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Open AccessArticle

Algorithms for Hidden Markov Models Restricted to Occurrences of Regular Expressions

Bioinformatics Research Centre, Aarhus University, C. F. Møllers Allé 8, DK-8000 Aarhus C, Denmark
Department of Computer Science, Aarhus University, Aabogade 34, DK-8200 Aarhus N, Denmark
Author to whom correspondence should be addressed.
Biology 2013, 2(4), 1282-1295;
Received: 28 June 2013 / Revised: 8 October 2013 / Accepted: 5 November 2013 / Published: 8 November 2013
(This article belongs to the Special Issue Developments in Bioinformatic Algorithms)
Hidden Markov Models (HMMs) are widely used probabilistic models, particularly for annotating sequential data with an underlying hidden structure. Patterns in the annotation are often more relevant to study than the hidden structure itself. A typical HMM analysis consists of annotating the observed data using a decoding algorithm and analyzing the annotation to study patterns of interest. For example, given an HMM modeling genes in DNA sequences, the focus is on occurrences of genes in the annotation. In this paper, we define a pattern through a regular expression and present a restriction of three classical algorithms to take the number of occurrences of the pattern in the hidden sequence into account. We present a new algorithm to compute the distribution of the number of pattern occurrences, and we extend the two most widely used existing decoding algorithms to employ information from this distribution. We show experimentally that the expectation of the distribution of the number of pattern occurrences gives a highly accurate estimate, while the typical procedure can be biased in the sense that the identified number of pattern occurrences does not correspond to the true number. We furthermore show that using this distribution in the decoding algorithms improves the predictive power of the model. View Full-Text
Keywords: Hidden Markov Model; decoding; Viterbi; forward; algorithm Hidden Markov Model; decoding; Viterbi; forward; algorithm
MDPI and ACS Style

Tataru, P.; Sand, A.; Hobolth, A.; Mailund, T.; Pedersen, C.N.S. Algorithms for Hidden Markov Models Restricted to Occurrences of Regular Expressions. Biology 2013, 2, 1282-1295.

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