Our model defines a conditional probability distribution over virtually all segmentations of a word w. To train our model, we wish to maximize the likelihood of the segmentations contained in the reference lattices by moving probability mass away from the segmentations that are not in the reference lattice.
we wish to minimize the following objective (which can be computed using the forward algorithm over the unpruned hypothesis lattices): The gradient with respect to the feature weights for a log linear model is simply: To compute these values, the first expectation is computed using forward-backward inference over the full lattice.