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arXiv · 2205.06915

Formal limitations of sample-wise information-theoretic generalization bounds

Hrayr Harutyunyan·Greg Ver Steeg·Aram Galstyan
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Abstract

Some of the tightest information-theoretic generalization bounds depend on the average information between the learned hypothesis and a single training example. However, these sample-wise bounds were derived only for expected generalization gap. We show that even for expected squared generalization gap no such sample-wise information-theoretic bounds exist. The same is true for PAC-Bayes and single-draw bounds. Remarkably, PAC-Bayes, single-draw and expected squared generalization gap bounds that depend on information in pairs of examples exist.

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Hrayr Harutyunyan, Greg Ver Steeg, Aram Galstyan. 2022-05-13. Formal limitations of sample-wise information-theoretic generalization bounds. https://doi.org/10.1109/itw54588.2022.9965850

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