Statistical Machine Translation

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# Statistical Machine Translation - PowerPoint PPT Presentation

Statistical Machine Translation Alona Fyshe Based on slides from Colin Cherry and Dekang Lin Basic statistics 0 <= P(x) <=1 P(A) Probability that A happens P(A,B) Probabiliy that A and B happen P(A|B) Probability that A happens given that we know B happened Basic statistics

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## Statistical Machine Translation

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### Statistical Machine Translation

Alona Fyshe

Based on slides from Colin Cherry and Dekang Lin

Basic statistics
• 0 <= P(x) <=1
• P(A)
• Probability that A happens
• P(A,B)
• Probabiliy that A and B happen
• P(A|B)
• Probability that A happens given that we know B happened
Basic statistics
• Conditional probability
Basic Statistics
• Use definition of conditional probability to derive the chain rule
Basic Statistics
• Just remember
• Definition of cond. prob.
• Bayes rule
• Chain rule
Goal
• Translate.
• I’ll use French (F) into English (E) as the running example.
• Mandatory French class in school until grade 6
• I speak “Cereal Box French”

Gratuit

Gagner

Chocolat

Glaçage

Sans gras

Sans cholestérol

Élevé dans la fibre

Machine Translation
• Translation is easy for (bilingual) people
• Process:
• Read the text in French
• Understand it
• Write it down in English
Machine Translation
• Translation is easy for (bilingual) people
• Process:
• Read the text in French
• Understand it
• Write it down in English
Machine Translation

Understanding language

Writing well formed text

• The human process is invisible, intangible
One approach: Babelfish
• A rule-based approach to machine translation
• A 30-year-old feat in Software Eng.
• Programming knowledge in by hand is difficult and expensive
Alternate Approach: Statistics
• We are trying to model P(E|F)
• I give you a French sentence
• You give me back English
• How are we going to model this?
• We could use Bayes rule:
Why Bayes rule at all?
• Why not model P(E|F) directly?
• P(F|E)P(E) decomposition allows us to be sloppy
• P(E) worries about good English
• P(F|E) worries about French that matches English
• The two can be trained independently
Crime Scene Analogy
• F is a crime scene. E is a person who may have committed the crime
• P(E|F) - look at the scene - who did it?
• P(E) - who had a motive? (Profiler)
• P(F|E) - could they have done it? (CSI - transportation, access to weapons, alabi)
• Some people might have great motives, but no means - you need both!
On voit Jon à la télévision

Table borrowed from Jason Eisner

On voit Jon à la télévision

Table borrowed from Jason Eisner

I speak English good.
• How are we going to model good English?
• How do we know these sentences are not good English?
• Jon appeared in TV.
• It back twelve saw.
• In Jon appeared TV.
• TV appeared on Jon.
• Je ne parle pas l'anglais.
I speak English good.
• Je ne parle pas l'anglais.
• These aren’t English words.
• It back twelve saw.
• These are English words, but it’s jibberish.
• Jon appeared in TV.
• “appeared in TV” isn’t proper English
I speak English good.
• Let’s say we have a huge collection of documents written in English
• Like, say, the Internet.
• It would be a pretty comprehensive list of English words
• Save for “named entities” People, places, things
• Might include some non-English words
• Speling mitsakes! lol!
• Could also tell if a phrase is good English
• Jon appeared in TV.
• “Jon appeared” 1,800,000 Google results
• “appeared in TV” 45,000 Google results
• “appeared on TV” 210,000 Google results
• It back twelve saw.
• “twelve saw” 1,100 Google results
• “It back twelve” 586 Google results
• “back twelve saw” 0 Google results
• Imperfect counting… why?
• Language is often modeled this way
• Collect statistics about the frequency of words and phrases
• N-gram statistics
• 1-gram = unigram
• 2-gram = bigram
• 3-gram = trigram
• 4-gram = four-gram
• 5-gram = five-gram
• Seriously, you want to query google for every phrase in the translation?
• Google created and released a 5-gram data set.
• Now you can query Google locally
• (kind of)
Language Modeling
• What’s P(e)?
• P(English sentence)
• P(e1, e2, e3 … ei)
• Using the chain rule
Language Modeling
• Markov assumption
• The choice of word ei depends only on the n words before ei
• Definition of conditional probability
Language Modeling
• Approximate probability using counts
• Use the n-gram corpus!
Language Modeling
• Use the n-gram corpus!
• Not surprisingly, given that you love to eat, loving to eat chocolate is more probable (0.177)
Language Modeling
• But what if
• Then P(e) = 0
• Happens even if the sentence is grammatically correct
• “Al Gore’s pink Hummer was stolen.”
Language Modeling
• Smoothing
• Many techniques
• Add one to every count
• No more zeros, no problems
• Backoff
• If P(e1, e2, e3, e4, e5) = 0 use something related to P(e1, e2, e3, e4)
Language Modeling
• Wait… Is this how people “generate” English sentences?
• Do you choose your fifth word based on B
• Admittedly, this is an approximation to process which is both
• intangible and
• hard for humans themselves to explain
• If you disagree, and care to defend yourself, consider a PhD in NLP
Back to Translation
• Anyway, where were we?
• Oh right…
• So, we’ve got P(e), let’s talk P(f|e)
Where will we get P(F|E)?

Machine

Learning

Magic

Cereal boxes

in English

Same cereal

Boxes,

in French

P(F|E) model

Where will we get P(F|E)?

Machine

Learning

Magic

Books in

English

Same books,

in French

P(F|E) model

We call collections stored in two languages parallel corpora or parallel texts

Translated Corpora
• Available in both French and English
• UN documents
• Available in Arabic, Chinese, English, French, Russian and Spanish
Problem:
• How are we going to generalize from examples of translations?
• I’ll spend the rest of this lecture telling you:
• What makes a useful P(F|E)
• How to obtain the statistics needed for P(F|E) from parallel texts
Strategy: Generative Story
• When modeling P(X|Y):
• Decompose the creation of X from Y into some number of operations
• Track statistics of individual operations
• For a new example X,Y: P(X|Y) can be calculated based on the probability of the operations needed to get X from Y

The quick fox jumps over the lazy dog

Le renard rapide saut par - dessus le chien parasseux

What if…?
New Information
• Call this new info a word alignment (A)
• With A, we can make a good story

The quick fox jumps over the lazy dog

Le renard rapide saut par - dessus le chien parasseux

P(F,A|E) Story

null The quick fox jumps over the lazy dog

P(F,A|E) Story

null The quick fox jumps over the lazy dog

f1

f2

f3

f10

Simplifying assumption: Choose the length of the French sentence f. All lengths have equal probability 

P(F,A|E) Story

null The quick fox jumps over the lazy dog

f1

f2

f3

f10

There are (l+1)m = (8+1)10 possible alignments

P(F,A|E) Story

null The quick fox jumps over the lazy dog

Le renard rapide saut par - dessus le chien parasseux

P(F,A|E) Story

null The quick fox jumps over the lazy dog

Le renard rapide saut par - dessus le chien parasseux

null The quick fox jumps over the lazy dog

null The quick fox jumps over the lazy dog

null The quick fox jumps over the lazy dog

null The quick fox jumps over the lazy dog

null The quick fox jumps over the lazy dog

null The quick fox jumps over the lazy dog

Le renard rapide saut par - dessus le chien parasseux

Le renard rapide saut par - dessus le chien parasseux

Le renard rapide saut par - dessus le chien parasseux

Le renard rapide saut par - dessus le chien parasseux

Le renard rapide saut par - dessus le chien parasseux

Le renard rapide saut par - dessus le chien parasseux

Getting Pt(f|e)
• We need numbers for Pt(f|e)
• Example: Pt(le|the)
• Count lines in a large collection of aligned text
Where do we get the lines?
• That sure looked like a lot of monkeys…
• Remember: some times the information hidden in the text just jumps out at you
• We’ll get alignments out of unaligned text by treating the alignment as a hidden variable
• We infer an A that maxes the prob. of our corpus
• Generalization of ideas in HMM training: called EM
Where’s “heaven” in Vietnamese?

Example borrowed from Jason Eisner

Where’s “heaven” in Vietnamese?

English: In the beginning God created the heavens and the earth.

Vietnamese: Ban dâu Dúc Chúa Tròi dung nên tròi dât.

English: God called the expanse heaven.

Vietnamese: Dúc Chúa Tròi dat tên khoang không la tròi.

English: … you are this day like the stars of heaven in number.

Vietnamese: … các nguoi dông nhu sao trên tròi.

Example borrowed from Jason Eisner

Where’s “heaven” in Vietnamese?

English: In the beginning God created the heavens and the earth.

Vietnamese: Ban dâu Dúc Chúa Tròi dung nên tròi dât.

English: God called the expanse heaven.

Vietnamese: Dúc Chúa Tròi dat tên khoang không la tròi.

English: … you are this day like the stars of heaven in number.

Vietnamese: … các nguoi dông nhu sao trên tròi.

Example borrowed from Jason Eisner

EM: Expectation Maximization
• Assume a probability distribution (weights) over hidden events
• Take counts of events based on this distribution
• Use counts to estimate new parameters
• Use parameters to re-weight examples.
• Rinse and repeat

0.65

0.25

0.05

null I like milk

null I like milk

null I like milk

Je aime le lait

Je aime le lait

Je aime le lait

0.01

0.01

0.01

null I like milk

null I like milk

null I like milk

Je aime le lait

Je aime le lait

Je aime le lait

0.01

0.001

null I like milk

null I like milk

Je aime le lait

Je aime le lait

Alignment Hypotheses
Weighted Alignments
• What we’ll do is:
• Consider every possible alignment
• Give each alignment a weight - indicating how good it is
• Count weighted alignments as normal
Good grief! We forgot about P(F|E)!
• No worries, a little more stats gets us what we need:
Big Example: Corpus

1

fast car

voiture rapide

2

fast

rapide

Possible Alignments

1a

1b

2

fast car

fast car

fast

voiture rapide

voiture rapide

rapide

Parameters

1a

1b

2

fast car

fast car

fast

voiture rapide

voiture rapide

rapide

Weight Calculations

1a

1b

2

fast car

fast car

fast

voiture rapide

voiture rapide

rapide

Count Lines

1a

1b

2

fast car

fast car

fast

1/2

1/2

1

voiture rapide

voiture rapide

rapide

Count Lines

1a

1b

2

fast car

fast car

fast

1/2

1/2

1

voiture rapide

voiture rapide

rapide

Count Lines

1a

1b

2

fast car

fast car

fast

1/2

1/2

1

voiture rapide

voiture rapide

rapide

Normalize

Parameters

1a

1b

2

fast car

fast car

fast

voiture rapide

voiture rapide

rapide

Weight Calculations

1a

1b

2

fast car

fast car

fast

voiture rapide

voiture rapide

rapide

Count Lines

1a

1b

2

fast car

fast car

fast

1/4

3/4

1

voiture rapide

voiture rapide

rapide

Count Lines

1a

1b

2

fast car

fast car

fast

1/4

3/4

1

voiture rapide

voiture rapide

rapide

Count Lines

1a

1b

2

fast car

fast car

fast

1/4

3/4

1

voiture rapide

voiture rapide

rapide

Normalize

After many iterations:

1a

1b

2

fast car

fast car

fast

~0

~1

1

voiture rapide

voiture rapide

rapide

Seems too easy?
• What if you have no 1-word sentence?
• Words in shorter sentences will get more weight - fewer possible alignments
• Weight is additive throughout the corpus: if a word e shows up frequently with some other word f, P(f|e) will go up
• Like our heaven example
The Final Product
• Now we have a model for P(F|E)
• Test it by aligning a corpus!
• IE: Find argmaxAP(A|F,E)
• Use it for translation:
• Combine with our n-gram model for P(E)
• Search space of English sentences for one that maximizes P(E)P(F|E) for a given F
Model could be a lot better:
• Word positions
• Multiple f’s generated by the same e
• Could take into account who generated your neighbors
• Could use syntax, parsing
• Could align phrases
Sure, but is it any better?
• We’ve got some good ideas for improving translation
• How can we quantify the change translation quality?
Sure, but is it any better?
• How to (automatically) measure translation?
• Original French

Dès qu'il fut dehors, Pierre se dirigea vers la rue de Paris, la principale rue du Havre, éclairée, animée, bruyante.

• Human translation to English

As soon as he got out, Pierre made his way to the Rue de Paris, the high-street of Havre, brightly lighted up, lively and noisy.

• Two machine tranlations back to French:
• Dès qu'il est sorti, Pierre a fait sa manière à la rue De Paris, la haut-rue de Le Havre, brillamment allumée, animée et bruyante.
• Dès qu'il en est sorti, Pierre s'est rendu à la Rue de Paris, de la grande rue du Havre, brillamment éclairés, animés et bruyants.

Bleu Score
• Bleu
• Bilingual Evaluation Understudy
• A metric for comparing translations
• Considers
• n-grams in common with the target translation
• Length of target translation
• Score of 1 is identical, 0 shares no words in common
• Even human translations don’t score 1
• 25 language pairs
• In the news (digg.com)
• In competition
• http://www.nist.gov/speech/tests/mt/doc/mt06eval_official_results.html
References(Inspiration, Sources of borrowed material)
• Colin Cherry, MT for NLP, 2005 http://www.cs.ualberta.ca/~colinc/ta/MT650.pdf
• Knight, K., Automating Knowledge Acquisition for Machine Translation , AI Magazine 18(4), 1997.
• Knight, K., A Statistical Machine Translation Tutorial Workbook, 1999, http://www.clsp.jhu.edu/ws99/projects/mt/mt-workbook.htm
• Eisner, J., JHU NLP Course notes: Machine Translation, 2001, http://www.cs.jhu.edu/~jason/465/PDFSlides/lect32-translation.pdf
• Olga Kubassova, Probability for NLP, http://www.comp.leeds.ac.uk/olga/ProbabilityTutorial.ppt
Enumerating all alignments

There are possible alignments!

Gah!

Null (0) Fast (1) car (2)

Voiture (1) rapide (2)

Let’s move these over here…

Null (0) Fast (1) car (2)

Voiture (1) rapide (2)

And now we can do this…

Null (0) Fast (1) car (2)

Voiture (1) rapide (2)

So, it turns out:

Requires only operations.

Can be used whenever your alignment choice for one word does not affect the probability of the rest of the alignment