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arXiv · 2206.14329

On the R\'{e}nyi Cross-Entropy

Ferenc Cole Thierrin·Fady Alajaji·Tamás Linder
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Abstract

The R\'{e}nyi 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.

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Ferenc Cole Thierrin, Fady Alajaji, Tamás Linder. 2022-06-28. On the R\'{e}nyi Cross-Entropy. https://arxiv.org/abs/2206.14329

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