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.
@article{arxiv.1912.03036,
title = {Improved PAC-Bayesian Bounds for Linear Regression},
author = {Vera Shalaeva and Alireza Fakhrizadeh Esfahani and Pascal Germain and Mihaly Petreczky},
journal= {arXiv preprint arXiv:1912.03036},
year = {2019}
}