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How good is PAC-Bayes at explaining generalisation?

11 March 2025
Antoine Picard-Weibel
Eugenio Clerico
Roman Moscoviz
Benjamin Guedj
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Abstract

We discuss necessary conditions for a PAC-Bayes bound to provide a meaningful generalisation guarantee. Our analysis reveals that the optimal generalisation guarantee depends solely on the distribution of the risk induced by the prior distribution. In particular, achieving a target generalisation level is only achievable if the prior places sufficient mass on high-performing predictors. We relate these requirements to the prevalent practice of using data-dependent priors in deep learning PAC-Bayes applications, and discuss the implications for the claim that PAC-Bayes ``explains'' generalisation.

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@article{picard-weibel2025_2503.08231,
  title={ How good is PAC-Bayes at explaining generalisation? },
  author={ Antoine Picard-Weibel and Eugenio Clerico and Roman Moscoviz and Benjamin Guedj },
  journal={arXiv preprint arXiv:2503.08231},
  year={ 2025 }
}
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