Given the agenda graph and n-best hypotheses, the system can predict the next system actions to maximize multilevel score functions .

the score function based on current input and discourse structure given the focus stack.

Therefore, we need to select the hypothesis that maximizes the scoring function among a set of n-best hypotheses of each utterance.

Secondly, the multilevel score functions are computed for each candidate node Ci given a hypothesis hi.

Otherwise, the best node which would be pushed onto the focus stack must be selected using multilevel score functions .

As explained in section 2, both models essentially learn a scoring function 3 : X —> R, where the domain X is different for the two models.

The graph-based model, MSTParser, learns a scoring function 3(2', j, l) E R over labeled dependencies.

The transition-based model, MaltParser, learns a scoring function 3(0, 25) E R over configurations and transitions.

The simplest parameterization is the arc-factored model that defines a real-valued score function for arcs 3(2', j, l) and further defines the score of a dependency graph as the sum of the

Given a real-valued score function 3(0, 25) (for transition 75 out of configuration 0), parsing can be performed by starting from the initial configuration and taking the optimal transition 75* = arg maxtET 3(0, 25) out of every configuration 0 until a terminal configuration is reached.

To learn a scoring function on transitions, these systems rely on discriminative learning methods, such as memory-based learning or support vector machines, using a strictly local learning procedure where only single transitions are scored (not complete transition sequences).