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Computer Science > Information Theory

arXiv:2206.14329 (cs)
[Submitted on 28 Jun 2022 (v1), last revised 6 Aug 2022 (this version, v3)]

Title:On the Rényi Cross-Entropy

Authors:Ferenc Cole Thierrin, Fady Alajaji, Tamás Linder
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Abstract:The Rényi cross-entropy measure between two distributions, a generalization of the Shannon cross-entropy, was recently used as a loss function for the improved design of deep learning generative adversarial networks. In this work, we examine the properties of this measure and derive closed-form expressions for it when one of the distributions is fixed and when both distributions belong to the exponential family. We also analytically determine a formula for the cross-entropy rate for stationary Gaussian processes and for finite-alphabet Markov sources.
Comments: Appeared in the Proceedings of CWIT'22 (updated version)
Subjects: Information Theory (cs.IT); Machine Learning (cs.LG)
Cite as: arXiv:2206.14329 [cs.IT]
  (or arXiv:2206.14329v3 [cs.IT] for this version)
  https://doi.org/10.48550/arXiv.2206.14329

Submission history

From: Fady Alajaji [view email]
[v1] Tue, 28 Jun 2022 23:48:19 UTC (654 KB)
[v2] Thu, 30 Jun 2022 00:55:09 UTC (651 KB)
[v3] Sat, 6 Aug 2022 04:12:50 UTC (651 KB)
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