Statistical Machine Translation Alona Fyshe Based on slides from Colin Cherry and Dekang Lin.

transcript

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

P(A | B) =P(A,B)

Basic Statistics

• Use definition of conditional probability to derive the chain rule

P(A | B) =P(A,B)

P(A,B) = P(B)P(A | B) = P(A)P(B | A)

P(A1, A2,K An )

= P(An | An−1,K A1)P(An−1,K A1)

= P(A1)P(A2 | A1)P(A3 | A1, A2)K P(An | A1K , An−1)

Basic Statistics

• Bayes Rule

P(A,B) = P(A | B)P(B)

P(A,B) = P(B | A)P(A)

P(A | B)P(B) = P(B | A)P(A)

P(A | B) =P(B | A)P(A)

Basic Statistics

• Just rememberDefinition of cond. prob.

Bayes rule

Chain rule

P(A | B) =P(A,B)

P(A | B) =P(B | A)P(A)

P(A1)P(A2 | A1)P(A3 | A1,A2)K P(An | A1K , An−1)

• Translate.• I’ll use French (F) into English (E)

as the running example.

Oh, Canada

• I’m Canadian Mandatory French class in school until grade 6 I speak “Cereal Box French”

GratuitGagnerChocolatGlaçageSans grasSans cholestérolÉlevé dans la fibre

Oh, Canada

Machine Translation

• Translation is easy for (bilingual) people

• Process:Read the text in FrenchUnderstand itWrite it down in English

Machine Translation

• Translation is easy for (bilingual) people

• Process:Read the text in FrenchUnderstand itWrite it down in English

Machine Translation

Understanding languageWriting well formed text

• Hard tasks for computers 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:

P(E | F) =P(F | E)P(E)

P(F)∝ P(F | E)P(E)

Alternate Approach: Statistics

P(E | F) =P(F | E)P(E)

P(F)∝ P(F | E)P(E)

Given a French sentence F, we could do a

search for an E that maximizes P(E | F)

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

good English? P(E) good match to French? P(F|E)

Jon appeared in TV.

It back twelve saw.

In Jon appeared TV.

Jon is happy today.

Jon appeared on TV.

TV appeared on Jon.

Jon was not happy.

Table borrowed from Jason Eisner

On voit Jon à la télévision

good English? P(E) good match to French? P(F|E)

Jon appeared in TV.

It back twelve saw.

In Jon appeared TV.

Jon is happy today.

Jon appeared on TV.

TV appeared on Jon.

Jon was not happy.

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.

• 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

• 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

Google, is this 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 wayCollect statistics about the frequency of

words and phrasesN-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

P(e1)P(e2 | e1)P(e3 | e1,e2)P(e4 | e1,e2,e3)K P(ei | e1,e2,K ei−1)

Language Modeling

• Markov assumption The choice of word ei depends only on

the n words before ei

• Definition of conditional probability

P(ei | ei−4,ei−3,ei−2,ei−1) =P(ei−4,ei−3,ei−2,ei−1,ei)

P(ei−4 ,ei−3,ei−2,ei−1)

P(ei | e1,e2,K ei−4,ei−3,ei−2,ei−1) = P(ei | ei−4,ei−3,ei−2,ei−1)

P(e1)P(e2 | e1)P(e3 | e1,e2)P(e4 | e1,e2,e3)K P(ei | e1,e2,K ei−1)

Language Modeling

P( pie | I, love, to,eat) =P(I, love, to,eat, pie)

P(I, love, to,eat)

Language Modeling

• Approximate probability using counts

• Use the n-gram corpus!

P(ei−4,ei−3,ei−2,ei−1,ei)

P(ei−4 ,ei−3,ei−2,ei−1)

P(ei−4,ei−3,ei−2,ei−1,ei)

P(ei−4 ,ei−3,ei−2,ei−1)=

C(ei−4 ,ei−3,ei−2,ei−1,ei)

C(ei−4,ei−3,ei−2,ei−1)

Language Modeling

• Use the n-gram corpus!

Not surprisingly, given that you love to eat, loving to eat chocolate is more probable (0.177)

P( pie | I, love, to,eat) =P(I, love, to,eat, pie)

P(I, love, to,eat)

=C(I, love, to,eat, pie)

C(I, love, to,eat)

=2,760

409,000= 0.0067

Language Modeling

• But what if

• Then P(e) = 0• Happens even if the sentence is

grammatically correct “Al Gore’s pink Hummer was stolen.”

C(ei−4,ei−3,ei−2,ei−1,ei) = 0

Language Modeling

• SmoothingMany techniques

• Add one smoothingAdd one to every countNo 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)

P(E | F) =P(F | E)P(E)

P(F)∝ P(F | E)P(E)

Where will we get P(F|E)?

Cereal boxes in English

Same cerealBoxes,

in French

MachineLearning

P(F|E) model

Where will we get P(F|E)?

Books inEnglish

Same books,in French

MachineLearning

P(F|E) model

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

Want to update your system? Just add more text!

Translated Corpora

• The Canadian Parliamentary Debates 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):Assume you start with YDecompose 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

What if…?

The quick fox jumps over the lazy dog

Le renard rapide saut par - dessus le chien parasseux

New Information

• Call this new info a word alignment (A)

• With A, we can make a good storyThe quick fox jumps over the lazy dog

P(F,A|E) Story

null The quick fox jumps over the lazy dog

P(F, A | E) = ?

P(F,A|E) Story

f1 f2 f3 … f10

P(F, A | E) = ε

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

P(F,A|E) Story

f1 f2 f3 … f10

P(F, A | E) =ε

(8 +1)10

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

P(F,A|E) Story

P(F,A | E) =ε

pt (Le | The) •

pt (renard | fox) •

pt (parasseux | lazy)

⎢ ⎢ ⎢ ⎢

⎥ ⎥ ⎥ ⎥

P(F,A|E) Story

P(F,A | E) =ε

(l +1)mpt ( f j | ea j

Getting Pt(f|e)

• We need numbers for Pt(f|e)

• Example: Pt(le|the) Count lines in a large collection of

aligned text

Pt ( f | e) =# e linked to f

# e linked to anything€

Pt (le | the) =# (le, the)

# (le, the)+# (la, the)+# (les, the)

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

Where’s “heaven” in Vietnamese?

Example borrowed from Jason Eisner

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.

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.

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

Alignment Hypotheses

null I like milk

Je aime le lait

null I like milk

Je aime le lait

null I like milk

Je aime le lait

null I like milk

Je aime le lait

null I like milk

Je aime le lait

null I like milk

Je aime le lait

null I like milk

Je aime le lait

null I like milk

Je aime le lait

0.65 0.25 0.05

0.01 0.01 0.01

0.01 0.001

Weighted Alignments

• What we’ll do is:Consider every possible alignmentGive each alignment a weight -

indicating how good it is

Count weighted alignments as normal

P(A | E,F) =P(F,A | E)

P(F | E)

Good grief! We forgot about P(F|E)!

• No worries, a little more stats gets us what we need:

P(F | E) = P(F, A | E)A∈A

∴ P(A | E,F) =P(F,A | E)

P(F, A | E)A∈A

Big Example: Corpus

fast car

voiture rapide

rapide

Possible Alignments

fast car

voiture rapide

rapide

fast car

voiture rapide

1a 1b 2

Parameters

fast car

voiture rapide

rapide

fast car

voiture rapide

1a 1b 2

P(voiture|fast) P(rapide|fast) P(voiture|car) P(rapide|car)

1/2 1/2 1/2 1/2

Weight Calculations

fast car

voiture rapide

rapide

fast car

voiture rapide

1a 1b 2

1/2 1/2 1/2 1/2

P(A,F|E) P(A|F,E)

1a 1/2*1/2=1/4 1/4 / 2/4 = 1/2

1b 1/2*1/2=1/4 1/4 / 2/4 = 1/2

2 1/2 1/2 / 1/2 = 1

Count Lines

fast car

voiture rapide

rapide

fast car

voiture rapide

1a 1b 2

1/2 1/2 1

Count Lines

fast car

voiture rapide

rapide

fast car

voiture rapide

1a 1b 2

1/2 1/2 1

#(voiture,fast) #(rapide,fast) #(voiture,car) #(rapide,car)

1/2 1/2+1 = 3/2 1/2 1/2

Count Lines

fast car

voiture rapide

rapide

fast car

voiture rapide

1a 1b 2

1/2 1/2 1

1/2 1/2+1 = 3/2 1/2 1/2

Normalize

1/4 3/4 1/2 1/2

Parameters

fast car

voiture rapide

rapide

fast car

voiture rapide

1a 1b 2

1/4 3/4 1/2 1/2

Weight Calculations

fast car

voiture rapide

rapide

fast car

voiture rapide

1a 1b 2

1/4 3/4 1/2 1/2

P(A,F|E) P(A|F,E)

1a 1/4*1/2=1/8 1/8 / 4/8 = 1/4

1b 1/2*3/4=3/8 3/8 / 4/8 = 3/4

2 3/4 3/4 / 3/4 = 1

Count Lines

fast car

voiture rapide

rapide

fast car

voiture rapide

1a 1b 2

1/4 3/4 1

Count Lines

fast car

voiture rapide

rapide

fast car

voiture rapide

1a 1b 2

1/4 3/4 1

1/4 3/4+1 = 7/4 3/4 1/4

Count Lines

fast car

voiture rapide

rapide

fast car

voiture rapide

1a 1b 2

1/4 3/4 1

1/4 3/4+1 = 7/4 3/4 1/4

Normalize

1/8 7/8 3/4 1/4

After many iterations:

fast car

voiture rapide

rapide

fast car

voiture rapide

1a 1b 2

~0 ~1 1

0.001 0.999 0.999 0.001

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 EnglishAs 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.

Example from http://www.readwriteweb.com/archives/google_translation_systran.php

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

Google Translate

• http://translate.google.com/translate_t 25 language pairs

• In the news (digg.com) http://www.readwriteweb.

com/archives/google_translation_systran.php

• In competition http://www.nist

.gov/speech/tests/mt/doc/mt06eval_official_results.html

Questions?

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

P(F | E) =ε

(l +1)mK pt ( f j | ea j

∏am = 0

∑a1 = 0

There are possible alignments!

l +1( )m

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

Voiture (1) rapide (2)

pt ( f1 | e0)pt ( f2 | e0) +

pt ( f1 | e0)pt ( f2 | e1) +

pt ( f1 | e0)pt ( f2 | e2) +

pt ( f1 | e1)pt ( f2 | e0) +

pt ( f1 | e1)pt ( f2 | e1) +

pt ( f1 | e1)pt ( f2 | e2) +

pt ( f1 | e2)pt ( f2 | e0) +

pt ( f1 | e2)pt ( f2 | e1) +

pt ( f1 | e2)pt ( f2 | e2) +

Let’s move these over here…

pt ( f1 | e0) pt ( f2 | e0) + pt ( f2 | e1) + pt ( f2 | e2)[ ] +

pt ( f1 | e1) pt ( f2 | e0) + pt ( f2 | e1) + pt ( f2 | e2)[ ] +

pt ( f1 | e2) pt ( f2 | e0) + pt ( f2 | e1) + pt ( f2 | e2)[ ]

And now we can do this…

pt ( f1 | e0) + pt ( f1 | e1) + pt ( f1 | e2)[ ] •

pt ( f2 | e0) + pt ( f2 | e1) + pt ( f2 | e2)[ ]

So, it turns out:

K pt ( f j | ea j)

∏am = 0

∑ =a1 = 0

∑ pt ( f j | ei)i= 0

∑j=1

Requires only operations.

m(l +1)

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

Statistical Machine Translation Alona Fyshe Based on slides from Colin Cherry and Dekang Lin.

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