Resolution:
## 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.
Miklós and Meyer |