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Machine Translation Course 9 Diana Trandab ă ț Academic year 2014-2015

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Statistical Machine Translation Bilingual text Monolingual text Translation model P(s|t) Language model P(t) Decoding algorithm argmax P(t)*P(s|t)

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Decoding How to translate new sentences? Probability models enable us to make predictions: – Given a particular English sentence, what is the most probable Foreign sentence corresponding to it? In math, we want to solve: argmax English p(English|Foreign) Problem: there are a lot of Foreign possible sentences to choose from!!! In combination with a language model, the decoder generates the most likely translation.

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Little story... A French speaking traveler equipped with a bilingual dictionary enters in a New-York store. While reviewing the price chart, he encounters a line that he does not understand: A sheet of paper........ 0.25$ We will look at a process this traveler could use to decode this strange sentence.

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Resources Sentence to translate: A sheet of paper Bilingual dictionary The traveler’s common sense: The traveller can intuitively evaluate the likelihood of a French sentence (since he is French). sourcetargetsourcetarget AUnofde AUneofdu sheetfeuillepaperpapier sheetdrap

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The traveler’s decoder With these resources in hand, the traveler can use the following algorithm to translate the sentence one word at a time: initialize the set of candidate translations H with an empty sentence. while there are incomplete sentences in H – pick the least completed translation h from H – for each possible translation for the next word to translate in h append at the end of h and store the result in hcopy if hcopy is likely following the traveler’s intuition, add it to H return the best candidate in H

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Search graph The traveler concludes that the most likely translation is Une feuille de papier.

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Search space complexity

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Decoder A decoder searches the target document t having the highest probability to translate a given source document s. Most decoders assume that the sentences of a document are independents one from each others. The decoder can thus translate each sentence individually. Shortcomings: – A sentence cannot be omitted, merged with another one, repositioned or sliced by the decoder. – The context of a sentence is not considered when it is translated.

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The decoder’s task The task of the decoder is to use its knowledge and a density function to find the best sequence of transformations that can be applied to an initial target sentence to translate a given source sentence. This problem can be reformulated as a classic AI problem: searching for the shortest path in an implicit graph. Two independent problems must be resolved in order to build a decoder: – Model representation The model defines what a transformation is and how to evaluate the quality of a translation. – Search space exploration Enumerating all possible sequences of transformations is often impracticable, we must smartly select the ones that will be evaluated.

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Model representation — Partial translation The partial translation is a translation that is being transformed. It is composed of: – the source sentence – the target sentence that is being built – a progress indicator that shows how to continue this translation The source and target sentences can be sequences of words, trees, non-contiguous sentences, etc.

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Model representation — Transformation A partial translation evolves when a transformation is applied to it. A transformation can take many forms: – translation of one word – translation of many words – reordering of the children of a node in a tree

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Model representation — Cost A cost quantify the quality of a partial translation. Usually, it evaluates at least: – the likelihood of the transformations – the fluency of the target sentence generated so far – the word reordering that occurred The cost is used to identify the partial translations to dismiss and to select the best complete translation when the search ends.

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Model representation — Transformation generator The transformation generator takes as input a partial translation and outputs the set of transformations that can be applied to it.

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Search space exploration — Hypothesis and search strategy A hypothesis is made of a partial translation and of a cost. The task of the search strategy is two-fold: – Deciding the order in which the hypotheses are explored. – Identify the hypotheses to dismiss (using the value of the cost).

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Putting it all together Each vertex is a hypothesis (partial translation and cost) Each edge corresponds to a transformation. The transformation generator enumerates the out-edges of each vertex. The search strategy defines how to explore the graph

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Slide from Koehn 2008

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Modified from Koehn 2008 (possible future paths are the same)

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Modified from Koehn 2008 (possible future paths are the same)

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Slide from Koehn 2008

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Great! See you next time!

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