1. A computer-implemented method, comprising: receiving, at a computing device having one or more processors, a sentence including one or more words; determining, at the computing device, an index set of possible head-modifier dependencies for the sentence, the index set including inner arcs and outer arcs, the inners arcs representing possible head-modifier dependency between words in the sentence separated by a distance less than or equal to a first distance threshold and outer arcs representing possible head-modifier dependency between words in the sentence separated by a distance greater than the first distance threshold; pruning, at the computing device, the outer arcs to exclude arcs representing possible head-modifier dependency between words in the sentence separated by a distance greater than a second distance threshold to obtain a first pruned index set, the second distance threshold being based on a determination of a longest head-modifier dependency distance observed in training data; pruning, at the computing device, the first pruned index set based on an augmented vine parsing algorithm to obtain a second pruned index set, the second pruned index set including: (i) each specific inner arc when a likelihood that the specific inner arc is appropriate is greater than a first threshold, and (ii) the outer arcs in the first pruned index set when a likelihood that there exists a possible outer arc that is appropriate is greater than the first threshold, wherein each specific inner arc corresponds to a specific index and wherein the likelihood that the specific inner arc is appropriate is determined based on a max-marginal value of its corresponding specific index; pruning, at the computing device, the second pruned index set based on a second parsing algorithm to obtain a third pruned index set, the second parsing algorithm being a first-order parsing model; pruning, at the computing device, the third pruned index set based on a third parsing algorithm to obtain a fourth pruned index set, the third parsing algorithm being a second-order parsing model; pruning, at the computing device, the fourth pruned index set based on a fourth parsing algorithm to obtain a fifth pruned index set, the fourth parsing algorithm being a third-order parsing model; determining, at the computing device, a most-likely parse for the sentence from the fifth pruned index set; and outputting, from the computing device, the most-likely parse.