The Peres-Shields Order Estimator for Fixed and Variable Length Markov Models with Applications to DNA Sequence Similarity

Abstract

AbstractRecently Peres and Shields discovered a new method for estimating the order of a stationary fixed order Markov chain [15]. They showed that the estimator is consistent by proving a threshold result. While this threshold is valid asymptotically in the limit, it is not very useful for DNA sequence analysis where data sizes are moderate. In this paper we give a novel interpretation of the Peres-Shields estimator as a sharp transition phenomenon. This yields a precise and powerful estimator that quickly identifies the core dependencies in data. We show that it compares favorably to other estimators, especially in the presence of noise and/or variable dependencies. Motivated by this last point, we extend the Peres-Shields estimator to Variable Length Markov Chains. We give an application to the problem of detecting DNA sequence similarity using genomic signatures. Abbreviations: Mk = Fixed order Markov model of order k, PST = Prediction suffix tree, MC = Markov chain, VLMC = Variable length Markov chain.KeywordsMarkov ChainAkaike Information CriterionBayesian Information CriterionSharp TransitionLower Order ModelThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.