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The Bayesian Stability Zoo

Shay Moran · Hilla Schefler · Jonathan Shafer

Great Hall & Hall B1+B2 (level 1) #1720
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[ Paper [ Poster [ OpenReview
Thu 14 Dec 3 p.m. PST — 5 p.m. PST


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.

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