Now showing 1 - 2 of 2
PublicationMaximization of Non-Monotone Submodular Functions(2014-01-24) Gillenwater, JenniferA litany of questions from a wide variety of scientific disciplines can be cast as non-monotone submodular maximization problems. Since this class of problems includes max-cut, it is NP-hard. Thus, general purpose algorithms for the class tend to be approximation algorithms. For unconstrained problem instances, one recent innovation in this vein includes an algorithm of Buchbinder et al. (2012) that guarantees a ½ - approximation to the maximum. Building on this, for problems subject to cardinality constraints, Buchbinderet al. (2014) o_er guarantees in the range [0:356; ½ + o(1)]. Earlier work has the best approximation factors for more complex constraints and settings. For constraints that can be characterized as a solvable polytope, Chekuri et al. (2011) provide guarantees. For the online secretary setting, Gupta et al. (2010) provide guarantees. In sum, the current body of work on non-monotone submodular maximization lays strong foundations. However, there remains ample room for future algorithm development. PublicationDependency Grammar Induction via Bitext Projection Constraints(2009-08-02) Ganchev, Kuzman; Gillenwater, Jennifer; Taskar, BenBroad-coverage annotated treebanks necessary to train parsers do not exist for many resource-poor languages. The wide availability of parallel text and accurate parsers in English has opened up the possibility of grammar induction through partial transfer across bitext. We consider generative and discriminative models for dependency grammar induction that use word-level alignments and a source language parser (English) to constrain the space of possible target trees. Unlike previous approaches, our framework does not require full projected parses, allowing partial, approximate transfer through linear expectation constraints on the space of distributions over trees. We consider several types of constraints that range from generic dependency conservation to language-specific annotation rules for auxiliary verb analysis. We evaluate our approach on Bulgarian and Spanish CoNLL shared task data and show that we consistently outperform unsupervised methods and can outperform supervised learning for limited training data.