On the R\'{e}nyi Cross-Entropy. (arXiv:2206.14329v2 [cs.IT] UPDATED)

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 …

arxiv cross-entropy entropy