We encode this in our factor graph setting using a single global factor T (shown as a large red square in Figure 2) with the following scoring function: φ T (y) = 1 y forms a legal taxonomy tree 0 otherwise Model.
for a given global assignment y, let Note that by substituting our model's factor scoring functions into Equation 1, we get: our model has the form of a standard loglinear model with feature function f .