Abstract
Decoding of phrase-based translation models in the general case is known to be NP-complete, by a reduction from the traveling salesman problem (Knight, 1999). In practice, phrase-based systems often impose a hard distortion limit that limits the movement of phrases during translation. However, the impact on complexity after imposing such a constraint is not well studied. In this paper, we describe a dynamic programming algorithm for phrase-based decoding with a fixed distortion limit. The runtime of the algorithm is O( nd! lh d+1) where n is the sentence length, d is the distortion limit, l is a bound on the number of phrases starting at any position in the sentence, and h is related to the maximum number of target language translations for any source word. The algorithm makes use of a novel representation that gives a new perspective on decoding of phrase-based models.
Highlights
Phrase-based translation models (Koehn et al, 2003; Och and Ney, 2004) are widely used in statistical machine translation
This paper describes an algorithm for phrasebased decoding with a fixed distortion limit whose runtime is linear in the length of the sentence, and for a fixed distortion limit is polynomial in other factors
The algorithm builds on the insight that decoding with a hard distortion limit is related to the bandwidth-limited traveling salesman problem (BTSP) (Lawler et al, 1985)
Summary
Phrase-based translation models (Koehn et al, 2003; Och and Ney, 2004) are widely used in statistical machine translation. The complexity of decoding with such a distortion limit is an open question: the NP-hardness result from Knight. For a hard distortion limit d, and sentence length n, the runtime is O(nd!lhd+1), where l is a bound on the number of phrases starting at any point in the sentence, and h is related to the maximum number of translations for any word in the source language sentence. The algorithm builds on the insight that decoding with a hard distortion limit is related to the bandwidth-limited traveling salesman problem (BTSP) (Lawler et al, 1985). The algorithm is amenable to beam search It is quite different from previous methods for decoding of phrase-based models, potentially opening up a very different way of thinking about decoding algorithms for phrasebased models, or more generally for models in statistical NLP that involve reordering
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