Michal Nánási. Decoding of Hidden Markov Models with Applications to Sequence Alignment. PhD thesis, Comenius University in Bratislava, 2014. Supervised by Broňa Brejová.

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We  study  two  important  problems  in  computational  biology:  sequence  annotation  and
sequence  alignment.   In  the  thesis  we  concentrate  on  the  use  of  hidden  Markov  models
(HMMs), well established generative probabilistic models.
In the first part, we study the sequence annotation problem, specifically the two-stage
HMM  decoding  algorithms  and  the  computational  complexity  of  related  problems.   In
particular, we demonstrate that two-stage algorithms can be used to increase the accuracy
of decoding,  and we prove the NP-hardness for three problems appropriate for the first
stage: the most probable set problem, the most probable restriction problem and the most
probable footprint problem.
The second part of the thesis focuses on alignment of sequences that contain tandem
repeats.  Tandem repeats are highly repetitive elements withing genomic sequences that
cause biases in alignments.  To address this issue, we introduce a new HMM that mod-
els  alignments  containing  tandem  repeats,  combine  it  with  existing  and  new  decoding
algorithms, and evaluate our approach experimentally.
In both problems, we use the decoding algorithms to improve the accuracy of HMM
predictions.   Decoding  algorithms  are  often  neglected,  and  most  of  the  development  is
focused on the structure of an HMM. However, a proper selection of a decoding method
can lead to significant improvements in the predictions.
Keywords:  hidden Markov models, decoding, annotation, alignment