The Bayesian Stability Zoo

Shay Moran, Hilla Schefler, Jonathan Shafer

Research output: Contribution to journalConference articlepeer-review


We show that many definitions of stability found in the learning theory literature are equivalent to one another. We distinguish between two families of definitions of stability: distribution-dependent and distribution-independent Bayesian stability. Within each family, we establish equivalences between various definitions, encompassing approximate differential privacy, pure differential privacy, replicability, global stability, perfect generalization, TV stability, mutual information stability, KL-divergence stability, and Rényi-divergence stability. Along the way, we prove boosting results that enable the amplification of the stability of a learning rule. This work is a step towards a more systematic taxonomy of stability notions in learning theory, which can promote clarity and an improved understanding of an array of stability concepts that have emerged in recent years.

Original languageEnglish
JournalAdvances in Neural Information Processing Systems
StatePublished - 2023
Event37th Conference on Neural Information Processing Systems, NeurIPS 2023 - New Orleans, United States
Duration: 10 Dec 202316 Dec 2023
Conference number: 37

All Science Journal Classification (ASJC) codes

  • Computer Networks and Communications
  • Information Systems
  • Signal Processing


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