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Context tree selection: A unifying view

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  • Garivier, A.
  • Leonardi, F.
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    Abstract

    Context tree models have been introduced by Rissanen in [25] as a parsimonious generalization of Markov models. Since then, they have been widely used in applied probability and statistics. The present paper investigates non-asymptotic properties of two popular procedures of context tree estimation: Rissanen’s algorithm Context and penalized maximum likelihood. First showing how they are related, we prove finite horizon bounds for the probability of over- and under-estimation. Concerning over-estimation, no boundedness or loss-of-memory conditions are required: the proof relies on new deviation inequalities for empirical probabilities of independent interest. The under-estimation properties rely on classical hypotheses for processes of infinite memory. These results improve on and generalize the bounds obtained in Duarte et al. (2006) [12], Galves et al. (2008) [18], Galves and Leonardi (2008) [17], Leonardi (2010) [22], refining asymptotic results of Böhlmann and Wyner (1999) [4] and Csiszár and Talata (2006) [9].

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    Bibliographic Info

    Article provided by Elsevier in its journal Stochastic Processes and their Applications.

    Volume (Year): 121 (2011)
    Issue (Month): 11 (November)
    Pages: 2488-2506

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    Handle: RePEc:eee:spapps:v:121:y:2011:i:11:p:2488-2506

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    Related research

    Keywords: Algorithm Context Penalized maximum likelihood Model selection Variable length Markov chains Bayesian information criterion Deviation inequalities;

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