Z-score
The Z-score measures the significance of predictions based on their over-representation. YMF [5] searches a restricted space defined by a consensus motif model and finds the candidates with the top Z-scores. The form of the Z-score is as follows:
where obs(m) is the actual number of occurrences of the motif m, E(m) is the expected number of its occurrences in the background model, and σ(m) is the standard deviation.
Consensus-based algorithms such as YMF are sometimes criticized for not being able to incorporate the true binding sites into the motif model. To focus on the objective function and spare the limitation induced by the consensus motif model, we fantasize a motif model for each dataset that comprises the planted binding sites completely and exclusively. We calculate the Z-scores of the predictions and the planted motifs for selected datasets, as shown in Figure 3. Note that the competition is actually not fair: with an expanded motif search space, the new optimum should be at least as high as the current prediction. Nevertheless, we consider the Z-score of the prediction as a touchstone: any score lower than it will not be competitive in the new search space. From Figure 3, we see that is exactly what happens in nearly all of the tested datasets. Note the similarity to results as shown in Figure 1 in the sense of our test: statistical over-representation as measured by Z-score does not necessarily mean binding preference either.
Figure 3  Objective function: Z-score. The figure shows the comparison between the Z-scores of the planted motifs (TFBS in the legend) and the predictions of YMF for some datasets. For the sake of comparison simplicity, we only used datasets ("Generic" and "Markov" types only, for the same reason as in Figure 1) when predictions of YMF and the planted motifs have the same length.