Improved PAC-Bayesian Bounds for Linear Regression

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 wellchosen 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.

Authors

• Vera Shalaeva
• Alireza Fakhrizadeh Esfahani
• Pascal Germain
• Mihaly Petreczky

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