Tuning as Linear Regression

2012 Conference of the North American Chapter of the Association for Computational Linguistics: Human Language Technologies, pages 543–547, Montr´eal, Canada, June 3-8, 2012. c⃝2012 Association for Computational Linguistics Tuning as Linear Regression Marzieh Bazrafshan, Tagyoung Chung and Daniel Gildea Department of Computer Science University of Rochester Rochester, NY 14627 Abstract We propose a tuning method for statistical ma- chine translation, based on the pairwise rank- ing approach. Hopkins and May (2011) pre- sented a method that uses a binary classifier. In this work, we use linear regression and show that our approach is as effective as us- ing a binary classifier and converges faster. 1 Introduction Since its introduction, the minimum error rate train- ing (MERT) (Och, 2003) method has been the most popular method used for parameter tuning in ma- chine translation. Although MERT has nice proper- ties such as simplicity, effectiveness and speed, it is known to not scale well for systems with large num- bers of features. One alternative that has been used for large numbers of features is the Margin Infused Relaxed Algorithm (MIRA) (Chiang et al., 2008). MIRA works well with a large number of features, but the optimization problem is much more compli- cated than MERT. MIRA also involves some modi- fications to the decoder itself to produce hypotheses with high scores against gold translations. Hopkins and May (2011) introduced the method of pairwise ranking optimization (PRO), which casts the problem of tuning as a ranking problem be- tween pairs of translation candidates. The problem is solved by doing a binary classification between “correctly ordered” and “incorrectly ordered” pairs. Hopkins and May (2011) use the maximum entropy classifier MegaM (Daum´e III, 2004) to do the binary classification. Their method compares well to the results of MERT, scales better for high dimensional feature spaces, and is simpler than MIRA. In this paper, we use the same idea for tuning, but, instead of using a classifier, we use linear regression. Linear regression is simpler than maximum entropy based methods. The most complex computation that it needs is a matrix inversion, whereas maximum en- tropy based classifiers use iterative numerical opti- mization methods. We implemented a parameter tuning program with linear regression and compared the results to PRO’s results. The results of our experiments are comparable to PRO, and in many cases (also on av- erage) we get a better maximum BLEU score. We also observed that on average, our method reaches the maximum BLEU score in a smaller number of iterations. The contributions of this paper include: First, we show that linear regression tuning is an effective method for tuning, and it is comparable to tuning with a binary maximum entropy classifier. Second, we show linear regression is faster in terms of the number of iterations it needs to reach the best re- sults. 2 Tuning as Ranking The parameter tuning problem in machine transla- tion is finding the feature weights of a linear trans- lation model that maximize the scores of the candi- date translations …

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