Specifically group them into pairs (y, z) where y and z are identical except that y i = 1 and y k = 0, but z i = 0 and z k = 1.
the two summations on the right-hand side of the following equality are carried out in parallel: Then, focusing on s first: where A = s • z is the number of true positives between s and z (s and y have an additional true positive at i by construction); T = y•y = z•z is the number of positive labels in y and z (identical by assumption); and is the probability of y and z evaluated on all positions except for i and k. This equality holds because of the zeroth-order Markov assumption (5) imposed on Pr(y).