Statistical Machine Translation Alona Fyshe Based on slides

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

Basic statistics • 0 <= P(x) <=1 • P(A) w Probability that A happens • P(A, B) w Probabiliy that A and B happen • P(A|B) w 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 • Bayes Rule

Basic Statistics • Just remember w Definition of cond. prob. w Bayes rule w Chain rule

Goal • Translate. • I’ll use French (F) into English (E) as the running example.

Oh, Canada • I’m Canadian w Mandatory French class in school until grade 6 w I speak “Cereal Box French” Gratuit Gagner Chocolat Glaçage Sans gras Sans cholestérol Élevé dans la fibre

Oh, Canada

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

Machine Translation Understanding language Writing well formed text • Hard tasks for computers w 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) w I give you a French sentence w You give me back English • How are we going to model this? w We could use Bayes rule:

Alternate Approach: Statistics

Why Bayes rule at all? • Why not model P(E|F) directly? • P(F|E)P(E) decomposition allows us to be sloppy w P(E) worries about good English w P(F|E) worries about French that matches English w The two can be trained independently

Crime Scene Analogy • F is a crime scene. E is a person who may have committed the crime w P(E|F) - look at the scene - who did it? w P(E) - who had a motive? (Profiler) w 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 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? w Jon appeared in TV. w It back twelve saw. w In Jon appeared TV. w TV appeared on Jon. w Je ne parle pas l'anglais.

I speak English good. • Je ne parle pas l'anglais. w These aren’t English words. • It back twelve saw. w These are English words, but it’s jibberish. • Jon appeared in TV. w “appeared in TV” isn’t proper English

I speak English good. • Let’s say we have a huge collection of documents written in English w Like, say, the Internet. • It would be a pretty comprehensive list of English words w Save for “named entities” People, places, things w 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. w “Jon appeared” 1, 800, 000 Google results w “appeared in TV” 45, 000 Google results w “appeared on TV” 210, 000 Google results • It back twelve saw. w “twelve saw” 1, 100 Google results w “It back twelve” 586 Google results w “back twelve saw” 0 Google results • Imperfect counting… why?

Google, is this good English? • Language is often modeled this way w Collect statistics about the frequency of words and phrases w N-gram statistics § 1 -gram = unigram § 2 -gram = bigram § 3 -gram = trigram § 4 -gram = four-gram § 5 -gram = five-gram

Google, is this good English? • Seriously, you want to query google for every phrase in the translation? • Google created and released a 5 -gram data set. w Now you can query Google locally § (kind of)

Language Modeling • What’s P(e)? w P(English sentence) w P(e 1, e 2, e 3 … ei) w Using the chain rule

Language Modeling • Markov assumption w The choice of word ei depends only on the n words before ei • Definition of conditional probability

Language Modeling

Language Modeling • Approximate probability using counts • Use the n-gram corpus!

Language Modeling • Use the n-gram corpus! w 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 w “Al Gore’s pink Hummer was stolen. ”

Language Modeling • Smoothing w Many techniques • Add one smoothing w Add one to every count w No more zeros, no problems • Backoff w If P(e 1, e 2, e 3, e 4, e 5) = 0 use something related to P(e 1, e 2, e 3, e 4)

Language Modeling • Wait… Is this how people “generate” English sentences? w Do you choose your fifth word based on B • Admittedly, this is an approximation to process which is both w intangible and w hard for humans themselves to explain • If you disagree, and care to defend yourself, consider a Ph. D in NLP

Back to Translation • Anyway, where we? w Oh right… w 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 Want to update your system? Just add more text!

Translated Corpora • The Canadian Parliamentary Debates w Available in both French and English • UN documents w 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: w What makes a useful P(F|E) w How to obtain the statistics needed for P(F|E) from parallel texts

Strategy: Generative Story • When modeling P(X|Y): w Assume you start with Y w Decompose the creation of X from Y into some number of operations w Track statistics of individual operations w 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 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 f 1 f 2 f 3 … f 10 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 f 1 f 2 f 3 … There are (l+1)m = (8+1)10 possible alignments f 10

P(F, A|E) Story null The quick fox jumps over the lazy dog Le renard rapide saut par - dessus le chien parasseux

Getting Pt(f|e) • We need numbers for Pt(f|e) • Example: Pt(le|the) w Count lines in a large collection of aligned text 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 Le renard rapide saut par - dessus le chien parasseux

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 w We’ll get alignments out of unaligned text by treating the alignment as a hidden variable w We infer an A that maxes the prob. of our corpus w 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

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

Alignment Hypotheses 0. 65 null I like milk 0. 25 null I like milk 0. 05 null I like milk Je aime le lait 0. 01 null I like milk Je aime le lait 0. 01 null I like milk 0. 001 null I like milk Je aime le lait

Weighted Alignments • What we’ll do is: w Consider every possible alignment w Give each alignment a weight - indicating how good it is w 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 1 a fast car voiture rapide 1 b fast car voiture rapide 2 fast rapide

Parameters 1 a 1 b fast car voiture rapide P(voiture|fast) 1/2 fast car voiture rapide P(rapide|fast) 1/2 P(voiture|car) 1/2 2 fast rapide P(rapide|car) 1/2

Count Lines 1 a fast car 1 b fast car 1/2 voiture rapide 2 fast 1 rapide

Count Lines 1 a fast car 1 b fast car 1/2 voiture rapide #(voiture, fast) 1/2 #(rapide, fast) 1/2+1 = 3/2 #(voiture, car) 1/2 2 fast 1 rapide #(rapide, car) 1/2

Count Lines 1 a 1 b fast car 1/2 voiture rapide #(voiture, fast) 1/2 #(rapide, fast) 1/2+1 = 3/2 #(voiture, car) 1/2 2 fast 1 rapide #(rapide, car) 1/2 Normalize P(voiture|fast) 1/4 P(rapide|fast) 3/4 P(voiture|car) 1/2 P(rapide|car) 1/2

Parameters 1 a 1 b fast car voiture rapide P(voiture|fast) 1/4 fast car voiture rapide P(rapide|fast) 3/4 P(voiture|car) 1/2 2 fast rapide P(rapide|car) 1/2

Count Lines 1 a fast car 1 b fast car 1/4 voiture rapide 3/4 voiture rapide 2 fast 1 rapide

Count Lines 1 a fast car 1 b fast car 1/4 voiture rapide 3/4 voiture rapide #(voiture, fast) 1/4 #(rapide, fast) 3/4+1 = 7/4 #(voiture, car) 3/4 2 fast 1 rapide #(rapide, car) 1/4

Count Lines 1 a 1 b fast car 1/4 voiture rapide 3/4 voiture rapide #(voiture, fast) 1/4 #(rapide, fast) 3/4+1 = 7/4 #(voiture, car) 3/4 2 fast 1 rapide #(rapide, car) 1/4 Normalize P(voiture|fast) 1/8 P(rapide|fast) 7/8 P(voiture|car) 3/4 P(rapide|car) 1/4

After many iterations: 1 a 1 b fast car ~0 voiture rapide ~1 voiture rapide P(voiture|fast) 0. 001 P(rapide|fast) 0. 999 P(voiture|car) 0. 999 2 fast 1 rapide P(rapide|car) 0. 001

Seems too easy? • What if you have no 1 -word sentence? w Words in shorter sentences will get more weight fewer possible alignments w 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! w IE: Find argmax. AP(A|F, E) • Use it for translation: w Combine with our n-gram model for P(E) w 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? w Original French Dès qu'il fut dehors, Pierre se dirigea vers la rue de Paris, la principale rue du Havre, éclairée, animée, bruyante. w 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. w 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 w Bilingual Evaluation Understudy w A metric for comparing translations • Considers w n-grams in common with the target translation w 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 w 25 language pairs • In the news (digg. com) w http: //www. readwriteweb. com/archives/google _translation_systran. php • In competition w http: //www. nist. gov/speech/tests/mt/doc/mt 06 eval_official_results. html

Questions? ?

References (Inspiration, Sources of borrowed material) • Colin Cherry, MT for NLP, 2005 http: //www. cs. ualberta. ca/~colinc/ta/MT 650. 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/ws 99/projects/mt/mt-workbook. htm • Eisner, J. , JHU NLP Course notes: Machine Translation, 2001, http: //www. cs. jhu. edu/~jason/465/PDFSlides/lect 32 -translation. pdf • Olga Kubassova, Probability for NLP, http: //www. comp. leeds. ac. uk/olga/Probability. Tutorial. 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