Pictorial description of the new algorithm for pair-HMMs. This figure shows a pictorial description of the differences between the forward-backward algorithm (a) and our new algorithm (b) for the Baum-Welch training of a pair-HMM. Each large rectangle corresponds to the projection of the three-dimensional dynamic programming matrix (spanned by the two input sequences X and Y and the states of the HMM) onto the sequence plane. (a) shows how the numerator in Equation 1 is calculated at the pair of sequence positions indicated by the black square using the standard forward and backward algorithm. (b) shows how our algorithm simultaneously calculates a strip of forward values f(Xk, Yq, m) and a strip of ti, j(XkYq, m) values at sequence position k in sequence X in order to estimate ti, j in Equation 1.
Miklós and Meyer BMC Bioinformatics 2005 6:231 doi:10.1186/1471-2105-6-231