کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
1155816 | 958774 | 2011 | 19 صفحه PDF | دانلود رایگان |
![عکس صفحه اول مقاله: Context tree selection: A unifying view Context tree selection: A unifying view](/preview/png/1155816.png)
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 Bühlmann and Wyner (1999) [4] and Csiszár and Talata (2006) [9].
► We give a non-asymptotic analysis of two context tree estimators.
► We show how penalized maximum likelihood and algorithm Context are related.
► We prove improved bounds for the probability of over- and under-estimation.
► For over-estimation, no boundedness or loss-of-memory conditions are required.
► We show new martingale bounds for self-normalized deviations of empirical probabilities.
Journal: Stochastic Processes and their Applications - Volume 121, Issue 11, November 2011, Pages 2488–2506