Sibson α-mutual information and its variational representations

Esposito AR, Gastpar M, Issa I. 2025. Sibson α-mutual information and its variational representations. IEEE Transactions on Information Theory.

Download (ext.)

Journal Article | Epub ahead of print | English

Scopus indexed
Author
Esposito, Amedeo RobertoISTA; Gastpar, Michael; Issa, Ibrahim
Department
Abstract
Information measures can be constructed from Rényi divergences much like mutual information from Kullback-Leibler divergence. One such information measure is known as Sibson α-mutual information and has received renewed attention recently in several contexts: concentration of measure under dependence, statistical learning, hypothesis testing, and estimation theory. In this paper, we survey and extend the state of the art. In particular, we introduce variational representations for Sibson α-mutual information and employ them in each described context to derive novel results. Namely, we produce generalized Transportation-Cost inequalities and Fano-type inequalities. We also present an overview of known applications, spanning from learning theory and Bayesian risk to universal prediction.
Publishing Year
Date Published
2025-07-11
Journal Title
IEEE Transactions on Information Theory
Publisher
Institute of Electrical and Electronics Engineers
ISSN
eISSN
IST-REx-ID

Cite this

Esposito AR, Gastpar M, Issa I. Sibson α-mutual information and its variational representations. IEEE Transactions on Information Theory. 2025. doi:10.1109/TIT.2025.3587340
Esposito, A. R., Gastpar, M., & Issa, I. (2025). Sibson α-mutual information and its variational representations. IEEE Transactions on Information Theory. Institute of Electrical and Electronics Engineers. https://doi.org/10.1109/TIT.2025.3587340
Esposito, Amedeo Roberto, Michael Gastpar, and Ibrahim Issa. “Sibson α-Mutual Information and Its Variational Representations.” IEEE Transactions on Information Theory. Institute of Electrical and Electronics Engineers, 2025. https://doi.org/10.1109/TIT.2025.3587340.
A. R. Esposito, M. Gastpar, and I. Issa, “Sibson α-mutual information and its variational representations,” IEEE Transactions on Information Theory. Institute of Electrical and Electronics Engineers, 2025.
Esposito AR, Gastpar M, Issa I. 2025. Sibson α-mutual information and its variational representations. IEEE Transactions on Information Theory.
Esposito, Amedeo Roberto, et al. “Sibson α-Mutual Information and Its Variational Representations.” IEEE Transactions on Information Theory, Institute of Electrical and Electronics Engineers, 2025, doi:10.1109/TIT.2025.3587340.
All files available under the following license(s):
Copyright Statement:
This Item is protected by copyright and/or related rights. [...]

Link(s) to Main File(s)
Access Level
OA Open Access

Export

Marked Publications

Open Data ISTA Research Explorer

Sources

arXiv 2405.08352

Search this title in

Google Scholar