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Conference Papers Year : 2023

A historical perspective on Schützenberger-Pinsker inequalities


This paper presents a tutorial overview of so-called Pinsker inequalities which establish a precise relationship between information and statistics, and whose use have become ubiquitous in many infor- mation theoretic applications. According to Stigler’s law of eponymy, no scientific discovery is named after its original discoverer. Pinsker’s inequality is no exception: Years before the publication of Pinsker’s book in 1960, the French medical doctor, geneticist, epidemiologist, and mathe- matician Marcel-Paul (Marco) Schützenberger, in his 1953 doctoral the- sis, not only proved what is now called Pinsker’s inequality (with the optimal constant that Pinsker himself did not establish) but also the op- timal second-order improvement, more than a decade before Kullback’s derivation of the same inequality. We review Schûtzenberger and Pinsker contributions as well as those of Volkonskii & Rozanov, Sakaguchi, McKean, Csiszár, Kullback, Kemperman, Vajda, Bretagnolle & Huber, Krafft & Schmitz, Toussaint, Reid & Williamson, Gilardoni, as well as the op- timal derivation of Fedotov, Harremoës, & Topsøe.
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hal-04136990 , version 1 (06-07-2023)


  • HAL Id : hal-04136990 , version 1


Olivier Rioul. A historical perspective on Schützenberger-Pinsker inequalities. 6th International Conference on Geometric Science of Information (GSI 2023), Aug 2023, Saint Malo, France. ⟨hal-04136990⟩
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