Tighter Generalisation Bounds via Interpolation

Paul Viallard (1) , Maxime Haddouche (2, 3) , Umut Şimşekli (4) , Benjamin Guedj (5, 2, 3)

1 LACODAM - Large Scale Collaborative Data Mining
2 Inria-London - The Inria London Programme
3 MODAL - MOdel for Data Analysis and Learning
4 SIERRA - Statistical Machine Learning and Parsimony
5 UCL-CS - Department of Computer science [University College of London]

This paper contains a recipe for deriving new PAC-Bayes generalisation bounds based on the $(f, \Gamma)$-divergence, and, in addition, presents PAC-Bayes generalisation bounds where we interpolate between a series of probability divergences (including but not limited to KL, Wasserstein, and total variation), making the best out of many worlds depending on the posterior distributions properties. We explore the tightness of these bounds and connect them to earlier results from statistical learning, which are specific cases. We also instantiate our bounds as training objectives, yielding non-trivial guarantees and practical performances.

Mots clés: Machine Learning (stat.ML); Machine Learning (cs.LG); FOS: Computer and information sciences

Domaines: Statistiques [math.ST]

Paul Viallard, Maxime Haddouche, Umut Şimşekli, Benjamin Guedj. Tighter Generalisation Bounds via Interpolation. 2024. ⟨hal-04456925⟩