Polyhedral outer approximations with application to natural language parsing

  • Authors:
  • André F. T. Martins;Noah A. Smith;Eric P. Xing

  • Affiliations:
  • Carnegie Mellon University, Pittsburgh, PA and Instituto Superior Técnico, Lisboa, Portugal;Carnegie Mellon University, Pittsburgh, PA;Carnegie Mellon University, Pittsburgh, PA

  • Venue:
  • ICML '09 Proceedings of the 26th Annual International Conference on Machine Learning
  • Year:
  • 2009

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Abstract

Recent approaches to learning structured predictors often require approximate inference for tractability; yet its effects on the learned model are unclear. Meanwhile, most learning algorithms act as if computational cost was constant within the model class. This paper sheds some light on the first issue by establishing risk bounds for max-margin learning with LP relaxed inference and addresses the second issue by proposing a new paradigm that attempts to penalize "time-consuming" hypotheses. Our analysis relies on a geometric characterization of the outer polyhedra associated with the LP relaxation. We then apply these techniques to the problem of dependency parsing, for which a concise LP formulation is provided that handles non-local output features. A significant improvement is shown over arc-factored models.