Training a Log-Linear Parser with Loss Functions via Softmax-Margin

Proceedings of the 2011 Conference on Empirical Methods in Natural Language Processing, pages 333–343, Edinburgh, Scotland, UK, July 27–31, 2011. c⃝2011 Association for Computational Linguistics Training a Log-Linear Parser with Loss Functions via Softmax-Margin Michael Auli School of Informatics University of Edinburgh m.auli@sms.ed.ac.uk Adam Lopez HLTCOE Johns Hopkins University alopez@cs.jhu.edu Abstract Log-linear parsing models are often trained by optimizing likelihood, but we would prefer to optimise for a task-specific metric like F- measure. Softmax-margin is a convex objec- tive for such models that minimises a bound on expected risk for a given loss function, but its na¨ıve application requires the loss to de- compose over the predicted structure, which is not true of F-measure. We use softmax- margin to optimise a log-linear CCG parser for a variety of loss functions, and demonstrate a novel dynamic programming algorithm that enables us to use it with F-measure, lead- ing to substantial gains in accuracy on CCG- Bank. When we embed our loss-trained parser into a larger model that includes supertagging features incorporated via belief propagation, we obtain further improvements and achieve a labelled/unlabelled dependency F-measure of 89.3%/94.0% on gold part-of-speech tags, and 87.2%/92.8% on automatic part-of-speech tags, the best reported results for this task. 1 Introduction Parsing models based on Conditional Random Fields (CRFs; Lafferty et al., 2001) have been very successful (Clark and Curran, 2007; Finkel et al., 2008). In practice, they are usually trained by max- imising the conditional log-likelihood (CLL) of the training data. However, it is widely appreciated that optimizing for task-specific metrics often leads to better performance on those tasks (Goodman, 1996; Och, 2003). An especially attractive means of accomplishing this for CRFs is the softmax-margin (SMM) ob- jective (Sha and Saul, 2006; Povey and Woodland, 2008; Gimpel and Smith, 2010a) (§2). In addition to retaining a probabilistic interpretation and optimiz- ing towards a loss function, it is also convex, mak- ing it straightforward to optimise. Gimpel and Smith (2010a) show that it can be easily implemented with a simple change to standard likelihood-based train- ing, provided that the loss function decomposes over the predicted structure. Unfortunately, the widely-used F-measure met- ric does not decompose over parses. To solve this, we introduce a novel dynamic programming algo- rithm that enables us to compute the exact quanti- ties needed under the softmax-margin objective us- ing F-measure as a loss (§3). We experiment with this and several other metrics, including precision, recall, and decomposable approximations thereof. Our ability to optimise towards exact metrics en- ables us to verify the effectiveness of more effi- cient approximations. We test the training proce- dures on the state-of-the-art Combinatory Categorial Grammar (CCG; Steedman 2000) parser of Clark and Curran (2007), obtaining substantial improve- ments under a variety of conditions. We then embed this model into a more accurate model that incor- porates additional supertagging features via loopy belief propagation. The improvements are additive, obtaining the best reported results on this task (§4). 2 Softmax-Margin Training The softmax-margin objective modifies the standard likelihood objective …

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