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Context tree selection: A unifying view

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  • Garivier, A.
  • Leonardi, F.

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: 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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    Cited by:

    1. Aline Duarte & Ricardo Fraiman & Antonio Galves & Guilherme Ost & Claudia D. Vargas, 2019. "Retrieving a Context Tree from EEG Data," Mathematics, MDPI, vol. 7(5), pages 1-13, May.
    2. Ioannis Kontoyiannis & Lambros Mertzanis & Athina Panotopoulou & Ioannis Papageorgiou & Maria Skoularidou, 2022. "Bayesian context trees: Modelling and exact inference for discrete time series," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 84(4), pages 1287-1323, September.

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