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## Section: New Results

### Axis 2: Improved PAC-Bayesian Bounds for Linear Regression

Participant: Pascal Germain, Vera Shalaeva

We improve the PAC-Bayesian error bound for linear regression provided in the literature. 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.

It is a joint work with Mihaly Petreczky and Alireza Fakhrizadeh Esfahani from Université de Lille. It has been accepted for publication as part of the AAAI 2020 conference [38].