Entropy (Jun 2023)

The Interplay between Error, Total Variation, Alpha-Entropy and Guessing: Fano and Pinsker Direct and Reverse Inequalities

  • Olivier Rioul

DOI
https://doi.org/10.3390/e25070978
Journal volume & issue
Vol. 25, no. 7
p. 978

Abstract

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Using majorization theory via “Robin Hood” elementary operations, optimal lower and upper bounds are derived on Rényi and guessing entropies with respect to either error probability (yielding reverse-Fano and Fano inequalities) or total variation distance to the uniform (yielding reverse-Pinsker and Pinsker inequalities). This gives a general picture of how the notion of randomness can be measured in many areas of computer science.

Keywords