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Context tree selection: A unifying view


  • Garivier, A.
  • Leonardi, F.


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: Rissanenâs 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].

Suggested Citation

  • Garivier, A. & Leonardi, F., 2011. "Context tree selection: A unifying view," Stochastic Processes and their Applications, Elsevier, vol. 121(11), pages 2488-2506, November.
  • Handle: RePEc:eee:spapps:v:121:y:2011:i:11:p:2488-2506

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