Dependency Parsing with Bounded Block Degree and Well-nestedness via Lagrangian Relaxation and Branch-and-Bound

Abstract

We present a novel dependency parsing method which enforces two structural properties on dependency trees: bounded block degree and well-nestedness. These properties are useful to better represent the set of admissible dependency structures in treebanks and connect dependency parsing to context-sensitive grammatical formalisms. We cast this problem as an Integer Linear Program that we solve with Lagrangian Relaxation from which we derive a heuristic and an exact method based on a Branch-and-Bound search. Experimentally, we see that these methods are efficient and competitive compared to a baseline unconstrained parser, while enforcing structural properties in all cases.

Span-based discontinuous constituency parsing: a family of exact chart-based algorithms with time complexities from O(nˆ6) down to O(nˆ3)

“…For example, a verbal phrase is not constrained to contain a verb. As such, they can be assimilated to the mainstream approach to bi-lexical dependency parsing where one considers candidate outputs only in a restricted class of graphs: non-projective (McDonald et al, 2005), projective (Eisner, 1997) or bounded block degree and wellnested spanning aborescences (Gómez-Rodríguez et al, 2009Corro et al, 2016), among others (Kuhlmann and Nivre, 2006;Satta and Kuhlmann, 2013;Pitler et al, 2012). These approaches assume that intricate relations in the syntactic content can be implicitly learned by the scoring function.…”

Efficient Discontinuous Phrase-Structure Parsing via the Generalized Maximum Spanning Arborescence

“…Finally, we restricted our grammar to spinal trees but it could be possible to allow full lexicalized TAG-like trees, with substitution nodes and even obligatory adjunction sites. Derivations compat-ible with the TAG formalism (or more generally LCFRS) could be recovered by the use of a constrained version of MSA (Corro et al, 2016).…”

“…Exact pruning based on duality has already been studied in parsing, with branch and bound (Corro et al, 2016) or column generation (Riedel et al, 2012) and in machine translation with beam search (Rush et al, 2013).…”

“…Lagrangian relaxation has been successfully applied to various NLP tasks (Koo et al, 2010;Le Roux et al, 2013;Almeida and Martins, 2013;Das et al, 2012;Corro et al, 2016). Intuitively, given an integer linear program, it consists in relaxing some linear constraints which make the program difficult to solve and penalizing their violation in the objective function.…”

“…To accelerate the resolution, our method relies heavily on problem reduction (Beasley, 1993), which uses the primal/dual bounds to filter out suboptimal assignments. Exact pruning based on duality has already been studied in parsing, with branch and bound (Corro et al, 2016) or column generation (Riedel et al, 2012) and in machine translation with beam search (Rush et al, 2013).…”