Cube summing, approximate inference with non-local features, and dynamic programming without semirings

  • Authors:
  • Kevin Gimpel;Noah A. Smith

  • Affiliations:
  • Carnegie Mellon University, Pittsburgh, PA;Carnegie Mellon University, Pittsburgh, PA

  • Venue:
  • EACL '09 Proceedings of the 12th Conference of the European Chapter of the Association for Computational Linguistics
  • Year:
  • 2009

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Abstract

We introduce cube summing, a technique that permits dynamic programming algorithms for summing over structures (like the forward and inside algorithms) to be extended with non-local features that violate the classical structural independence assumptions. It is inspired by cube pruning (Chiang, 2007; Huang and Chiang, 2007) in its computation of non-local features dynamically using scored k-best lists, but also maintains additional residual quantities used in calculating approximate marginals. When restricted to local features, cube summing reduces to a novel semiring (k-best+residual) that generalizes many of the semirings of Goodman (1999). When non-local features are included, cube summing does not reduce to any semiring, but is compatible with generic techniques for solving dynamic programming equations.