Computational Complexity of Problems on Probabilistic Grammars and Transducers

Casacuberta, Francisco; Higuera, Colin de la

doi:10.1007/978-3-540-45257-7_2

Cited by 51 publications

(48 citation statements)

References 16 publications

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“…The problem of finding the most probable string is discussed by Paz (1971), Casacuberta and de la Higuera (2000), Sima'an (2002) and Blondel and Canterini (2003).…”

Section: Further Informationmentioning

confidence: 99%

Algorithmic Aspects of Natural Language Processing

Nederhof

Satta

2009

Chapman &Amp; Hall/CRC Applied Algorithms and Data Structures Series

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“…The problem of finding the most probable string is discussed by Paz (1971), Casacuberta and de la Higuera (2000), Sima'an (2002) and Blondel and Canterini (2003).…”

Section: Further Informationmentioning

confidence: 99%

Algorithmic Aspects of Natural Language Processing

Nederhof

Satta

2009

Chapman &Amp; Hall/CRC Applied Algorithms and Data Structures Series

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“…The search of the optimal y in (5) using definition (3) is a difficult computational problem (Casacuberta & de la Higuera, 2000). The only possible algorithmic solution is the use of some variant of the A algorithm (e.g., the Stack-Decoding (Bahl, Jelinek & Mercer, 1983)), which presents exponential computational costs in the worst case and, therefore, may not be feasible for use in some real applications.…”

Section: Definitionsmentioning

confidence: 99%

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Picó

Casacuberta

2001

Machine Learning

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Abstract. Formal translations constitute a suitable framework for dealing with many problems in pattern recognition and computational linguistics. The application of formal transducers to these areas requires a stochastic extension for dealing with noisy, distorted patterns with high variability. In this paper, some estimation criteria are proposed and developed for the parameter estimation of regular syntax-directed translation schemata. These criteria are: maximum likelihood estimation, minimum conditional entropy estimation and conditional maximum likelihood estimation. The last two criteria were proposed in order to deal with situations when training data is sparse. These criteria take into account the possibility of ambiguity in the translations: i.e., there can be different output strings for a single input string. In this case, the final goal of the stochastic framework is to find the highest probability translation of a given input string. These criteria were tested on a translation task which has a high degree of ambiguity.

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“…Translation models, such as the phrase-based translation model that we focus on in this paper (Koehn et al, 2003), define multiple derivations for each translation, making the probability of a translation the sum over all of its derivations. Unfortunately, finding the maximum probability translation is NP-hard for this model (Casacuberta and Higuera, 2000), making approximations necessary. The most common of these approximations is the Viterbi approximation, which can be computed in polynomial time via dynamic programming (DP).…”

Section: Introductionmentioning

confidence: 99%

Monte Carlo techniques for phrase-based translation

Arun

Haddow

Koehn

et al. 2010

Machine Translation

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Abstract. Recent advances in statistical machine translation have used approximate beam search for NP-complete inference within probabilistic translation models. We present an alternative approach of sampling from the posterior distribution defined by a translation model. We define a novel Gibbs sampler for sampling translations given a source sentence and show that it effectively explores this posterior distribution. In doing so we overcome the limitations of heuristic beam search and obtain theoretically sound solutions to inference problems such as finding the maximum probability translation and minimum risk training and decoding.

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Computational Complexity of Problems on Probabilistic Grammars and Transducers

Cited by 51 publications

References 16 publications

Algorithmic Aspects of Natural Language Processing

Algorithmic Aspects of Natural Language Processing

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Monte Carlo techniques for phrase-based translation

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