Machine Translation

Important Notions

Translation as a noisy channel problem:
- Translation of source text S into target text T:
  argmax_T P(T | S) = argmax_T P(T) P(S | T)
- Language model: P(T)
- Translation model: P(S | T)
Alignment:
- Sentence alignment: ( S = [S_S,1...S_S,n] | T = [S_T,1,a(1)...S_T,m,a(m)] )
- Word alignment: ( S = [w_S,1...w_S,n] | T = [w_T,1,a(1)...w_T,m,a(m)] )
  (where a(i) is the set of positions occupied by the sentences/words in S that are aligned to the ith sentence/word in T)
Translation modeling:
- Translation: P(w_S,i | w_T,j,a(j)) (for i in a(j))
- Fertility: P(N | w_T,j,a(j)) (where N is the cardinality of a(j))
- Distortion: P(i | j,m) (for i in a(j))
Language modeling