Abstract
In this note we propose a simplified approach to recent reverse Pinsker inequalities due to O. Binette. More precisely, we give direct proofs of optimal variational bounds on f-divergence with possible constraints on relative information extrema. Our arguments are closer in spirit to those of Sason and Verdú.
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References
Binette, O., A Note on Reverse Pinsker Inequalities, IEEE Trans. Inform. Theory, 2019, vol. 65, no. 7, pp. 4094–4096. https://doi.org/10.1109/TIT.2019.2896192
Prelov, V.V., On the Maximum Values of f-Divergence and Rényi Divergence under a Given Variational Distance, Probl. Peredachi Inf., 2020, vol. 56, no. 1, pp. 3–15 [Probl. Inf. Transm. (Engl. Transl.), 2020, vol. 56, no. 1, pp. 1–12]. https://doi.org/10.1134/S0032946020010019
Prelov, V.V., On the Maximum \(f\)-Divergence of Probability Distributions Given the Value of Their Coupling Probl. Peredachi Inf., 2021, vol. 57, no. 4, pp. 24–33 [Probl. Inf. Transm.] (Engl. Transl.), 2021, vol. 57, no. 4, pp. 321–330. https://doi.org/10.1134/S0032946021040025
Sason, I. and Verdú, S., \(f\)-Divergence Inequalities, IEEE Trans. Inform. Theory, 2016, vol. 62, no. 11, pp. 5973–6006. https://doi.org/10.1109/TIT.2016.2603151
Acknowledgments
The second author would like to thank Prof. Yang Yang (NJUST) for helpful communications on information theory and its applications in learning theory.
Funding
The research of Y.C. Huang was partially supported by the National NSF grant of China, no. 11801274. This note was completed while Y.C. Huang was on leave, funded by the CSC Postdoctoral/Visiting Scholar Program no. 202006865011, at LAGA, Université Sorbonne Paris Nord.
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Translated from Problemy Peredachi Informatsii, 2022, Vol. 58, No. 4, pp. 3–5. https://doi.org/10.31857/S0555292322040015
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Gui, X., Huang, Y. Remarks on Reverse Pinsker Inequalities. Probl Inf Transm 58, 297–299 (2022). https://doi.org/10.1134/S0032946022040019
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DOI: https://doi.org/10.1134/S0032946022040019