# Improved PAC-Bayesian Bounds for Linear Regression

arXiv: https://arxiv.org/abs/1912.03036 · HTML: https://mlsanity.com/paper/1912.03036/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Dec 2019.

## Built on by (most cited first, 12 of 12)

- [PAC-Bayesian Generalization Bounds for Adversarial Generative Models](https://mlsanity.com/paper/2302.08942/) (2023)
- [Scalable PAC-Bayesian Meta-Learning via the PAC-Optimal Hyper-Posterior: From Theory to Practice](https://mlsanity.com/paper/2211.07206/) (2022)
- [PAC-Bayesian theory for stochastic LTI systems](https://mlsanity.com/paper/2103.12866/) (2021)
- [PAC-Bayesian bounds for learning LTI-ss systems with input from empirical loss](https://mlsanity.com/paper/2303.16816/) (2023)
- [Towards A Unified PAC-Bayesian Framework for Norm-based Generalization Bounds](https://mlsanity.com/paper/2601.08100/) (2026)
- [PAC-Bayes Bounds for Multivariate Linear Regression and Linear Autoencoders](https://mlsanity.com/paper/2512.12905/) (2025)
- [Length independent generalization bounds for deep SSM architectures via Rademacher contraction and stability constraints](https://mlsanity.com/paper/2405.20278/) (2024)
- [PAC-Bayesian-Like Error Bound for a Class of Linear Time-Invariant Stochastic State-Space Models](https://mlsanity.com/paper/2212.14838/) (2022)
- [PAC-Bayesian Reinforcement Learning Trains Generalizable Policies](https://mlsanity.com/paper/2510.10544/) (2025)
- [PAC--Bayes Bounds on Quotient Parameter Spaces: Geometry-induced Implicit-Bias Priors](https://mlsanity.com/paper/2607.18422/) (2026)
- [Stability-based Generalization Bounds for Variational Inference](https://mlsanity.com/paper/2502.12353/) (2025)
- [A PAC-Bayesian View of Generalisation for Physics-Informed Machine Learning](https://mlsanity.com/paper/2605.26341/) (2026)

## 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.