Figure 1

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(X _k , Y _q , m) and a strip of t_{i, j}(X _k Y _q , m) values at sequence position k in sequence X in order to estimate t_{i, j}in Equation 1.