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Improved PAC-Bayesian Bounds for Linear Regression

Vera Shalaeva 1 Alireza Fakhrizadeh Esfahani 2, 3 Pascal Germain 1 Mihaly Petreczky 2, 3 
1 MODAL - MOdel for Data Analysis and Learning
LPP - Laboratoire Paul Painlevé - UMR 8524, Université de Lille, Sciences et Technologies, Inria Lille - Nord Europe, METRICS - Evaluation des technologies de santé et des pratiques médicales - ULR 2694, Polytech Lille - École polytechnique universitaire de Lille
Abstract : 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.
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Submitted on : Friday, December 6, 2019 - 9:41:57 AM
Last modification on : Thursday, March 24, 2022 - 3:42:56 AM
Long-term archiving on: : Saturday, March 7, 2020 - 2:09:11 PM


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  • HAL Id : hal-02396556, version 1
  • ARXIV : 1912.03036


Vera Shalaeva, Alireza Fakhrizadeh Esfahani, Pascal Germain, Mihaly Petreczky. Improved PAC-Bayesian Bounds for Linear Regression. AAAI 2020 - Thirty-Fourth AAAI Conference on Artificial Intelligence, Feb 2020, New York, United States. ⟨hal-02396556⟩



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