Given a sentence x, graph-based models formulates the parsing process as a searching problem: where y * (x) is tree with highest score, Y (x) is the set of all trees compatible with x, θ are model parameters and Score(x,ŷ(x); θ) represents how likely that a particular treeŷ(x) is the correct analysis for x.
the size of Y (x) is exponential large, which makes it impractical to solve equation (1) directly.