A Crossing-Sensitive Third-Order Factorization for Dependency Parsing

Parsers that parametrize over wider scopes are generally more accurate than edge-factored models. For graph-based non-projective parsers, wider factorizations have so far im-plied large increases in the computational complexity of the parsing problem. This paper introduces a “crossing-sensitive ” generaliza-tion of a third-order factorization that trades off complexity in the model structure (i.e., scoring with features over multiple edges) with complexity in the output structure (i.e., producing crossing edges). Under this model, the optimal 1-Endpoint-Crossing tree can be found in O(n4) time, matching the asymp-totic run-time of both the third-order projec-tive parser and the edge-factored 1-Endpoint-Crossing parser. The crossing-sensitive third-order parser is significantly more accurate than the third-order projective parser under many experimental settings and significantly less accurate on none.