Tighter Information-Theoretic Generalization Bounds from Supersamples

Ziqiao Wang, Yongyi Mao
Proceedings of the 40th International Conference on Machine Learning, PMLR 202:36111-36137, 2023.

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v202-wang23w, title = {Tighter Information-Theoretic Generalization Bounds from Supersamples}, author = {Wang, Ziqiao and Mao, Yongyi}, booktitle = {Proceedings of the 40th International Conference on Machine Learning}, pages = {36111--36137}, year = {2023}, editor = {Krause, Andreas and Brunskill, Emma and Cho, Kyunghyun and Engelhardt, Barbara and Sabato, Sivan and Scarlett, Jonathan}, volume = {202}, series = {Proceedings of Machine Learning Research}, month = {23--29 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v202/wang23w/wang23w.pdf}, url = {https://proceedings.mlr.press/v202/wang23w.html}, 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.} }
Endnote
%0 Conference Paper %T Tighter Information-Theoretic Generalization Bounds from Supersamples %A Ziqiao Wang %A Yongyi Mao %B Proceedings of the 40th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2023 %E Andreas Krause %E Emma Brunskill %E Kyunghyun Cho %E Barbara Engelhardt %E Sivan Sabato %E Jonathan Scarlett %F pmlr-v202-wang23w %I PMLR %P 36111--36137 %U https://proceedings.mlr.press/v202/wang23w.html %V 202 %X 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.
APA
Wang, Z. & Mao, Y.. (2023). Tighter Information-Theoretic Generalization Bounds from Supersamples. Proceedings of the 40th International Conference on Machine Learning, in Proceedings of Machine Learning Research 202:36111-36137 Available from https://proceedings.mlr.press/v202/wang23w.html.

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