft Actor-Critic Learningcited by 3
  6. 2021Convolutional Normalizing Flows for Deep Gaussian Processescited by 2
  7. 2024Multi-View Majority Vote Learning Algorithms: Direct Minimization of PAC-Bayesian Boundscited by 1
  8. 2026Reframing Long-Tailed Learning via Loss Landscape Geometrycited by 1
  9. 2022Streaming PAC-Bayes Gaussian process regression with a performance guarantee for online decision makingcited by 0
  10. 2024Misclassification excess risk bounds for PAC-Bayesian classification via convexified losscited by 0
  11. 2025Deep Actor-Critics with Tight Risk Certificatescited by 0
  12. 2025Relative Information Gain and Gaussian Process Regressioncited by 0