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The Profile Hidden Markov Model (PHMM) can be poor at capturing dependency between
observations because of the statistical assumptions it makes. To overcome this limitation, the
dependency between residues in a multiple sequence alignment (MSA) which is the
representative of a PHMM can be combined with the PHMM. Based on the fact that
sequences appearing in the final MSA are written based on their similarity; the one-by-one
dependency between corresponding amino acids of two current sequences can be append to
PHMM. This perspective makes it possible to consider a generalization of PHMM. For
estimating the parameters of modified PHMM (emission and transition probabilities), we
introduce new forward and backward algorithms. For this purpose, we consider the
generalized PHMM as a Bayesian Network (BN). A Bayesian network is a specific type of
graphical model which is a directed acyclic graph (DAG). The performance of modified
PHMM is discussed by applying it to the twenty protein families in Pfam database. Results
show that the modified PHMM significantly increases the accuracy of ordinary PHMM.
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