The Mathematics of Statistical Machine Translation: Parameter Estimation

5 Results

1. How were the IBM models trained on the Hansards?
   On about 1.8 million Hansard sentence pairs, with 12 EM iterations in which each model was initialized from the previous one, starting with every \(t(f \mid e)\) equal. Only about 1% of word pairs ever co-occur, and translation probabilities below a threshold were pruned, leaving about 39 French words per English word.
   • Brown et al., 1993, The Mathematics of Statistical Machine Translation (Computational Linguistics), §5
2. Why does perplexity jump when training switches from Model 2 to Model 3?
   Not because Model 3 is worse, but because it is deficient: most of its probability is squandered on objects that aren’t strings of French words.
   • Brown et al., 1993, The Mathematics of Statistical Machine Translation (Computational Linguistics), §5
3. What did the learned probabilities show for nodding, should, the and farmers?
   Nodding has large fertility (il fait signe que oui, hoche la tête…); should rarely has fertility above 1 but spreads over many forms of devoir; the usually gives le/la/les/l’ but has fertility 0 about 14% of the time; farmers typically has fertility 2, producing agriculteurs plus an article.
   • Brown et al., 1993, The Mathematics of Statistical Machine Translation (Computational Linguistics), §5
4. Are learned translation probabilities like \(t(\text{le} \mid \text{the})\) constants of nature?
   No: they reflect the training data. \(t(\text{le} \mid \text{the})\) was 0.497 here vs 0.610 in an earlier experiment with 40,000 sentence pairs and the 9,000 most common words.
   • Brown et al., 1993, The Mathematics of Statistical Machine Translation (Computational Linguistics), §5
5. What do alignments like Speaker → l’Orateur and starred → marquées de un astérisque show?
   Training discovers multi-word correspondences from scratch: Speaker learned to produce the article too, and starred was connected to exactly the right four words, starting from all French words being equally likely translations.
   • Brown et al., 1993, The Mathematics of Statistical Machine Translation (Computational Linguistics), §5