Scoring and Optimization

Lecture 13: Scoring and Optimization

Lecture video:	web TODO Youtube

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Features of MT Models

Phrase Translation Probabilities

Phrase translation probabilities are calculated from occurrences of phrase pairs extracted from the parallel training data. Usually, MT systems work with the following two conditional probabilities:

• $P(\mathbf {e} |\mathbf {f} )$
• $P(\mathbf {f} |\mathbf {e} )$

These probabilities are estimated by simply counting how many times (for the first formula) we saw $\mathbf {e}$ aligned to $\mathbf {f}$ and how many times we saw $\mathbf {f}$ in total. For example, based on the following excerpt from (sorted) extracted phrase pairs, we estimate that $P({\text{naznačena v programu}}|{\text{estimated in the programme}})=3/9$.

estimated in the programme ||| naznačena v programu
estimated in the programme ||| naznačena v programu
estimated in the programme ||| naznačena v programu
estimated in the programme ||| odhadován v programu
estimated in the programme ||| odhadovány v programu
estimated in the programme ||| odhadovány v programu 
estimated in the programme ||| předpokládal program
estimated in the programme ||| v programu uvedeným
estimated in the programme ||| v programu uvedeným

Lexical Weights

Lexical weights are a method for smoothing the phrase table. Infrequent phrases have unreliable probability estimates; for instance many long phrases occur together only once in the corpus, resulting in $P(\mathbf {e} |\mathbf {f} )=P(\mathbf {f} |\mathbf {e} )=1$. Several methods exist for computing lexical weights. The most common one is based on word alignment inside the phrase. The probability of each foreign word $f_{j}$ is estimated as the average of lexical translation probabilities $w(f_{j},e_{i})$ over the English words aligned to it. Thus for the phrase $(\mathbf {e} ,\mathbf {f} )$ with the set of alignment points $a$, the lexical weight is:

${\text{lex}}(\mathbf {f} |\mathbf {e} ,a)=\prod _{j=1}^{l_{f}}{\frac {1}{|{i|(i,j)\in a}|}}\sum _{\forall (i,j)\in a}w(f_{j},e_{i})$