Properties of Kullback-Leibler cross-entropy minimization in nonextensive framework

IEEE International Symposium on Information Theory - Proceedings

Volumn 2005, Issue , 2005, Pages 2374-2378

  Dukkipati, Ambedkar ^a   Narasimha Murty, M ^a   Bhatnagar, Shalabh ^a  

^a INDIAN INSTITUTE OF SCIENCE   (India)

Author keywords

[No Author keywords available]

Indexed keywords

KULLBACK LEIBLER CROSS ENTROPY; MATHEMATICAL STRUCTURE; SHANNON ENTROPY; TSALLIS ENTROPY;

COMPUTATIONAL METHODS; ENTROPY; MATHEMATICAL OPERATORS; OPTIMIZATION; PARAMETER ESTIMATION; STATISTICS;

INFORMATION THEORY;

EID: 33749446843     PISSN: 21578099     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/ISIT.2005.1523773     Document Type: Conference Paper

References (27)

1. R. V. L. Hartley, "Transmission of information," Bell System Technical Journal, vol. 7, pp. 535, 1928.
2. C. Tsallis, "Possible generalization of Boltzmann Gibbs statistics," J. Stat. Phys., vol. 52, pp. 479, 1988.
3. Constantino Tsallis and Daniel A. Stariolo, "Generalized simulated annealing," Physica A, vol. 233, pp. 345-406, 1996.
4. Ambedkar Dukkipati, M. Narasimha Murty, and Shalabh Bhatnagar, "Information theoretic justification of Boltzmann selection and its generalization to Tsallis case," in (to be published) Proceedings of the IEEE Congress on Evolutionary Computation(CEC). 2005, IEEE Press.
5. Constantino Tsallis, "Generalized entropy-based criterion for consistent testing," Physical Review E, vol. 58, pp. 1442-1445, 1998.
6. Hiroki Suyari, "Generalization of Shannon-Khinchin axioms to nonextensive systems and the uniqueness theorem for the nonextensive entropy," IEEE Transactions on Information Theory, vol. 50, no. 8, pp. 1783-1787, 2004.
7. Lisa Borland, Angel R. Plastino, and Constantino Tsallis, "Information gain within nonextensive thermostatistics," Journal of Mathematical Physics, vol. 39, no. 12, pp. 6490-6501, December 1998.
8. S. Furuichi, K. Yanagi, and K. Kuriyama, "Fundamental properties of Tsallis relative entropy," Journal of Mathematical Physics, vol. 45, pp. 4868-4877, 2004.
9. S. Kullback, Information Theory and Statistics, Wiley, New York, 1959.
10. E. T. Jaynes, "Information theory and statistical mechanics," Physical Review, vol. 106, no. 4, pp. 620-630, 1957.
11. John E. Shore, "Properties of cross-entropy minimization," IEEE Transactions on Information Theory, vol. IT-27, no. 4, pp. 472-482, 1981.
12. Imre Csiszár, "I-divergence of probability distributions and minimization problems," Ann. Prob., vol. 3, no. 1, pp. 146-158, 1975.
13. A. Hobson, Concepts in Statistical Mechanics, Gordon and Breach, New York, 1971.
14. John E. Shore and R. M. Gray, "Minimum cross-entropy pattern classification and cluster analysis," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 4, no. 1, pp. 11-18, 1982.
15. J. E. Shore and R. W. Johnson, "Axiomatic derivation of the principle of maximum entropy and the principle of minimum cross-entropy," IEEE Transactions on Information Theory, vol. IT-26, no. 1, pp. 26-37, 1980.
16. A. S. Cherney and V. P. Maslov, "On minimization and maximization of entropy in various disciplines," SIAM journal of Theory of Probability and Its Applications, vol. 48, no. 3, pp. 447-464, 2004.
17. Eduard Vives and Antoni Planes, "Is Tsallis thermodynamics nonextensive?," Physical Review Letters, vol. 88, pp. 020601, 2002.
18. Constantino Tsallis, Renio S. Mendes, and A. R. Plastino, "The role of constraints within generalized nonextensive statistics," Physica A, vol. 261, pp. 534-554, 1998.
19. E. M. F. Curado and C. Tsallis, "Generalized statistical mechanics: connections with thermodynamics," J. Phys. A: Math. Gen., vol. 24, pp. 69-72, 1991.
20. Ambedkar Dukkipati, M. Narasimha Murty, and Shalabh Bhatnagar, "Nonextensive triangle equality and other properties of Tsallis relative-entropy minimization," arXiv:math-ph/0501025, 2005, Submitted to Physica A.
21. C. Tsallis, "What are the numbers that experiments provide?," Quimica Nova, vol. 17, pp. 468, 1994.
22. L. Nivanen, A. Le Méhauté, and Q. A. Wang, "Generalized algebra within a nonextensive statistics," Rep. Math. Phys., vol. 52, pp. 437-434, 2003.
23. Ernesto P. Borges, "A possible deformed algebra and calculus inspired in nonextensive thermostatistics," Physica A, vol. 340, pp. 95-101, 2004.
24. Hiroki Suyari and Makoto Tsukada, "Law of error in Tsallis statistics," IEEE Transactions on Information Theory, vol. 51, no. 2, pp. 753-757, 2005.
25. A. Plastino and A. R. Plastino, "On the universality of thermodynamics' Legendre transform structure," Phys. Lett. A, vol. 226, pp. 257-263, 1997.
26. R. S. Mendes, "Some general relations in arbitrary thermostatistics," Physica A, vol. 242, pp. 299-308, 1997.
27. Shigeru Furuichi, "Chain rules and subadditivities for Tsallis entropies," arXiv:cond-mat/0405600, 2004.