全景网站app,互联网运营推广,seo 网站 结构,电视直播网站开发文章目录 一、BLEU-N得分#xff08;Bilingual Evaluation Understudy#xff09;1. 定义2. 计算N1N2BLEU-N 得分 3. 程序 给定一个生成序列“The cat sat on the mat”和两个参考序列“The cat is on the mat”“The bird sat on the bush”分别计算BLEU-N和ROUGE-N得分(N1或… 文章目录 一、BLEU-N得分Bilingual Evaluation Understudy1. 定义2. 计算N1N2BLEU-N 得分 3. 程序 给定一个生成序列“The cat sat on the mat”和两个参考序列“The cat is on the mat”“The bird sat on the bush”分别计算BLEU-N和ROUGE-N得分(N1或N 2时). 生成序列 x the cat sat on the mat \mathbf{x}\text{the cat sat on the mat} xthe cat sat on the mat参考序列 s ( 1 ) the cat is on the mat \mathbf{s}^{(1)}\text{the cat is on the mat} s(1)the cat is on the mat s ( 2 ) the bird sat on the bush \mathbf{s}^{(2)}\text{the bird sat on the bush} s(2)the bird sat on the bush
一、BLEU-N得分Bilingual Evaluation Understudy 1. 定义 设 为模型生成的候选序列 s ( 1 ) , ⋯ , s ( K ) \mathbf{s^{(1)}}, ⋯ , \mathbf{s^{(K)}} s(1),⋯,s(K) 为一组参考序列 为从生成的候选序列中提取所有N元组合的集合。BLEU算法的精度Precision定义如下 P N ( x ) ∑ w ∈ W min ( c w ( x ) , max k 1 K c w ( s ( k ) ) ) ∑ w ∈ W c w ( x ) P_N(\mathbf{x}) \frac{\sum_{w \in \mathcal{W}} \min(c_w(\mathbf{x}), \max_{k1}^{K} c_w(\mathbf{s}^{(k)}))}{\sum_{w \in \mathcal{W}} c_w(\mathbf{x})} PN(x)∑w∈Wcw(x)∑w∈Wmin(cw(x),maxk1Kcw(s(k)))
其中 c w ( x ) c_w(\mathbf{x}) cw(x) 是N元组合 w w w 在生成序列 x \mathbf{x} x中出现的次数 c w ( s ( k ) ) c_w(\mathbf{s}^{(k)}) cw(s(k)) 是N元组合 w w w 在参考序列 s ( k ) \mathbf{s}^{(k)} s(k) 中出现的次数。 为了处理生成序列长度短于参考序列的情况引入长度惩罚因子 b ( x ) b(\mathbf{x}) b(x) b ( x ) { 1 if l x l s exp ( 1 − l s l x ) if l x ≤ l s b(\mathbf{x}) \begin{cases} 1 \text{if } l_x l_s \\ \exp\left(1 - \frac{l_s}{l_x}\right) \text{if } l_x \leq l_s \end{cases} b(x){1exp(1−lxls)if lxlsif lx≤ls
其中 l x l_x lx 是生成序列的长度 l s l_s ls 是参考序列的最短长度。 BLEU算法通过计算不同长度的N元组合的精度并进行几何加权平均得到最终的BLEU分数 BLEU-N ( x ) b ( x ) × exp ( ∑ N 1 N ′ α N log P N ( x ) ) \text{BLEU-N}(\mathbf{x}) b(\mathbf{x}) \times \exp\left( \sum_{N1}^{N} \alpha_N \log P_N(\mathbf{x})\right) BLEU-N(x)b(x)×exp N1∑N′αNlogPN(x)
其中 N ′ N N′ 为最长N元组合的长度 α N \alpha_N αN 是不同N元组合的权重一般设为 1 / N ′ 1/N 1/N′。
2. 计算
N1
生成序列 x the cat sat on the mat \mathbf{x}\text{the cat sat on the mat} xthe cat sat on the mat参考序列 s ( 1 ) the cat is on the mat \mathbf{s}^{(1)}\text{the cat is on the mat} s(1)the cat is on the mat s ( 2 ) the bird sat on the bush \mathbf{s}^{(2)}\text{the bird sat on the bush} s(2)the bird sat on the bush W the, cat, sat, on, mat \mathcal{W}\text{ {the, cat, sat, on, mat}} W the, cat, sat, on, mat w the w\text{the} wthe c w ( x ) 2 , c w ( s ( 1 ) ) 2 , c w ( s ( 2 ) ) 2 c_w(\mathbf{x})2, c_w(\mathbf{s^{(1)}})2,c_w(\mathbf{s^{(2)}})2 cw(x)2,cw(s(1))2,cw(s(2))2 max k 1 K c w ( s ( k ) ) ) 2 \max_{k1}^{K} c_w(\mathbf{s}^{(k)}))2 maxk1Kcw(s(k)))2 min ( c w ( x ) , max k 1 K c w ( s ( k ) ) ) 2 \min(c_w(\mathbf{x}), \max_{k1}^{K} c_w(\mathbf{s}^{(k)}))2 min(cw(x),maxk1Kcw(s(k)))2 w cat w\text{cat} wcat c w ( x ) 1 , c w ( s ( 1 ) ) 1 , c w ( s ( 2 ) ) 0 c_w(\mathbf{x})1, c_w(\mathbf{s^{(1)}})1,c_w(\mathbf{s^{(2)}})0 cw(x)1,cw(s(1))1,cw(s(2))0 max k 1 K c w ( s ( k ) ) ) 1 \max_{k1}^{K} c_w(\mathbf{s}^{(k)}))1 maxk1Kcw(s(k)))1 min ( c w ( x ) , max k 1 K c w ( s ( k ) ) ) 1 \min(c_w(\mathbf{x}), \max_{k1}^{K} c_w(\mathbf{s}^{(k)}))1 min(cw(x),maxk1Kcw(s(k)))1 w sat w\text{sat} wsat c w ( x ) 1 , c w ( s ( 1 ) ) 0 , c w ( s ( 2 ) ) 1 c_w(\mathbf{x})1, c_w(\mathbf{s^{(1)}})0, c_w(\mathbf{s^{(2)}})1 cw(x)1,cw(s(1))0,cw(s(2))1 max k 1 K c w ( s ( k ) ) ) 1 \max_{k1}^{K} c_w(\mathbf{s}^{(k)}))1 maxk1Kcw(s(k)))1 min ( c w ( x ) , max k 1 K c w ( s ( k ) ) ) 1 \min(c_w(\mathbf{x}), \max_{k1}^{K} c_w(\mathbf{s}^{(k)}))1 min(cw(x),maxk1Kcw(s(k)))1 w on w\text{on} won c w ( x ) 1 , c w ( s ( 1 ) ) 1 , c w ( s ( 2 ) ) 1 c_w(\mathbf{x})1, c_w(\mathbf{s^{(1)}})1,c_w(\mathbf{s^{(2)}})1 cw(x)1,cw(s(1))1,cw(s(2))1 max k 1 K c w ( s ( k ) ) ) 1 \max_{k1}^{K} c_w(\mathbf{s}^{(k)}))1 maxk1Kcw(s(k)))1 min ( c w ( x ) , max k 1 K c w ( s ( k ) ) ) 1 \min(c_w(\mathbf{x}), \max_{k1}^{K} c_w(\mathbf{s}^{(k)}))1 min(cw(x),maxk1Kcw(s(k)))1 w mat w\text{mat} wmat c w ( x ) 1 , c w ( s ( 1 ) ) 1 , c w ( s ( 2 ) ) 0 c_w(\mathbf{x})1, c_w(\mathbf{s^{(1)}})1,c_w(\mathbf{s^{(2)}})0 cw(x)1,cw(s(1))1,cw(s(2))0 max k 1 K c w ( s ( k ) ) ) 1 \max_{k1}^{K} c_w(\mathbf{s}^{(k)}))1 maxk1Kcw(s(k)))1 min ( c w ( x ) , max k 1 K c w ( s ( k ) ) ) 1 \min(c_w(\mathbf{x}), \max_{k1}^{K} c_w(\mathbf{s}^{(k)}))1 min(cw(x),maxk1Kcw(s(k)))1 ∑ w ∈ W min ( c w ( x ) , max k 1 K c w ( s ( k ) ) ) 2 1 1 1 1 1 6 \sum_{w \in \mathcal{W}} \min(c_w(\mathbf{x}), \max_{k1}^{K} c_w(\mathbf{s}^{(k)}))2111116 ∑w∈Wmin(cw(x),maxk1Kcw(s(k)))2111116 ∑ w ∈ W c w ( x ) 1 1 1 1 1 1 6 \sum_{w \in \mathcal{W}} c_w(\mathbf{x})1111116 ∑w∈Wcw(x)1111116 P 1 ( x ) ∑ w ∈ W min ( c w ( x ) , max k 1 K c w ( s ( k ) ) ) ∑ w ∈ W c w ( x ) 6 6 1 P_1(\mathbf{x}) \frac{\sum_{w \in \mathcal{W}} \min(c_w(\mathbf{x}), \max_{k1}^{K} c_w(\mathbf{s}^{(k)}))}{\sum_{w \in \mathcal{W}} c_w(\mathbf{x})} \frac{6}{6}1 P1(x)∑w∈Wcw(x)∑w∈Wmin(cw(x),maxk1Kcw(s(k)))661
N2
生成序列 x the cat sat on the mat \mathbf{x}\text{the cat sat on the mat} xthe cat sat on the mat参考序列 s ( 1 ) the cat is on the mat \mathbf{s}^{(1)}\text{the cat is on the mat} s(1)the cat is on the mat s ( 2 ) the bird sat on the bush \mathbf{s}^{(2)}\text{the bird sat on the bush} s(2)the bird sat on the bush W the cat, cat sat, sat on, on the, the mat \mathcal{W}\text{{the cat, cat sat, sat on, on the, the mat} } Wthe cat, cat sat, sat on, on the, the mat w w w c w ( x ) c_w(\mathbf{x}) cw(x) c w ( s ( 1 ) ) c_w(\mathbf{s^{(1)}}) cw(s(1)) c w ( s ( 2 ) ) c_w(\mathbf{s^{(2)}}) cw(s(2)) max k 1 K c w ( s ( k ) ) ) \max_{k1}^{K} c_w(\mathbf{s}^{(k)})) maxk1Kcw(s(k))) min ( c w ( x ) , max k 1 K c w ( s ( k ) ) ) \min(c_w(\mathbf{x}), \max_{k1}^{K} c_w(\mathbf{s}^{(k)})) min(cw(x),maxk1Kcw(s(k)))the cat11011cat sat10000sat on10111on the11111the mat11011 ∑ w ∈ W min ( c w ( x ) , max k 1 K c w ( s ( k ) ) ) 1 0 1 1 1 4 \sum_{w \in \mathcal{W}} \min(c_w(\mathbf{x}), \max_{k1}^{K} c_w(\mathbf{s}^{(k)}))101114 ∑w∈Wmin(cw(x),maxk1Kcw(s(k)))101114 ∑ w ∈ W c w ( x ) 1 1 1 1 1 5 \sum_{w \in \mathcal{W}} c_w(\mathbf{x})111115 ∑w∈Wcw(x)111115 P 2 ( x ) ∑ w ∈ W min ( c w ( x ) , max k 1 K c w ( s ( k ) ) ) ∑ w ∈ W c w ( x ) 4 5 P_2(\mathbf{x}) \frac{\sum_{w \in \mathcal{W}} \min(c_w(\mathbf{x}), \max_{k1}^{K} c_w(\mathbf{s}^{(k)}))}{\sum_{w \in \mathcal{W}} c_w(\mathbf{x})} \frac{4}{5} P2(x)∑w∈Wcw(x)∑w∈Wmin(cw(x),maxk1Kcw(s(k)))54
BLEU-N 得分 为了处理生成序列长度短于参考序列的情况引入长度惩罚因子 b ( x ) b(\mathbf{x}) b(x) b ( x ) { 1 if l x l s exp ( 1 − l s l x ) if l x ≤ l s b(\mathbf{x}) \begin{cases} 1 \text{if } l_x l_s \\ \exp\left(1 - \frac{l_s}{l_x}\right) \text{if } l_x \leq l_s \end{cases} b(x){1exp(1−lxls)if lxlsif lx≤ls其中 l x l_x lx 是生成序列的长度 l s l_s ls 是参考序列的最短长度。 这里 l x l s ( 1 ) l s ( 2 ) 6 l_xl_{s^{(1)}}l_{s^{(2)}}6 lxls(1)ls(2)6因此 b ( x ) e ( 1 − l s l x ) e 0 1 b(\mathbf{x}) e^{\left( 1 - \frac{l_s}{l_x} \right)}e^01 b(x)e(1−lxls)e01 BLEU算法通过计算不同长度的N元组合的精度并进行几何加权平均得到最终的BLEU分数 BLEU-N ( x ) b ( x ) × exp ( 1 N ′ ∑ N 1 N ′ α N log P N ( x ) ) \text{BLEU-N}(\mathbf{x}) b(\mathbf{x}) \times \exp\left(\frac{1}{N} \sum_{N1}^{N} \alpha_N \log P_N(\mathbf{x})\right) BLEU-N(x)b(x)×exp N′1N1∑N′αNlogPN(x) 其中 N ′ N N′ 为最长N元组合的长度 α N \alpha_N αN 是不同N元组合的权重一般设为 1 / N ′ 1/N 1/N′。 BLEU-N ( x ) 1 × exp ( ∑ N 1 2 1 2 log P N ( x ) ) exp ( 1 2 log P 1 ( x ) 1 2 log P 2 ( x ) ) exp ( 1 2 log 1 1 2 log 4 5 ) exp ( 0 log 4 5 ) 4 5 \text{BLEU-N}(\mathbf{x}) 1 \times\exp\left( \sum_{N1}^{2} \frac{1}{2} \log P_N(\mathbf{x})\right)\\ \exp\left(\frac{1}{2}\log P_1(\mathbf{x})\frac{1}{2}\log P_2(\mathbf{x)}\right)\\ \exp\left(\frac{1}{2}\log 1\frac{1}{2}\log \frac{4}{5}\right)\\ \exp\left(0\log \sqrt\frac{4}{5}\right)\\ \sqrt\frac{4}{5} BLEU-N(x)1×exp(N1∑221logPN(x))exp(21logP1(x)21logP2(x))exp(21log121log54)exp(0log54 )54
3. 程序
main_string the cat sat on the mat
string1 the cat is on the mat
string2 the bird sat on the bush# 计算单词
unique_words set(main_string.split())
total_occurrences, matching_occurrences 0, 0for word in unique_words:count_main_string main_string.count(word)total_occurrences count_main_stringmatching_occurrences min(count_main_string, max(string1.count(word), string2.count(word)))similarity_word matching_occurrences / total_occurrences
print(fN1: {similarity_word})# 计算双词
word_tokens main_string.split()
bigrams set([f{word_tokens[i]} {word_tokens[i 1]} for i in range(len(word_tokens) - 1)])
total_occurrences, matching_occurrences 0, 0for bigram in bigrams:count_main_string main_string.count(bigram)total_occurrences count_main_stringmatching_occurrences min(count_main_string, max(string1.count(bigram), string2.count(bigram)))similarity_bigram matching_occurrences / total_occurrences
print(fN2: {similarity_bigram})
输出
N1: 1.0
N2: 0.8
