BLEU指标的计算示例_blue指标计算代码

题目如下：

根据下图例子，计算下面机器翻译译文的BLEU-4值 (列出1-4元文法的统计数)。

解：由题意得

$1-4元的统计数如下表所示：$
1-gram count ref count-clip it 1 0 0 is 1 1 1 a 1 1 1 nice 1 1 1 day 1 1 1 today 1 1 1

$$\begin{array}{|c|c|c|c|} \hline \text{1-gram} & \text{count} & \text{ref} & \text{count-clip} \\ \hline \text{it} & 1 & 0 & 0 \\ \hline \text{is} & 1 & 1 & 1 \\ \hline \text{a} & 1 & 1 & 1 \\ \hline \text{nice} & 1 & 1 & 1 \\ \hline \text{day} & 1 & 1 & 1 \\ \hline \text{today} & 1 & 1 & 1 \\ \hline \end{array}$$ 1-gramitisanicedaytoday​count111111​ref011111​count-clip011111​​

2-gram count ref count-clip it is 1 0 0 is a 1 1 1 a nice 1 1 1 nice day 1 1 1 day today 1 0 0

$$\begin{array}{|c|c|c|c|} \hline \text{2-gram} & \text{count} & \text{ref} & \text{count-clip} \\ \hline \text{it is} & 1 & 0 & 0 \\ \hline \text{is a} & 1 & 1 & 1 \\ \hline \text{a nice} & 1 & 1 & 1 \\ \hline \text{nice day} & 1 & 1 & 1 \\ \hline \text{day today} & 1 & 0 & 0 \\ \hline \end{array}$$ 2-gramit isis aa nicenice dayday today​count11111​ref01110​count-clip01110​​

3-gram count ref count-clip it is a 1 0 0 is a nice 1 1 1 a nice day 1 1 1 nice day today 1 0 0

$$\begin{array}{|c|c|c|c|} \hline \text{3-gram} & \text{count} & \text{ref} & \text{count-clip} \\ \hline \text{it is a} & 1 & 0 & 0 \\ \hline \text{is a nice} & 1 & 1 & 1 \\ \hline \text{a nice day} & 1 & 1 & 1 \\ \hline \text{nice day today} & 1 & 0 & 0 \\ \hline \end{array}$$ 3-gramit is ais a nicea nice daynice day today​count1111​ref0110​count-clip0110​​

4-gram count ref count-clip it is a nice 1 0 0 is a nice day 1 1 1 a nice day today 1 0 0

$$\begin{array}{|c|c|c|c|} \hline \text{4-gram} & \text{count} & \text{ref} & \text{count-clip} \\ \hline \text{it is a nice} & 1 & 0 & 0 \\ \hline \text{is a nice day} & 1 & 1 & 1 \\ \hline \text{a nice day today} & 1 & 0 & 0 \\ \hline \end{array}$$ 4-gramit is a niceis a nice daya nice day today​count111​ref010​count-clip010​​

由表可得
$$p_1=\frac{5}{6}，p_2=\frac{3}{5}，p_3=\frac{2}{4}，p_4=\frac{1}{3}$$
易知
$$c=6,r=5$$
即
$$c>r$$
故
$$BP=1$$
画表如下：
Translation p 1 p 2 p 3 p 4 BP 人工译文： Today is a nice day 机器译文： It is a nice day today 5 6 3 5 2 4 1 3 1 ‾ \overline{

$$\begin{array}{lllllll} &\text{Translation}&p_1&p_2&p_3&p_4&\text{BP}\\ \hline\text{人工译文：}&\text{Today is a nice day}&&&&&\\ \text{机器译文：}&\text{It is a nice day today}&\frac56&\frac35&\frac24&\frac13&1 \end{array}$$ } 人工译文：机器译文：​TranslationToday is a nice dayIt is a nice day today​p1​65​​p2​53​​p3​42​​p4​31​​BP1​​​
因为 $N=4$ ,故 $w_n=\frac{1}{4}$

所以
BLEU-4 = B P ∗ exp ⁡ ( ∑ n = 1 N w n l o g P n ) = 1 × exp ⁡ ( 1 4 × ( log ⁡ ( p 1 ) + log ⁡ ( p 2 ) + log ⁡ ( p 3 ) + l o g ( p 4 ) ) ) = exp ⁡ ( 1 4 × log ⁡ ( p 1 p 2 p 3 p 4 ) ) = exp ⁡ ( 1 4 × l o g ( 5 6 × 3 5 × 2 4 × 1 3 ) ) = exp ⁡ ( 1 4 × l o g ( 1 12 ) ) ≈ 0.537

$$\begin{aligned} \text{BLEU-4}&=\mathrm{BP}*\exp(\sum_{n=1}^Nw_n\mathrm{log}P_n) \\ &= 1 \times \exp(\frac14 \times (\log(p_1) + \log(p_2) + \log(p_3) + log(p_4))) \\ &= \exp(\frac14 \times \log(p_1p_2p_3p_4)) \\ &= \exp(\frac14 \times log(\frac56 \times \frac35 \times \frac24 \times \frac13)) \\ &= \exp(\frac14 \times log(\frac{1}{12})) \\ &\approx 0.537 \end{aligned}$$ BLEU-4​=BP∗exp(n=1∑N​wn​logPn​)=1×exp(41​×(log(p1​)+log(p2​)+log(p3​)+log(p4​)))=exp(41​×log(p1​p2​p3​p4​))=exp(41​×log(65​×53​×42​×31​))=exp(41​×log(121​))≈0.537​

倘若大佬发现什么错误，敬请斧正，感谢感谢！