Exponential Inequalities for Empirical Unbounded Context Trees

Progress in Probability

Volumn 60, Issue , 2008, Pages 257-269

  Galves, Antonio ^a   Leonardi, Florencia ^a  

^a UNIVERSITY OF SÃO PAULO   (Brazil)

Author keywords

algorithm Context; unbounded context trees; Variable memory processes

Indexed keywords

EID: 85145394065     PISSN: 10506977     EISSN: 22970428     Source Type: Book Series    
DOI: 10.1007/978-3-7643-8786-0_12     Document Type: Chapter

References (14)

1. P. Bühlmann and A. J. Wyner. Variable length Markov chains. Ann. Statist., 27:480–513, 1999.
2. F. Comets, R. Fernández, and P. Ferrari. Processes with long memory: Regenerative construction and perfect simulation. Ann. Appl. Probab., 12(3):921– 943, 2002.
3. I. Csiszár and Z. Talata. Context tree estimation for not necessarily finite memory processes, via BIC and MDL. IEEE Trans. Inform. Theory, 52(3):1007–1016, 2006.
4. J. Dedecker and P. Doukhan. A new covariance inequality and applications. Stochastic Process. Appl., 106(1):63–80, 2003.
5. J. Dedecker and C. Prieur. New dependence coefficients. examples and applications to statistics. Probab. Theory Related Fields, 132:203–236, 2005.
6. D. Duarte, A. Galves, and N.L. Garcia. Markov approximation and consistent estimation of unbounded probabilistic suffix trees. Bull. Braz. Math. Soc., 37(4):581–592, 2006.
7. R. Fernández and A. Galves. Markov approximations of chains of infinite order. Bull. Braz. Math. Soc., 33(3):295–306, 2002.
8. F. Ferrari and A. Wyner. Estimation of general stationary processes by variable length Markov chains. Scand. J. Statist., 30(3):459–480, 2003.
9. L. Finesso, C-C. Liu, and P. Narayan. The optimal error exponent for Markov order estimation. IEEE Trans. Inform. Theory, 42(5):1488–1497, 1996.
10. A. Galves, V. Maume-Deschamps, and B. Schmitt. Exponential inequalities for VLMC empirical trees. ESAIM Prob. Stat. (accepted), 2006.
11. J. Rissanen. A universal data compression system. IEEE Trans. Inform. Theory, 29(5):656–664, 1983.
12. D. Ron, Y. Singer, and N. Tishby. The power of amnesia: Learning probabilistic automata with variable memory length. Machine Learning, 25(2-3):117– 149, 1996.
13. M.J. Weinberger, J. Rissanen, and M. Feder. A universal finite memory source. IEEE Trans. Inform. Theory, 41(3):643–652, 1995.
14. F.M. Willems, Y.M. Shtarkov, and T.J. Tjalkens. The context-tree weighting method: Basic properties. IEEE Trans. Inform. Theory, IT-44:653–664, 1995.