This paper provides an algorithmic framework for learning statistical models involving directed spanning trees, or equivalently non-projective dependency structures. We show how partition functions and marginals for directed spanning trees can be computed by an adaptation of Kirchhoff’s Matrix-Tree Theorem. To demonstrate an application of the method, we perform experiments which use the algorithm in training both log-linear and max-margin dependency parsers. The new training methods give improvements in accuracy over perceptron-trained models.
CitationKoo, T. [et al.]. Structured prediction models via the matrix-tree theorem. A: Conference on Empirical Methods in Natural Language Processing. "Joint Conference on Empirical Methods in Natural Language Processing and Computational Natural Language Learning (EMNLP-CoNLL)". Praga: 2007, p. 141-150.
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