IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v121y2011i11p2488-2506.html
   My bibliography  Save this article

Context tree selection: A unifying view

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304414911001591
    Download Restriction: Full text for ScienceDirect subscribers only

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Hart, Andrew & Matzinger, Heinrich, 2006. "Markers for error-corrupted observations," Stochastic Processes and their Applications, Elsevier, vol. 116(5), pages 807-829, May.
    2. Matzinger, Heinrich & Rolles, Silke W. W., 2003. "Reconstructing a piece of scenery with polynomially many observations," Stochastic Processes and their Applications, Elsevier, vol. 107(2), pages 289-300, October.
    Full references (including those not matched with items on IDEAS)

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:spapps:v:121:y:2011:i:11:p:2488-2506. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Dana Niculescu). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/505572/description#description .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.