# Improved PAC-Bayesian Bounds for Linear Regression

@article{Shalaeva2020ImprovedPB, title={Improved PAC-Bayesian Bounds for Linear Regression}, author={Vera Shalaeva and Alireza Fakhrizadeh Esfahani and Pascal Germain and Mih{\'a}ly Petreczky}, journal={ArXiv}, year={2020}, volume={abs/1912.03036} }

In this paper, we improve the PAC-Bayesian error bound for linear regression derived in Germain et al. (2016). The improvements are two-fold. 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.

## 5 Citations

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Several applications are presented, including PAC-Bayesian bounds for various classes of losses and non-asymptotic intervals for Monte Carlo estimates and a generalized version of Hammersley-Chapman-Robbins inequality.

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This work presents a novel analysis of the generalization performance of Bayesian model averaging under model misspecification and i.i.d. data using a new family of second-order PAC-Bayes bounds, and derives a newfamily of Bayes-like algorithms, which can be implemented as variational and ensemble methods.

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