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)
6.2 基于繁衍率的模型 185
这里用特殊的空标记 NULL 表示翻译对空的情况;
• 最后,把生成的所有汉语单词放在合适的位置。比如“科学家”和“们”分别放在
s 的位置 1 和位置 2。可以用符号 π 记录生成的单词在源语言句子 s 中的位置。
比如“Scientists”生成的汉语单词在 s 中的位置表示为 π
1
= {π
11
= 1,π
12
= 2}。
为了表述清晰,这里重新说明每个符号的含义。s、t、m 和 l 分别表示源语言句
子、目标语言译文、源语言单词数量以及译文单词数量。φ、τ 和 π 分别表示产出率、
生成的源语言单词以及它们在源语言句子中的位置。φ
i
表示第 i 个目标语言单词 t
i
的产出率。τ
i
和 π
i
分别表示 t
i
生成的源语言单词列表及其在源语言句子 s 中的位置
列表。
可以看出,一组 τ 和 π(记为 < τ,π >)可以决定一个对齐 a 和一个源语句子 s。
相反的,一个对齐 a 和一个源语句子 s 可以对应多组 < τ,π >。如图6.6所示,不同的
< τ,π > 对应同一个源语言句子和词对齐。它们的区别在于目标语单词“Scientists”
生成的源语言单词“科学家”和“们”的顺序不同。这里把不同的 < τ,π > 对应到的
相同的源语句子 s 和对齐 a 记为 < s,a >。因此计算 P (s, a|t) 时需要把每个可能结果
的概率加起来,如下:
P (s,a|t) =
X
<τ,π>∈<s,a>
P (τ,π|t) (6.9)
s
τ
ϕ
t
科学家
们
并不
知道
τ
0
1.NULL
τ
1
1.
科学家
2.
们
τ
2
1.NULL
τ
3
1. 并不
τ
4
1. 知道
...
... ...
< τ,π >
1
... ...
科学家
们
并不
知道
τ
0
1.NULL
τ
1
1.
们
2.
科学家
τ
2
1.NULL
τ
3
1. 并不
τ
4
1. 知道
...
... ...
< τ,π >
2
... ...
图 6.6 不同 τ 和 π 对应相同的源语言句子和词对齐的情况
不过 < s,a > 中有多少组 < τ, π > 呢?通过图6.5中的例子,可以推出 < s,a > 应
该包含
Q
l
i=0
φ
i
! 个不同的二元组 < τ,π >。这是因为在给定源语言句子和词对齐时,