Joint Estimation of Intersecting Context Tree Models |
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Authors: | ANTONIO GALVES AURÉLIEN GARIVIER ELISABETH GASSIAT |
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Institution: | 1. Universidade de S?o Paulo;2. CNRS UMR 5141 & Institut Mathématique de Toulouse, Telecom ParisTech;3. Université Paris Sud CNRS UMR 8628 |
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Abstract: | We study a problem of model selection for data produced by two different context tree sources. Motivated by linguistic questions, we consider the case where the probabilistic context trees corresponding to the two sources are finite and share many of their contexts. In order to understand the differences between the two sources, it is important to identify which contexts and which transition probabilities are specific to each source. We consider a class of probabilistic context tree models with three types of contexts: those which appear in one, the other, or both sources. We use a BIC penalized maximum likelihood procedure that jointly estimates the two sources. We propose a new algorithm which efficiently computes the estimated context trees. We prove that the procedure is strongly consistent. We also present a simulation study showing the practical advantage of our procedure over a procedure that works separately on each data set. |
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Keywords: | BIC context tree models joint estimation penalized maximum likelihood variable length markov chains |
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