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P a e i 1j the probability of an alignment given

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Unformatted text preview: system, developed at IBM •  Simple genera1ve model to produce F given E=e1, e2, …eI •  Choose J, the number of words in F: F=f1, f2, …fJ •  Choose a 1 ­to ­many alignment A=a1, a2, …aJ •  For each posi1on in F, generate a word fj from the aligned word in E: ea j Dan Jurafsky IBM Model 1: Genera$ve Process 0 1 2 3 4 5 6 NULL J=9 Mary didn’t slap the green witch Maria no dió una bofetada a la bruja verde A= 1 2 3 3 3 0 4 6 5 1.  Choose J, the number of words in F: F=f1, f2, …fJ 2.  Choose a 1 ­to ­many alignment A=a1, a2, …aJ 3.  For each posi1on in F, generate a word fj from the aligned word in E: ea j Dan Jurafsky Compu$ng P(F | E) in IBM Model 1: P(F|E,A) •  Let ea j : the English word assigned to Spanish word fj t(fx,ey): probability of transla1ng ey as fx •  If we knew E, the alignment A, and J, then: J P( F | E, A) = ! t ( f j , ea j ) j =1 •  The probability of the Spanish sentence if we knew the English source, the alignment, and J Dan Jurafsky Compu$ng P(F | E) in IBM Model 1: P(A|E) •  A normaliza1on factor, since there are (I + 1)J possible alignments: ! P( A | E ) = ( I + 1)J •  The probability of an alignment given the English sentence. Dan Jurafsky Compu$ng P(F | E) in IBM Model 1: P(F,A|E) and then P(F|E) ! P( A | E ) = ( I + 1)J J P( F | E, A) = ! t ( f j , ea j ) j =1 The probability of genera1ng F through a par1cular alignment: J ! P ( F, A | E ) = t ( f j , ea ) J! ( I + 1) j=1 To...
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