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arXiv · 1906.00930

A necessary and sufficient stability notion for adaptive generalization

Katrina Ligett·Moshe Shenfeld
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Abstract

We introduce a new notion of the stability of computations, which holds under post-processing and adaptive composition. We show that the notion is both necessary and sufficient to ensure generalization in the face of adaptivity, for any computations that respond to bounded-sensitivity linear queries while providing accuracy with respect to the data sample set. The stability notion is based on quantifying the effect of observing a computation's outputs on the posterior over the data sample elements. We show a separation between this stability notion and previously studied notion and observe that all differentially private algorithms also satisfy this notion.

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Katrina Ligett, Moshe Shenfeld. 2019-06-03. A necessary and sufficient stability notion for adaptive generalization. https://arxiv.org/abs/1906.00930

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