mlsanityData to 7 Oct 2026

Improved PAC-Bayesian Bounds for Linear Regression

arXiv 1912.03036 ↗First posted 6 Dec 2019cs.LG stat.MLcited by 12

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Abstract (arXiv)

In this paper, we improve the PAC-Bayesian error bound for linear regression derived in Germain et al. [10]. The improvements are twofold. First, the proposed error bound is tighter, and converges to the generalization loss with a well-chosen temperature parameter. Second, the error bound also holds for training data that are not independently sampled. In particular, the error bound applies to certain time series generated by well-known classes of dynamical models, such as ARX models.

Key facts. Cited by 12 papers in the map (data through 7 Oct 2026). First posted on arXiv 6 Dec 2019.

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Cited by year (2026 to 7 Oct)

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

12 papers.

  1. 2023PAC-Bayesian Generalization Bounds for Adversarial Generative Modelscited by 13
  2. 2022Scalable PAC-Bayesian Meta-Learning via the PAC-Optimal Hyper-Posterior: From Theory to Practicecited by 11
  3. 2021PAC-Bayesian theory for stochastic LTI systemscited by 6
  4. 2026Towards A Unified PAC-Bayesian Framework for Norm-based Generalization Boundscited by 4
  5. 2023PAC-Bayesian bounds for learning LTI-ss systems with input from empirical losscited by 3
  6. 2025PAC-Bayes Bounds for Multivariate Linear Regression and Linear Autoencoderscited by 3
  7. 2024Length independent generalization bounds for deep SSM architectures via Rademacher contraction and stability constraintscited by 2
  8. 2022PAC-Bayesian-Like Error Bound for a Class of Linear Time-Invariant Stochastic State-Space Modelscited by 1
  9. 2025PAC-Bayesian Reinforcement Learning Trains Generalizable Policiescited by 1
  10. 2026PAC--Bayes Bounds on Quotient Parameter Spaces: Geometry-induced Implicit-Bias Priorscited by 1
  11. 2025Stability-based Generalization Bounds for Variational Inferencecited by 0
  12. 2026A PAC-Bayesian View of Generalisation for Physics-Informed Machine Learningcited by 0