Improved PAC-Bayesian Bounds for Linear Regression

  • Vera Shalaeva INRIA Lille Nord-Europe
  • Alireza Fakhrizadeh Esfahani Univ. Lille
  • Pascal Germain INRIA Lille Nord-Europe
  • Mihaly Petreczky Univ. Lille


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.

AAAI Technical Track: Machine Learning