On Pairs of f-divergences and their joint range

IEEE Transactions on Information Theory

Volumn 57, Issue 6, 2011, Pages 3230-3235

  Harremoës, Peter ^a   Vajda, Igor ^b  

^a Copenhagen Business College ^*  (Denmark)

^b NONE

Author keywords

Convexity; f divergence; joint range

Indexed keywords

CONVEX ANALYSIS; CONVEX HULL; CONVEXITY; F-DIVERGENCE; JOINT RANGE; TWO-POINT;

EID: 79957648635     PISSN: 00189448     EISSN: None     Source Type: Journal    
DOI: 10.1109/TIT.2011.2137353     Document Type: Article

References (15)

1. I. Csiszár, "Eine informationstheoretische Ungleichung und ihre Anwendung auf den Beweis der ergodizität von Markoffschen Ketten," Publ. Math. Inst. Hung. Acad., vol. 8, pp. 95-108, 1963.
2. T. Morimoto, "Markov processes and the h-theorem," J. Phys. Soc. Jap., vol. 12, pp. 328-331, 1963.
3. S. M. Ali and S. D. Silvey, "A general class of coefficients of divergence of one distribution from another," J. Roy. Statist. Soc. Ser. B, vol. 28, pp. 131-142, 1966.
4. F. Liese and I. Vajda, Convex Statistical Distances. Leipzig, Germany: Teubner, 1987.
5. F. Liese and I. Vajda, "On divergence and informations in statistics and information theory," IEEE Trans. Inf. Theory, vol. 52, no. 10, pp. 4394-4412, Oct. 2006. (Pubitemid 46445281)
6. T. R. C. Read and N. Cressie, Goodness of Fit Statistics for Discrete Multivariate Data. Berlin, Germany: Springer, 1988.
7. A. R. Barron, L. Györfi, and E. C. van der Meulen, "Distribution estimates consistent in total variation and in two types of information divergence," IEEE Trans. Inf. Theory, vol. 38, no. 9, pp. 1437-1454, Sep. 1992.
8. A. Fedotov, P. Harremoës, and F. Topsøe, "Refinements of Pinsker's inequality," IEEE Trans. Inf. Theory, vol. 49, no. 6, pp. 1491-1498, Jun. 2003.
9. J. Briët and P. Harremoës, "Properties of classical and quantum Jensen- Shannon divergence," Phys. Rev. A., vol. 79, p. 052311, May 2009, (11 pages).
10. F. Topsøe, "Bounds for entropy and divergence of distributions over a two-element set," J. Ineq. Pure Appl. Math., 2001 [Online]. Available: http://jipam.vu.edu.au/accepted-papers/04400.html
11. R. R. Phelps, Lectures on Choquet's Theorem. No. 1757 in Lecture Notes in Mathematics, 2nd ed. New York: Springer, 2001.
12. V. Boltyanski and H. Martini, "Carathodory's theorem and H-convexity," J. Combin. Theory Ser. A, vol. 93, no. 2, pp. 292-309, 2001.
13. T. van Erven and P. Harremoës, "Rényi divergence and majorization," in Proc. IEEE Int. Symp. Information Theory, Jun. 2010, pp. 1335-1339.
14. T. van Erven, "When Data Compression and Statistics Dissagree.," Ph.D. dissertation, Leiden Univ., Leiden, The Netherlands, 2010.
15. A. L. Gibbs and F. E. Su, "On choosing and bounding probability metrics," Int. Statist. Rev., vol. 70, pp. 419-435, 2002.