At word level, how can I state that this word is the best translation of an other word?
Since the translation of a word depends on the words before and after, I suggest you to use a parallel corpora to estimate the probability of having specific translation for a word based on the words before or after.
You can use association measures such as Log Likelihood, DICE, etc. or you can go "probabilistic" and employ IBM's famous word alignment models (just Google search for GIZA++) to obtain a probability that a word is translated by another. All these methods make use of a parallel corpus as Ali said.
On a side note, there is no such thing as "a word is the best translation for another word" since this translation depends on the source word sense. Thus there are several "best translations" of a single word, and, depending on your domain of application, a sense is more likely to be used. It follows that a probabilistic lexicon is in order because it can offer the necessary bias to the translation machine.
Some pointer papers on the subject:
Dan Tufiș: A Cheap and Fast Way to Build Useful Translation Lexicons. COLING 2002 (for the association measures idea)
Brown et al. 1993. The Mathematics of Statistical Machine Translation: Parameter Estimation (the classic IBM models paper)
Thank you Radu, The idea of using association measure is very interesting.
Let me add some suggestions as to which publications address this question:
Nguyen Bach, Fei Huang, & Yaser Al-Onaizan: Goodness: a method for measuring machine translation confidence. ACL-HLT 2011: Proceedings of the 49th Annual Meeting of the Association for Computational Linguistics, Portland, Oregon, June 19-24, 2011; pp.211-219
With lots of references to earlier paper.
Fei had an earlier paper, where he treated sentence level confidence:
Fei Huang. 2009. Confidence measure for word alignment. In Proceedings of the ACL-IJCNLP ’09, pages 932–940, Morristown, NJ, USA. Association for Computational Linguistics.
Also, there was a JHU workshop in 2004:
John Blatz, Erin Fitzgerald, George Foster, Simona Gandrabur, Cyril Goutte, Alex Kulesza, Alberto Sanchis, and Nicola Ueffing. 2004. Confidence estimation for machine
translation. In The JHU Workshop Final Report, Baltimore, Maryland, USA, April.
And Nicola Ueffing did extensive research on this:
Nicola Ueffing and Hermann Ney. 2007. Word-level confidence estimation for machine translation. Computational Linguistics, 33(1):9–40
Her PhD thesis should be accessible from the RWTH i6 web pages.
Sorry for this bias towards publications from the places I spend most of my MT years :-)
There is a workshop on translation quality estimation this year with a shared task.
I would recommend you take a look at the workshop papers
http://statmt.org/wmt12/quality-estimation-task.html
If you are curious about the top performers on the shared task, you can read the system description paper of the top 3 systems, 2 from Language Weaver and 1 from Uppsala University.
The SDL Language Weaver Systems in the WMT12 Quality Estimation Shared Task,
Radu Soricut, Nguyen Bach and Ziyuan Wang
Tree Kernels for Machine Translation Quality Estimation,
Christian Hardmeier, Joakim Nivre and Jörg Tiedemann
As Radu mentioned, there is no such thing as the best translation of one word because it depends on the specific sense associated with the source text word. Further, I would even add that there is no reason to study one-word translations because we speak with many words closely associated syntactically. So the meaning of a word depends ultimately on the interaction of the meaning of each and other words it is used with.
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