@inproceedings{ec737012b71346b4beb22cb5dd48966c,
title = "Optimal transport to r{\'e}nyi entropies",
abstract = "Recently, an optimal transportation argument was proposed by the author to provide a simple proof of Shannon{\textquoteright}s entropy-power inequality. Interestingly, such a proof could have been given by Shannon himself in his 1948 seminal paper. In fact, by 1948 Shannon established all the ingredients necessary for the proof and the transport argument takes the form of a simple change of variables. In this paper, the optimal transportation argument is extended to R{\'e}nyi entropies in relation to Shannon{\textquoteright}s entropy-power inequality and to a reverse version involving a certain conditional entropy. The transportation argument turns out to coincide with Barthe{\textquoteright}s proof of sharp direct and reverse Young{\textquoteright}s convolutional inequalities and can be applied to derive recent R{\'e}nyi entropy-power inequalities.",
keywords = "Entropy-power inequality, Optimal transport, R{\'e}nyi entropy",
author = "Olivier Rioul",
note = "Publisher Copyright: {\textcopyright} 2017, Springer International Publishing AG.; 3rd International Conference on Geometric Science of Information, GSI 2017 ; Conference date: 07-11-2017 Through 09-11-2017",
year = "2017",
month = jan,
day = "1",
doi = "10.1007/978-3-319-68445-1\_17",
language = "English",
isbn = "9783319684444",
series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",
publisher = "Springer Verlag",
pages = "143--150",
editor = "Frank Nielsen and Frederic Barbaresco and Frank Nielsen",
booktitle = "Geometric Science of Information - 3rd International Conference, GSI 2017, Proceedings",
}