On R\'enyi and Tsallis entropies and divergences for exponential families

E. D. Hellinger, “Die orthogonalinvarianten quadratischer formen von unendlich vielen variablen,” 1907, thesis of the university of Göttingen

1907

Earlier work this paper cites.

A. Bhattacharyya, “On a measure of divergence between two statistical populations defined by their probability distributions,” Bulletin of Calcutta Mathematical Society , vol. 35, pp. 99–110, 1943

1943

Earlier work this paper cites.

C. E. Shannon, “A mathematical theory of communication,” The Bell System Technical Journal , vol. 27, pp. 379–423, 1948

1948

Earlier work this paper cites.

H. Chernoff, “A measure of asymptotic efficiency for tests of a hypothesis based on the sum of observations,” Annals of Mathematical Statistics , vol. 23, pp. 493–507, 1952

1952

Earlier work this paper cites.

A. Rényi, “On measures of entropy and information,” in Proceedings of the 4th Berkeley Symposium on Mathematical Statistics and Probabilities , vol. 1, 1961, pp. 547–561

1961

Earlier work this paper cites.

J. Havrda and F. Chárvat, “Quantification method of classification processes,” Kiberbetika Cislo , vol. 1, no. 3, pp. 30–34, 1967

1967

Earlier work this paper cites.

I. Csiszár, “Information-type measures of difference of probability distributions and indirect observation,” Studia Scientiarum Mathematicarum Hungarica , vol. 2, pp. 229–318, 1967

1967

Earlier work this paper cites.

L. M. Bregman, “The relaxation method of finding the common point of convex sets and its application to the solution of problems in convex programming,” USSR Computational Mathematics and Mathematical Physics , vol. 7, pp. 200–217, 1967

1967

Cited alongside, same era.

O. Barndorff-Nielsen, Information and exponential families in statistical theory . Wiley, 1978

1978

Cited alongside, same era.

C. R. Rao and T. K. Nayak, “Cross entropy, dissimilarity measures, and characterizations of quadratic entropy,” IEEE Transactions on Information Theory , vol. 31, no. 5, pp. 589 – 593, sep 1985

1985

Cited alongside, same era.

T. M. Cover and J. A. Thomas, Elements of information theory . New York, NY, USA: Wiley-Interscience, 1991

1991

Cited alongside, same era.

A. Darbellay and I. Vajda, “Entropy Expressions for Multivariate Continuous Distributions,” IEEE Transactions on Information Theory , vol. 46, no. 2, pp. pp. 709–712, 2000

K. Zografos and S. Nadarajah, “Expressions for Rényi and Shannon entropies for multivariate distributions,” Statistics & Probability Letters , vol. 71, no. 1, pp. 71 – 84, 2005

2005

Later among the works it cites.

A. Banerjee, S. Merugu, I. S. Dhillon, and J. Ghosh, “Clustering with Bregman divergences,” Journal of Machine Learning Research , vol. 6, pp. 1705–1749, 2005

2005

Later among the works it cites.

H. Suyari and M. Tsukada, “Tsallis differential entropy and divergences derived from the generalized Shannon-Khinchin axioms,” in Proceedings of the 2009 IEEE international conference on Symposium on Information Theory (ISIT) , ser. ISIT’09, vol. 1. Piscataway, NJ, USA: IEEE Press, 2009, pp. 149–153

2009

Later among the works it cites.

F. Nielsen and V. Garcia, “Statistical exponential families: A digest with flash cards,” 2009, arXiv.org:0911.4863

2009

Later among the works it cites.