English

R\'{e}nyi Cross-Entropy Measures for Common Distributions and Processes with Memory

Information Theory 2022-10-06 v2 math.IT

Abstract

Two R\'{e}nyi-type generalizations of the Shannon cross-entropy, the R\'{e}nyi cross-entropy and the Natural R\'{e}nyi cross-entropy, were recently used as loss functions for the improved design of deep learning generative adversarial networks. In this work, we build upon our results in [1] by deriving the R\'{e}nyi and Natural R\'{e}nyi differential cross-entropy measures in closed form for a wide class of common continuous distributions belonging to the exponential family and tabulating the results for ease of reference. We also summarise the R\'{e}nyi-type cross-entropy rates between stationary Gaussian processes and between finite-alphabet time-invariant Markov sources.

Keywords

Cite

@article{arxiv.2208.06983,
  title  = {R\'{e}nyi Cross-Entropy Measures for Common Distributions and Processes with Memory},
  author = {Ferenc Cole Thierrin and Fady Alajaji and Tamás Linder},
  journal= {arXiv preprint arXiv:2208.06983},
  year   = {2022}
}
R2 v1 2026-06-25T01:42:14.254Z