Context Tree Selection: A Unifying View
Abstract
The present paper investigates non-asymptotic properties of two popular procedures of context tree (or Variable Length Markov Chains) estimation: Rissanen's algorithm Context and the Penalized Maximum Likelihood criterion. First showing how they are related, we prove finite horizon bounds for the probability of over- and under-estimation. Concerning overestimation, no boundedness or loss-of-memory conditions are required: the proof relies on new deviation inequalities for empirical probabilities of independent interest. The underestimation properties rely on loss-of-memory and separation conditions of the process. These results improve and generalize the bounds obtained previously. Context tree models have been introduced by Rissanen as a parsimonious generalization of Markov models. Since then, they have been widely used in applied probability and statistics.
Cite
@article{arxiv.1011.2424,
title = {Context Tree Selection: A Unifying View},
author = {Aurélien Garivier and Florencia Leonardi},
journal= {arXiv preprint arXiv:1011.2424},
year = {2011}
}