Context Tree Estimation in Variable Length Hidden Markov Models

Article, Preprint English OPEN
Dumont , Thierry (2014)
  • Publisher: Institute of Electrical and Electronics Engineers
  • Related identifiers: doi: 10.1109/TIT.2014.2314094
  • Subject: consistent estimator | Mathematics - Statistics Theory | hidden Markov models | context tree | Computer Science - Information Theory | Variable length | mixture inequalities | [ STAT.TH ] Statistics [stat]/Statistics Theory [stat.TH] | [ MATH.MATH-ST ] Mathematics [math]/Statistics [math.ST]

We address the issue of context tree estimation in variable length hidden Markov models. We propose an estimator of the context tree of the hidden Markov process which needs no prior upper bound on the depth of the context tree. We prove that the estimator is strongly c... View more
  • References (21)
    21 references, page 1 of 3

    [1] L. Finesso, “Consistent estimation of the order for Markov and hidden Markov chains,” 1990, ph.D. Thesis, Univ. of Maryland.

    [2] E. Gassiat and S. Boucheron, “Optimal error exponents in hidden Markov model order estimation,” IEEE Trans. Info. Theory, vol. 48, pp. 964-980, 2003.

    [3] J. Rissanen, “A universal data compression system,” IEEE Trans. Inform. Theory, vol. 29, pp. 656 - 664, 1983.

    [4] Z. L. W. J. Wang, Y. and Z. Liu, “Mining complex time-series by learning markovian models,” in Proceedings ICDM'06, sixth international conference on data mining, China, 2005.

    [5] Y. Wang, “The variable-length hidden markov model and its applications on sequential data mining,” Departement of computer science, Tech. Rep., 2005.

    [6] F. Evennou, “Techniques et technologies de localisation avancées pour terminaux mobiles dans les environnements indoor,” 2007, ph.D. Thesis, Univ. Joseph Fourier, Grenoble, France.

    [7] R. van Handel, “On the minimal penalty for Markov order estimation,” Probab. Th. Rel. Fields, 2011, to appear.

    [8] E. Gassiat and R. van Handel, “Pathwise fluctuations of likelihood ratios and consistent order estimation,” 2010,

    [9] E. Gassiat and C. Keribin, “The likelihood ratio tets for the number of components in a mixture with Markov regime,” ESAIM P&S, 2000.

    [10] A. Chambaz, A. Garivier, and E. Gassiat, “A MDL approach to HMM with Poisson and Gaussian emissions. Application to order indentification,” Journal of Stat. Planning and Inf., vol. 139, pp. 962-977, 2009.

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