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Drifting Markov Models with Polynomial Drift and Applications to DNA Sequences
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Nicolas Vergne
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February 21, 2008
In this article, we introduce the drifting Markov models (DMMs) which are inhomogeneous Markov models designed for modeling the heterogeneities of sequences (in our case DNA or protein sequences) in a more flexible way than homogeneous Markov chains or even hidden Markov models (HMMs). We focus here on the polynomial drift: the transition matrix varies in a polynomial way. To show the reliability of our models on DNA, we exhibit high similarities between the probability distributions of nucleotides obtained by our models and the frequencies of these nucleotides computed by using a sliding window. In a further step, these DMMs can be used as the states of an HMM: on each of its segments, the observed process can be modeled by a drifting Markov model. Search of rare words in DNA sequences remains possible with DMMs and according to the fits provided, DMMs turn out to be a powerful tool for this purpose. The software is available on request from the author. It will soon be integrated on seq++ library (http://stat.genopole.cnrs.fr/seqpp/).
Published Online: 2008-2-21
©2011 Walter de Gruyter GmbH & Co. KG, Berlin/Boston
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Keywords for this article
drifting Markov models;
Markov models;
DNA sequences;
heterogeneity;
rare words
Articles in the same Issue
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- Comparing the Characteristics of Gene Expression Profiles Derived by Univariate and Multivariate Classification Methods
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