Abstract
In this paper we obtain non-uniform exponential upper bounds for the rate of convergence of a version of the algorithm Context, when the underlying tree is not necessarily bounded. The algorithm Context is a well-known tool to estimate the context tree of a Variable Length Markov Chain. As a consequence of the exponential bounds we obtain a strong consistency result. We generalize in this way several previous results in the field.
This work is part of PRONEX/FAPESP’s project Stochastic behavior, critical phenomena and rhythmic pattern identification in natural languages (grant number 03/09930-9) and CNPq’s projects Stochastic modeling of speech (grant number 475177/2004-5) and Rhythmic patterns, prosodic domains and probabilistic modeling in Portuguese Corpora (grant number 485999/2007-2). AG is partially supported by a CNPq fellowship (grant 308656/2005-9) and FL is supported by a FAPESP fellowship (grant 06/56980-0).
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© 2008 Birkhäuser Verlag Basel/Switzerland
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Galves, A., Leonardi, F. (2008). Exponential Inequalities for Empirical Unbounded Context Trees. In: Sidoravicius, V., Vares, M.E. (eds) In and Out of Equilibrium 2. Progress in Probability, vol 60. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-8786-0_12
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DOI: https://doi.org/10.1007/978-3-7643-8786-0_12
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