How good is PAC-Bayes at explaining generalisation?

Antoine Picard-Weibel; Eugenio Clerico; Roman Moscoviz; Benjamin Guedj

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arXiv · 2503.08231

How good is PAC-Bayes at explaining generalisation?

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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Antoine Picard-Weibel, Eugenio Clerico, Roman Moscoviz, Benjamin Guedj. 2025-03-11. How good is PAC-Bayes at explaining generalisation?. https://arxiv.org/abs/2503.08231

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