BLEU Bilingual Evaluation Understudy

Tags: #nlp #BLEU #evaluation

Equation

$$ \text{BLEU}_{w}(\hat{S},S)=BP(\hat{S};S) \times \exp{\sum^{\infty}_{n=1}w_{n} \ln p_{n}(\hat{S};S)}, p_{n}(\hat{S};S)=\frac{\sum^{M}_{i=1}\sum_{s \in G_{n}(\hat{y})} \min(C(s,\hat{y}),\max_{y \in S_{i}} C(s,y))}{\sum^{M}_{i=1}\sum_{s \in G_{n}(\hat{y})}C(s, \hat{y})}, p_{n}(\hat{y};y)=\frac{\sum_{s \in G_{n}(\hat{y})} \min(C(s,\hat{y}), C(s,y))}{\sum_{s \in G_{n}(\hat{y})}C(s, \hat{y})}, BP(\hat{S};S) = e^{-(r/c-1)^{+}}$$

Latex Code

                                             \text{BLEU}_{w}(\hat{S},S)=BP(\hat{S};S) \times \exp{\sum^{\infty}_{n=1}w_{n} \ln p_{n}(\hat{S};S)},

p_{n}(\hat{S};S)=\frac{\sum^{M}_{i=1}\sum_{s \in G_{n}(\hat{y})} \min(C(s,\hat{y}),\max_{y \in S_{i}} C(s,y))}{\sum^{M}_{i=1}\sum_{s \in G_{n}(\hat{y})}C(s, \hat{y})},

p_{n}(\hat{y};y)=\frac{\sum_{s \in G_{n}(\hat{y})} \min(C(s,\hat{y}), C(s,y))}{\sum_{s \in G_{n}(\hat{y})}C(s, \hat{y})}, 

BP(\hat{S};S) = e^{-(r/c-1)^{+}}

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Introduction

BLEU (Bilingual Evaluation Understudy)

Equation


$$\text{BLEU}_{w}(\hat{S},S)=BP(\hat{S};S) \times \exp{\sum^{\infty}_{n=1}w_{n} \ln p_{n}(\hat{S};S)}$$ $$p_{n}(\hat{S};S)=\frac{\sum^{M}_{i=1}\sum_{s \in G_{n}(\hat{y})} \min(C(s,\hat{y}),\max_{y \in S_{i}} C(s,y))}{\sum^{M}_{i=1}\sum_{s \in G_{n}(\hat{y})}C(s, \hat{y})}$$ $$p_{n}(\hat{y};y)=\frac{\sum_{s \in G_{n}(\hat{y})} \min(C(s,\hat{y}), C(s,y))}{\sum_{s \in G_{n}(\hat{y})}C(s, \hat{y})}$$ $$BP(\hat{S};S) = e^{-(r/c-1)^{+}}$$

Latex Code

            \text{BLEU}_{w}(\hat{S},S)=BP(\hat{S};S) \times \exp{\sum^{\infty}_{n=1}w_{n} \ln p_{n}(\hat{S};S)},

            p_{n}(\hat{S};S)=\frac{\sum^{M}_{i=1}\sum_{s \in G_{n}(\hat{y})} \min(C(s,\hat{y}),\max_{y \in S_{i}} C(s,y))}{\sum^{M}_{i=1}\sum_{s \in G_{n}(\hat{y})}C(s, \hat{y})},

            p_{n}(\hat{y};y)=\frac{\sum_{s \in G_{n}(\hat{y})} \min(C(s,\hat{y}), C(s,y))}{\sum_{s \in G_{n}(\hat{y})}C(s, \hat{y})}, 

            BP(\hat{S};S) = e^{-(r/c-1)^{+}}

Explanation

$$\hat{S}$$: denotes the candidate corpus, $$S$$ denotes the reference corpus; $$P_{n}(\hat{S};S)$$: Modified N-Gram Precision, which is the generalization of single sentence pair n-gram precision as $$p_{n}(\hat{y};y)$$ $$C(s, \hat{y})$$: C denotes the substring count, which is the number of n-substrings in $$\hat{y}$$ that appears in y. $$G_{n}(y)$$: $$G_{n}(y)$$ denotes the set of N-Gram in the sentence y; $$BP(S;S)$$: denotes the brevity penalty, which penalize the condition that candidate string which contains the n-grams as few times as possible.

Discussion

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  • Nicholas Baker
    I hope my efforts are enough to pass this exam.
    2023-06-16 00:00

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    Paul Martin reply to Nicholas Baker
    Best Wishes.
    2023-06-30 00:00:00.0

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  • Olivia Evans
    I'm ready to tackle this test head-on.
    2023-12-14 00:00

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    Lawrence Howard reply to Olivia Evans
    Best Wishes.
    2023-12-19 00:00:00.0

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  • Mildred Turner
    All I'm asking for is to pass this test!
    2024-02-27 00:00

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    Bonnie Simmons reply to Mildred Turner
    You can make it...
    2024-03-20 00:00:00.0

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