Variational characterizations of Sibson's α-mutual information
Esposito AR, Gastpar M, Issa I. 2024. Variational characterizations of Sibson’s α-mutual information. Proceedings of the 2024 IEEE International Symposium on Information Theory . ISIT: International Symposium on Information Theory, 2110–2115.
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Conference Paper
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Author
Esposito, Amedeo RobertoISTA;
Gastpar, Michael;
Issa, Ibrahim
Department
Abstract
Sibson's α -mutual information has received renewed attention recently in several contexts: concentration of measure under dependence, statistical learning, hypothesis testing, and estimation theory. In this work, we introduce several variational representations of Sibson's α -mutual information: 1) as a supremum over joint distributions of (a combination of) KL divergences; and 2) as a supremum over functions of opportune expected values. Leveraging them, we produce a variety of novel and known results, including a generalization of transportation-cost inequalities and Fano's inequality.
Publishing Year
Date Published
2024-08-19
Proceedings Title
Proceedings of the 2024 IEEE International Symposium on Information Theory
Acknowledgement
The work in this paper was supported in part by the Swiss National Science Foundation under Grant 200364.
Page
2110-2115
Conference
ISIT: International Symposium on Information Theory
Conference Location
Athens, Greece
Conference Date
2024-07-07 – 2024-07-12
ISBN
ISSN
IST-REx-ID
Cite this
Esposito AR, Gastpar M, Issa I. Variational characterizations of Sibson’s α-mutual information. In: Proceedings of the 2024 IEEE International Symposium on Information Theory . Institute of Electrical and Electronics Engineers; 2024:2110-2115. doi:10.1109/ISIT57864.2024.10619378
Esposito, A. R., Gastpar, M., & Issa, I. (2024). Variational characterizations of Sibson’s α-mutual information. In Proceedings of the 2024 IEEE International Symposium on Information Theory (pp. 2110–2115). Athens, Greece: Institute of Electrical and Electronics Engineers. https://doi.org/10.1109/ISIT57864.2024.10619378
Esposito, Amedeo Roberto, Michael Gastpar, and Ibrahim Issa. “Variational Characterizations of Sibson’s α-Mutual Information.” In Proceedings of the 2024 IEEE International Symposium on Information Theory , 2110–15. Institute of Electrical and Electronics Engineers, 2024. https://doi.org/10.1109/ISIT57864.2024.10619378.
A. R. Esposito, M. Gastpar, and I. Issa, “Variational characterizations of Sibson’s α-mutual information,” in Proceedings of the 2024 IEEE International Symposium on Information Theory , Athens, Greece, 2024, pp. 2110–2115.
Esposito AR, Gastpar M, Issa I. 2024. Variational characterizations of Sibson’s α-mutual information. Proceedings of the 2024 IEEE International Symposium on Information Theory . ISIT: International Symposium on Information Theory, 2110–2115.
Esposito, Amedeo Roberto, et al. “Variational Characterizations of Sibson’s α-Mutual Information.” Proceedings of the 2024 IEEE International Symposium on Information Theory , Institute of Electrical and Electronics Engineers, 2024, pp. 2110–15, doi:10.1109/ISIT57864.2024.10619378.
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