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Biology 2013, 2(4), 1282-1295; doi:10.3390/biology2041282
Article

Algorithms for Hidden Markov Models Restricted to Occurrences of Regular Expressions

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Received: 28 June 2013; in revised form: 8 October 2013 / Accepted: 5 November 2013 / Published: 8 November 2013
(This article belongs to the Special Issue Developments in Bioinformatic Algorithms)
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Abstract: 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.
Keywords: Hidden Markov Model; decoding; Viterbi; forward; algorithm Hidden Markov Model; decoding; Viterbi; forward; algorithm
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.

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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.

AMA Style

Tataru P, Sand A, Hobolth A, Mailund T, Pedersen CNS. Algorithms for Hidden Markov Models Restricted to Occurrences of Regular Expressions. Biology. 2013; 2(4):1282-1295.

Chicago/Turabian Style

Tataru, Paula; Sand, Andreas; Hobolth, Asger; Mailund, Thomas; Pedersen, Christian N.S. 2013. "Algorithms for Hidden Markov Models Restricted to Occurrences of Regular Expressions." Biology 2, no. 4: 1282-1295.



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