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Consistent Estimation of Partition Markov Models

Department of Statistics, University of Campinas, Rua Sérgio Buarque de Holanda, 651, Campinas, São Paulo 13083-859, Brazil
Author to whom correspondence should be addressed.
Academic Editor: Maxim Raginsky
Entropy 2017, 19(4), 160;
Received: 1 March 2017 / Revised: 31 March 2017 / Accepted: 4 April 2017 / Published: 6 April 2017
(This article belongs to the Special Issue Information Theory in Machine Learning and Data Science)
PDF [291 KB, uploaded 9 April 2017]


The Partition Markov Model characterizes the process by a partition L of the state space, where the elements in each part of L share the same transition probability to an arbitrary element in the alphabet. This model aims to answer the following questions: what is the minimal number of parameters needed to specify a Markov chain and how to estimate these parameters. In order to answer these questions, we build a consistent strategy for model selection which consist of: giving a size n realization of the process, finding a model within the Partition Markov class, with a minimal number of parts to represent the process law. From the strategy, we derive a measure that establishes a metric in the state space. In addition, we show that if the law of the process is Markovian, then, eventually, when n goes to infinity, L will be retrieved. We show an application to model internet navigation patterns. View Full-Text
Keywords: Bayesian Information Criterion; distance measure; model selection; statistical inference in Markov processes Bayesian Information Criterion; distance measure; model selection; statistical inference in Markov processes
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).

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García, J.E.; González-López, V.A. Consistent Estimation of Partition Markov Models. Entropy 2017, 19, 160.

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