Tighter Information-Theoretic Generalization Bounds from Supersamples

Ziqiao Wang; Yongyi Mao

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arXiv · 2302.02432

Tighter Information-Theoretic Generalization Bounds from Supersamples

Ziqiao Wang·Yongyi Mao

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Abstract

In this work, we present a variety of novel information-theoretic generalization bounds for learning algorithms, from the supersample setting of Steinke & Zakynthinou (2020)-the setting of the "conditional mutual information" framework. Our development exploits projecting the loss pair (obtained from a training instance and a testing instance) down to a single number and correlating loss values with a Rademacher sequence (and its shifted variants). The presented bounds include square-root bounds, fast-rate bounds, including those based on variance and sharpness, and bounds for interpolating algorithms etc. We show theoretically or empirically that these bounds are tighter than all information-theoretic bounds known to date on the same supersample setting.

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stat.ML cs.IT cs.LG math.IT

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BibTeX RIS

Ziqiao Wang, Yongyi Mao. 2023-02-05. Tighter Information-Theoretic Generalization Bounds from Supersamples. https://arxiv.org/abs/2302.02432

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