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Remarks on Reverse Pinsker Inequalities

  • INFORMATION THEORY
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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

  1. 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

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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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Authors and Affiliations

  1. School of Transportation Engineering, East China Jiaotong University, Nanchang, Jiangxi Province, China

    X. Y. Gui

  2. Institut Galilée, LAGA, CNRS (UMR 7539), Université Sorbonne Paris Nord, Villetaneuse, France

    Y. C. Huang

  3. School of Mathematical Sciences, Nanjing Normal University, Nanjing, China

    Y. C. Huang

Authors
  1. X. Y. Gui
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  2. Y. C. Huang
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Additional information

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

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