Redundancy of the context-tree weighting method on renewal and Markov renewal processes

IEEE Transactions on Information Theory

Volumn 52, Issue 12, 2006, Pages 5579-5586

  Garivier, Aurélien ^a  

^a UNIVERSITÉ PARIS SACLAY   (France)

Author keywords

Adaptivity; Context tree weighting (CTW) method; Minimax; Redundancy; Renewal processes; Source coding

Indexed keywords

COMPUTATIONAL METHODS; ERROR ANALYSIS; INFORMATION THEORY; OPTIMIZATION; REDUNDANCY;

ADAPTIVITY; CONTEXT-TREE WEIGHTING METHOD; LOGARITHMIC FACTOR; MINIMAX; RENEWAL PROCESSES; SOURCE CODING;

MARKOV PROCESSES;

EID: 33947420757     PISSN: 00189448     EISSN: None     Source Type: Journal    
DOI: 10.1109/TIT.2006.885484     Document Type: Article

References (20)

1. I. Csiszár and P. C. Shields, "Redundancy rates for renewal and other processes," IEEE Trans. Inf. Theory, vol. 42, no. 6, pp. 2065-2072, Nov. 1996.
2. N. Weinberger, J. Marcelo, Merhav, and M. Feder, "Optimal sequential probability assignment for individual sequences," IEEE Trans. Inf. Theory, vol. 40, Mar. 1994.
3. J. Rissanen, "Universal coding, information, prediction, and estimation," IEEE Trans. Inf. Theory, vol. 30, Jul. 1984.
4. J. Rissanen and G. J. Langdon, "Universal modeling and coding," IEEE Trans. Inf. Theory, vol. 27, no. 1, pp. 12-23, Jan. 1981.
5. D. Haussler, "A general minimax result for relative entropy," IEEE Trans. Inf. Theory, vol. 43, no. 4, pp. 1276-1280, 1997.
6. R. Krichevsky and V. Trofimov, "The performance of universal encoding," IEEE Trans. Inf. Theory, vol. 27, no. 2, pp. 199-207, Mar. 1981.
7. Q. Xie and A. Barron, "Minimax redundancy for the class of memoryless sources," IEEE Trans. Inf. Theory, vol. 43, no. 2, pp. 646-657, Mar. 1997.
8. Y. M. Willems, M. J. Frans, Shtarkov, and T. J. Tjalkens, "The context-tree weighting method: Basic properties," IEEE Trans. Inf. Theory, vol. 41, May 1995.
9. P. C. Shields, "Universal redundancy rate do not exist," IEEE Trans. Inf. Theory, vol. 39, Mar. 1993.
10. Y. M. Shtar'kov, "Universal sequential coding of individual messages," Problemy Peredachi Informatsii, vol. 23, no. 3, pp. 3-17, 1987.
11. I. Csiszár and P. C. Shields, "The consistency of the BIG Markov order estimator," Ann. Statist., vol. 28, no. 6, pp. 1601-1619, 2000.
12. I. Csiszár and Z. Talata, "Context tree estimation for not necessarily finite memory processes, via BIC and MDL," IEEE Trans. Inf. Theory, vol. 52, no. 3, Mar. 2006.
13. A. B. Tsybakov, Introduction à l'estimation nonparamétrique, ser. Mathématiques & Applications. Berlin, Germany: Springer-Verlag, 2004, vol.41.
14. P. Bühlmann and A. J. Wyner, "Variable length Markov chains," Ann. Statist., vol. 27, no. 2, pp. 480-513, 1999.
15. O. Catoni, Statistical Learning Theory and Stochastic Optimization, ser. Lecture Notes in Mathematics. Berlin, Germany: Springer-Verlag, 2001, vol. 1851.
16. F. Willems, The Context-Tree Weighting Method: Extensions [Online]. Available: citeseer.ist.psu.edu/willems94contexttree.html 1994
17. J. Barron, A. Rissanen, and B. Yu, "The minimum description length principle in coding and modeling," IEEE Trans. Inf. Theory, vol. 44, no. 6, pp. 2743-2760, 1998.
18. Y. Vardi, "Nonparametric estimation in renewal processes," Ann. Statist., vol. 10, no. 3, pp. 772-785, 1982.
19. J. Rissanen, "A universal data compression system," IEEE Trans. Inf. Theory, vol. 29, Sep. 1983.
20. J. Rissanen, "Fast universal coding with context models," IEEE Trans. Inf. Theory, vol. 45, no. 4, pp. 1065-1071, 1999.