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R\'enyi divergence is related to R\'enyi entropy much like Kullback-Leibler divergence is related to Shannon's entropy, and comes up in many settings.
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Including also the ensuing Editor’s Note
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B. J. Thelen, “Fisher information and dichotomies in equivalence/contiguity,” The Annals of Probability
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A. A. Fedotov, P. Harremoës, and F. Topsøe, “Refinements of Pinsker’s inequality,” IEEE Transactions on Information Theory
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J. Naudts, “Estimators, escort probabilities, and ϕ \phi -exponential families in statistical physics,” Journal of Inequalities in Pure and Applied Mathematics
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1989
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Wiley, 1991
T. M. Cover and J. A. Thomas, Elements of Information Theory · 1991
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S. van de Geer, “Hellinger-consistency of certain nonparametric maximum likelihood estimators,” The Annals of Statistics
1993
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I. Csiszár, “Generalized cutoff rates and Rényi’s information measures,” IEEE Transactions on Information Theory
1995
Cited alongside, same era.
Springer-Verlag, 1996
A. N. Shiryaev, Probability · 1996
Cited alongside, same era.
D. Haussler and M. Opper, “Mutual information, metric entropy and cumulative relative entropy risk,” The Annals of Statistics
1997
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Springer, 1997
O. Kallenberg, Foundations of Modern Probability · 1997
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2004
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P. Harremoës, “Interpretations of Rényi entropies and divergences,” Physica A: Statistical Mechanics and its Applications
2006
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T. Zhang, “From ϵ \epsilon -entropy to KL-entropy: Analysis of minimum information complexity density estimation,” The Annals of Statistics
2006
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F. Liese and I. Vajda, “On divergences and informations in statistics and information theory,” IEEE Transactions on Information Theory
2006
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R. Sundaresan, “Guessing under source uncertainty with side information,” in Proceedings of the IEEE International Symposium on Information Theory (ISIT)
2006
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The MIT Press, 2007
P. D. Grünwald, The Minimum Description Length Principle · 2007
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Springer, 2007
F. Topsøe, Entropy, Search, Complexity · 2007
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Y. Mansour, M. Mohri, and A. Rostamizadeh, “Multiple source adaptation and the Rényi divergence,” in Proceedings of the Twenty-Fifth Conference on Uncertainty in Artificial Intelligence (UAI)
2009
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P. Harremoës and K. K. Holst, “Convergence of Markov chains in information divergence,” Journal of Theoretical Probability
2009
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PhD thesis, Leiden University, 2010
T. van Erven, When Data Compression and Statistics Disagree: Two Frequentist Challenges for the Minimum Description Length Principle · 2010
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T. van Erven and P. Harremoës, “Rényi divergence and majorization,” in Proceedings of the IEEE International Symposium on Information Theory (ISIT)
2010
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2010
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G. L. Gilardoni, “On Pinsker’s and Vajda’s type inequalities for Csiszár’s f f -divergences,” IEEE Transactions on Information Theory
2010
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O. Shayevitz, “On Rényi measures and hypothesis testing,” in IEEE International Symposium on Information Theory Proceedings
2011
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M. Gil, “On Rényi divergence measures for continuous alphabet sources,” Master’s thesis, Queen’s University, 2011
2011
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M. Gil, F. Alajaji, and T. Linder, “Rényi divergence measures for commonly used univariate continuous distributions,” Information Sciences
2013
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