Joint estimation of intersecting context tree models

Details Joint estimation of intersecting context tree models Joint estimation of intersecting context tree models

2011-02-03

arxiv.org/abs/1102.0673v2

Mathematics

Statistics Theory

Scientific paper

10.1016/j.spa.2011.06.012

Data produced by two different sources is classified using variable length Markov chains. In many realistic situations it is conceiveable that the probabilistic context trees corresponding to the two sources share many of the contexts modeling the sources. Therefore, to understand the differences between the two sources, it is important to identify which ones are the contexts and corresponding transition probabilities which are specifically associated to only one of the sources. This is the model selection issue we address here. To identify the relevant contexts we use a BIC penalized maximum likelihood procedure to jointly model the data corresponding to the two sources. To do this we consider a class of probabilistic context tree models having three types of contexts: the ones which appear in only one of the two sources; and the contexts which intervene in both sources. We propose a new algorithm allowing to efficiently compute 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 dataset.

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