A General Framework for the Practical Disintegration of PAC-Bayesian Bounds

Paul Viallard (1) , Pascal Germain (2) , Amaury Habrard (3, 4, 5) , Emilie Morvant (3)

1 SIERRA - Statistical Machine Learning and Parsimony
2 Department of Computer Science and Software Engineering [Québec]
3 LabHC - Laboratoire Hubert Curien
4 UJM - Université Jean Monnet - Saint-Étienne
5 MALICE - Apprentissage automatique avec intégration des connaissances en ingénierie de surface : théorie et algorithmes

PAC-Bayesian bounds are known to be tight and informative when studying the generalization ability of randomized classifiers. However, they require a loose and costly derandomization step when applied to some families of deterministic models such as neural networks. As an alternative to this step, we introduce new PAC-Bayesian generalization bounds that have the originality to provide disintegrated bounds, i.e., they give guarantees over one single hypothesis instead of the usual averaged analysis. Our bounds are easily optimizable and can be used to design learning algorithms. We illustrate this behavior on neural networks, and we show a significant practical improvement over the state-of-the-art framework.

Keywords: Disintegration; PAC-Bayesian; Generalization Bound; Neural Networks

Domains: Machine Learning [stat.ML]

Paul Viallard, Pascal Germain, Amaury Habrard, Emilie Morvant. A General Framework for the Practical Disintegration of PAC-Bayesian Bounds. Machine Learning, 2023, 113 (2), pp.519-604. ⟨10.1007/s10994-023-06391-0⟩. ⟨hal-03143025v3⟩