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MT System Combination Silja Hildebrand MT System Combination - - PowerPoint PPT Presentation

MT System Combination Silja Hildebrand MT System Combination System Combination in MT Methods of machine translation Rule based Statistical Hierarchical Syntax based Output is different Make use of the individual strengths of the


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Silja Hildebrand – MT System Combination

MT System Combination

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Silja Hildebrand – MT System Combination

System Combination in MT Methods of machine translation

Rule based Statistical Hierarchical Syntax based

Output is different Make use of the individual strengths of the different systems to improve translation quality Selecting the best output on a sentence-by-sentence basis Synthetic combination of the output from the original systems Fixing mistakes of one system by using another system afterwards

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Silja Hildebrand – MT System Combination

Several MT System Outputs

hoffman has fortunately drug come to realize in a timely manner for performing arts to open up the cause hoffmann was obsessed drug, in a timely manner to create a career hoffman was mesmerized by drug but woke up in a timely manner to create career hoffman previously enamored drug. luckily i realized create career hoffman were drug fortunately awakening in a timely manner to create career hoffman was obsessed timely wake up to create a career drug Reference Translation: hoffman was addicted to drugs, fortunately awaking in a timely manner to begin an acting career

Statistical Phrase Based Statistical Hierarchical Example Based Translation hypotheses are in order of the systems testset BLEU score

Chinese-English MT06

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Silja Hildebrand – MT System Combination

Parallel Combination

Source Language Text

MT System MT System MT System MT System MT System Combination

Translation

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Silja Hildebrand – MT System Combination

Selection of whole hypotheses

Hypothesis Selection from N-best Lists Minimum Bayes Risk Re-ranking Hypothesis Selection from Forests

Synthesis of new hypotheses

Confusion Network based Combination Joint Decoding with Flexible Ordering Parallel Combination Approaches

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Silja Hildebrand – MT System Combination

Parallel Combination: Hypothesis Selection

Source Language Text

MT System MT System MT System MT System MT System Combination

Translation

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Silja Hildebrand – MT System Combination

hoffman has fortunately drug come to realize in a timely manner for performing arts to open up the cause hoffmann was obsessed drug, in a timely manner to create a career hoffman was mesmerized by drug but woke up in a timely manner to create career hoffman previously enamored drug. luckily i realized create career hoffman were drug fortunately awakening in a timely manner to create career hoffman was obsessed timely wake up to create a career drug Reference Translation: hoffman was addicted to drugs, fortunately awaking in a timely manner to begin an acting career

Hypothesis Selection

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Silja Hildebrand – MT System Combination

hoffman has fortunately drug come to realize in a timely manner for performing arts to open up the cause hoffmann was obsessed drug, in a timely manner to create a career hoffman was mesmerized by drug but woke up in a timely manner to create career hoffman previously enamored drug. luckily i realized create career hoffman were drug fortunately awakening in a timely manner to create career hoffman was obsessed timely wake up to create a career drug Reference Translation: hoffman was addicted to drugs, fortunately awaking in a timely manner to begin an acting career hoffman was mesmerized by drug but woke up in a timely manner to create career

Hypothesis Selection

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Silja Hildebrand – MT System Combination

Language model System bias / trained system weights Boost hypothesis from each system according to its

  • verall (BLEU) score on development data

MT System confidence score System tells you what it thinks how well it translated the sentence Problematic:

Most systems use a score, that is not a real confidence measure

  • r probability

not comparable between sentences within a system not comparable between systems

Need to be normalized How to decide which hypothesis to pick?

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Silja Hildebrand – MT System Combination

Hypothesis Selection from N-best Lists

source sentence 1 source sentence 2 source sentence 3

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Silja Hildebrand – MT System Combination

Hypothesis Selection from N-best Lists

source sentence 1 source sentence 2 source sentence 3

Pick the best hypothesis from the different systems for each source sentence

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Silja Hildebrand – MT System Combination

Hypothesis Selection from N-best Lists

source sentence 1 source sentence 1 source sentence 2 source sentence 3 source sentence 2

Pick the best hypothesis from the different systems for each source sentence Use n-best list re-ranking approach Add n-best hypotheses from each system Re-rank joint n-best list

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Silja Hildebrand – MT System Combination

Hypothesis Selection from N-best Lists

source sentence 1 source sentence 1 source sentence 2 source sentence 3 source sentence 2

Pick the best hypothesis from the different systems for each source sentence Use n-best list re-ranking approach Add n-best hypotheses from each system Re-rank joint n-best list Find good features: add n-best list based features

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Silja Hildebrand – MT System Combination

Consistently calculated for the joint n-best list

Language model Statistical word lexicon System weights Rank in system’s n-best list N-gram overlap features N-best list n-gram probability N-best list sentence length features

Minimum error rate training to determine feature weights on a development test set

N-best list re-ranking: Features

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Silja Hildebrand – MT System Combination

n-best list for one source sentence

N-gram Agreement Features

e5

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Silja Hildebrand – MT System Combination

n-best list for one source sentence n = 1 word agreement: 90%

N-gram Agreement Features

e5

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Silja Hildebrand – MT System Combination

n-best list for one source sentence n = 1 word agreement: 90% n = 3 tri-gram agreement: 50%

N-gram Agreement Features

e5

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Silja Hildebrand – MT System Combination

n-best list for one source sentence n = 1 word agreement: 90% n = 3 tri-gram agreement: 50% n = 5 5-gram agreement: 30%

N-gram Agreement Features

e5

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Silja Hildebrand – MT System Combination

N-gram Agreement vs. N-gram Probability

n-best list for one source sentence

San Francisco

…500 hypotheses …

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Silja Hildebrand – MT System Combination

N-gram Agreement vs. N-gram Probability

n-best list for one source sentence

San Francisco

n = 2 bi-gram agreement: 0.6% …500 hypotheses …

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Silja Hildebrand – MT System Combination

N-gram Agreement vs. N-gram Probability

n-best list for one source sentence

San Francisco

n = 2 bi-gram agreement: 0.6% P( Francisco | San ) = 3 / 3 bi-gram probability: 100% …500 hypotheses …

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Silja Hildebrand – MT System Combination

N-gram Agreement vs. N-gram Probability

n-best list for one source sentence

San Francisco

n = 2 bi-gram agreement: 0.6% P( Francisco | San ) = 3 / 3 bi-gram probability: 100%

LM n-gram probability gives information on word order.

…500 hypotheses …

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Silja Hildebrand – MT System Combination

Source Language Text

MT System MT System MT System MT System MT System Combination

Translation

Synthesis of new translations Parallel Combination

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Silja Hildebrand – MT System Combination

Chinese-English MT06

Synthesis of new translations

hoffman has fortunately drug come to realize in a timely manner for performing arts to open up the cause hoffmann was obsessed drug, in a timely manner to create a career hoffman was mesmerized by drug but woke up in a timely manner to create career hoffman previously enamored drug. luckily i realized create career hoffman were drug fortunately awakening in a timely manner to create career hoffman was obsessed timely wake up to create a career drug hoffman was addicted to drugs, fortunately awaking in a timely manner to begin an acting career

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Silja Hildebrand – MT System Combination

Chinese-English MT06

Synthesis of new translations

hoffman has fortunately drug come to realize in a timely manner for performing arts to open up the cause hoffmann was obsessed drug, in a timely manner to create a career hoffman was mesmerized by drug but woke up in a timely manner to create career hoffman previously enamored drug. luckily i realized create career hoffman were drug fortunately awakening in a timely manner to create career hoffman was obsessed timely wake up to create a career drug hoffman was addicted to drugs, fortunately awaking in a timely manner to begin an acting career hoffman was mesmerized by drug

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Silja Hildebrand – MT System Combination

Chinese-English MT06

Synthesis of new translations

hoffman has fortunately drug come to realize in a timely manner for performing arts to open up the cause hoffmann was obsessed drug, in a timely manner to create a career hoffman was mesmerized by drug but woke up in a timely manner to create career hoffman previously enamored drug. luckily i realized create career hoffman were drug fortunately awakening in a timely manner to create career hoffman was obsessed timely wake up to create a career drug hoffman was addicted to drugs, fortunately awaking in a timely manner to begin an acting career in a timely manner to create career hoffman was mesmerized by drug fortunately awakening

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Silja Hildebrand – MT System Combination

Chinese-English MT06

Synthesis of new translations

hoffman has fortunately drug come to realize in a timely manner for performing arts to open up the cause hoffmann was obsessed drug, in a timely manner to create a career hoffman was mesmerized by drug but woke up in a timely manner to create career hoffman previously enamored drug. luckily i realized create career hoffman were drug fortunately awakening in a timely manner to create career hoffman was obsessed timely wake up to create a career drug hoffman was addicted to drugs, fortunately awaking in a timely manner to begin an acting career in a timely manner to create career hoffman was mesmerized by drug for performing arts fortunately awakening

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Silja Hildebrand – MT System Combination

hoffman has fortunately drug come to realize in a timely manner for performing arts to open up the cause hoffmann was obsessed drug, in a timely manner to create a career hoffman was mesmerized by drug but woke up in a timely manner to create career hoffman previously enamored drug. luckily i realized create career hoffman were drug fortunately awakening in a timely manner to create career hoffman was obsessed timely wake up to create a career drug

Confusion Network Based Combination Align Words, Build Confusion Network

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Silja Hildebrand – MT System Combination

hoffman has fortunately drug come to realize in a timely manner for performing arts to open up the cause hoffmann was obsessed drug, in a timely manner to create a career hoffman was mesmerized by drug but woke up in a timely manner to create career hoffman previously enamored drug. luckily i realized create career hoffman were drug fortunately awakening in a timely manner to create career hoffman was obsessed timely wake up to create a career drug

Confusion Network Based Combination Align Words, Build Confusion Network

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Silja Hildebrand – MT System Combination

hoffman has fortunately drug come to realize in a timely manner for performing arts to open up the cause hoffmann was obsessed drug, in a timely manner to create a career hoffman was mesmerized by drug but woke up in a timely manner to create career hoffman previously enamored drug. luckily i realized create career hoffman were drug fortunately awakening in a timely manner to create career hoffman was obsessed timely wake up to create a career drug

Confusion Network Based Combination Align Words, Build Confusion Network

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Silja Hildebrand – MT System Combination

hoffman has fortunately drug come to realize in a timely manner for performing arts to open up the cause hoffmann was obsessed drug, in a timely manner to create a career hoffman was mesmerized by drug but woke up in a timely manner to create career hoffman previously enamored drug. luckily i realized create career hoffman were drug fortunately awakening in a timely manner to create career hoffman was obsessed timely wake up to create a career drug

Confusion Network Based Combination Align Words, Build Confusion Network

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Silja Hildebrand – MT System Combination

hoffman has fortunately drug come to realize in a timely manner for performing arts to open up the cause hoffmann was obsessed drug, in a timely manner to create a career hoffman was mesmerized by drug but woke up in a timely manner to create career hoffman previously enamored drug. luckily i realized create career hoffman were drug fortunately awakening in a timely manner to create career hoffman was obsessed timely wake up to create a career drug

Confusion Network Based Combination Align Words, Build Confusion Network

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Silja Hildebrand – MT System Combination

hoffman has fortunately drug come to realize in a timely manner for performing arts to open up the cause hoffmann was obsessed drug, in a timely manner to create a career hoffman was mesmerized by drug but woke up in a timely manner to create career hoffman previously enamored drug. luckily i realized create career hoffman were drug fortunately awakening in a timely manner to create career hoffman was obsessed timely wake up to create a career drug

Confusion Network Based Combination Align Words, Build Confusion Network

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Silja Hildebrand – MT System Combination

hoffman has fortunately drug come to realize in a timely manner for performing arts to open up the cause hoffmann was obsessed drug, in a timely manner to create a career hoffman was mesmerized by drug but woke up in a timely manner to create career hoffman previously enamored drug. luckily i realized create career hoffman were drug fortunately awakening in a timely manner to create career hoffman was obsessed timely wake up to create a career drug

Confusion Network Based Combination Align Words, Build Confusion Network

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Silja Hildebrand – MT System Combination

hoffman has fortunately drug come to realize in a timely manner for performing arts to open up the cause hoffmann was obsessed drug, in a timely manner to create a career hoffman was mesmerized by drug but woke up in a timely manner to create career hoffman previously enamored drug. luckily i realized create career hoffman were drug fortunately awakening in a timely manner to create career hoffman was obsessed timely wake up to create a career drug

Confusion Network Based Combination

1 2

hoffman (5) hoffmann (1)

Align Words, Build Confusion Network

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Silja Hildebrand – MT System Combination

hoffman has fortunately drug come to realize in a timely manner for performing arts to open up the cause hoffmann was obsessed drug, in a timely manner to create a career hoffman was mesmerized by drug but woke up in a timely manner to create career hoffman previously enamored drug. luckily i realized create career hoffman were drug fortunately awakening in a timely manner to create career hoffman was obsessed timely wake up to create a career drug

Confusion Network Based Combination

1 2 3

hoffman (5) were (1) hoffmann (1) was (3) has (1)

ε (1)

Align Words, Build Confusion Network

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Silja Hildebrand – MT System Combination

hoffman has fortunately drug come to realize in a timely manner for performing arts to open up the cause hoffmann was obsessed drug, in a timely manner to create a career hoffman was mesmerized by drug but woke up in a timely manner to create career hoffman previously enamored drug. luckily i realized create career hoffman were drug fortunately awakening in a timely manner to create career hoffman was obsessed timely wake up to create a career drug

Confusion Network Based Combination

1 2 3 4

hoffman (5) were (1) hoffmann (1) was (3) has (1) ε (6) previously (1)

ε (1)

Align Words, Build Confusion Network

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Silja Hildebrand – MT System Combination

hoffman has fortunately drug come to realize in a timely manner for performing arts to open up the cause hoffmann was obsessed drug, in a timely manner to create a career hoffman was mesmerized by drug but woke up in a timely manner to create career hoffman previously enamored drug. luckily i realized create career hoffman were drug fortunately awakening in a timely manner to create career hoffman was obsessed timely wake up to create a career drug

Confusion Network Based Combination

1 2 3 5 4

hoffman (5) were (1) hoffmann (1) was (3) has (1) ε (6) previously (1)

  • bsessed (2)

ε (2) enamored (1) mesmerized (1)

ε (1)

Align Words, Build Confusion Network

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Silja Hildebrand – MT System Combination

hoffman has fortunately drug come to realize in a timely manner for performing arts to open up the cause hoffmann was obsessed drug, in a timely manner to create a career hoffman was mesmerized by drug but woke up in a timely manner to create career hoffman previously enamored drug. luckily i realized create career hoffman were drug fortunately awakening in a timely manner to create career hoffman was obsessed timely wake up to create a career drug

Confusion Network Based Combination

1 2 3 5 6 4

drug (6) hoffman (5) were (1) hoffmann (1) was (3) has (1) ε (6) previously (1)

  • bsessed (2)

ε (2) enamored (1) mesmerized (1)

ε (1)

Align Words, Build Confusion Network

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Silja Hildebrand – MT System Combination

hoffman has fortunately drug come to realize in a timely manner for performing arts to open up the cause hoffmann was obsessed drug, in a timely manner to create a career hoffman was mesmerized by drug but woke up in a timely manner to create career hoffman previously enamored drug. luckily i realized create career hoffman were drug fortunately awakening in a timely manner to create career hoffman was obsessed timely wake up to create a career drug

Confusion Network Based Combination

1 2 3 5 6 4

drug (6) hoffman (5) were (1) hoffmann (1) was (3) has (1) ε (6) previously (1) fortunately (2)

  • bsessed (2)

ε (2) enamored (1) mesmerized (1)

ε (1)

7

luckily (1) ε (6)

Align Words, Build Confusion Network

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Silja Hildebrand – MT System Combination

Choose one translation hypothesis as skeleton

Determines word order

Align each hypothesis to the skeleton using

TER (Translation Edit Rate) ITG (Inversion Transduction Grammar) based WER Statistical word alignment

Build confusion network with consensus votes Add LM score into network Train system weights, add into network Choose best path through the network (decode) Output consensus translation Confusion Network Decoding

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Silja Hildebrand – MT System Combination

Confusion Network Decoding: Example

I like eating chocolate ice-cream. I like to eat vanilla ice-cream. I like to eat ice-cream with chocolate. I like ice-cream.

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Silja Hildebrand – MT System Combination

Confusion Network Decoding: Example

I like eating chocolate ice-cream. I like to eat vanilla ice-cream. I like to eat ice-cream with chocolate. I like ice-cream. choose as skeleton

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Silja Hildebrand – MT System Combination

Confusion Network Decoding: Example

I like eating chocolate ice-cream. I like to eat vanilla ice-cream. I like to eat ice-cream with chocolate. I like ice-cream. . ice-cream ε ε ε ε like I . ice-cream with chocolate eat to like I . ice-cream ε vanilla eat to like I . ice-cream ε chocolate eating ε like I choose as skeleton

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Silja Hildebrand – MT System Combination

Confusion Network Decoding: Example

I like eating chocolate ice-cream. I like to eat vanilla ice-cream. I like to eat ice-cream with chocolate. I like ice-cream. . ice-cream ε ε ε ε like I . ice-cream with chocolate eat to like I . ice-cream ε vanilla eat to like I . ice-cream ε chocolate eating ε like I choose as skeleton skeleton determines word order

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Silja Hildebrand – MT System Combination

Confusion Network Decoding: Example

I like eating chocolate ice-cream. I like to eat vanilla ice-cream. I like to eat ice-cream with chocolate. I like ice-cream. . ice-cream ε ε ε ε like I . ice-cream with chocolate eat to like I . ice-cream ε vanilla eat to like I . ice-cream ε chocolate eating ε like I choose as skeleton skeleton determines word order

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Silja Hildebrand – MT System Combination

Confusion Network Decoding: Example

I like eating chocolate ice-cream. I like to eat vanilla ice-cream. I like to eat ice-cream with chocolate. I like ice-cream. . ice-cream ε ε ε ε like I . ice-cream with chocolate eat to like I . ice-cream ε vanilla eat to like I . ice-cream ε chocolate eating ε like I

1 2 3 5 6 8 4 7 9 I (4) like (4) to (2) ε (2) eat (2) eating (1) ε (1) ε (1) chocolate (2) vanilla (1) ε (3) with (1) ice-cream (4) . (4)

choose as skeleton skeleton determines word order

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Silja Hildebrand – MT System Combination

Confusion Network Decoding: Example

I like eating chocolate ice-cream. I like to eat vanilla ice-cream. I like to eat ice-cream with chocolate. I like ice-cream. . ice-cream ε ε ε ε like I . ice-cream with chocolate eat to like I . ice-cream ε vanilla eat to like I . ice-cream ε chocolate eating ε like I

1 2 3 5 6 8 4 7 9 I (4) like (4) to (2) ε (2) eat (2) eating (1) ε (1) ε (1) chocolate (2) vanilla (1) ε (3) with (1) ice-cream (4) . (4)

I like to eat chocolate ice-cream. choose as skeleton skeleton determines word order

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Silja Hildebrand – MT System Combination

Challenges Word alignment

TER alignment (Translation Edit Rate) ITG based alignment (Inversion Transduction Grammar) - invWER Use morphology, synonyms, POS tag Go to phrases

Difficult without source-target phrase alignment available

Double translations Dropped words Pairwise vs. incremental alignment

Next hypothesis is aligned to the existing network, not to the skeleton Order of adding hypothesis does make a difference, e.g. use increasing TER/decreasing BLEU of the system

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Silja Hildebrand – MT System Combination

I like big blue balloons I like blue kites I like balloons

Challenges: Double Translations

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Silja Hildebrand – MT System Combination

I like big blue balloons I like blue kites I like balloons balloons NULL NULL like I NULL blue kites like I balloons blue big like I

Challenges: Double Translations

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Silja Hildebrand – MT System Combination

I like big blue balloons I like blue kites I like balloons balloons NULL NULL like I NULL blue kites like I balloons blue big like I

Challenges: Double Translations

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Silja Hildebrand – MT System Combination

I like big blue balloons I like blue kites I like balloons balloons NULL NULL like I NULL blue kites like I balloons blue big like I

Challenges: Double Translations

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Silja Hildebrand – MT System Combination

I like big blue balloons I like blue kites I like balloons balloons NULL NULL like I NULL blue kites like I balloons blue big like I

Challenges: Double Translations

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Silja Hildebrand – MT System Combination

I like big blue balloons I like blue kites I like balloons balloons NULL NULL like I NULL blue kites like I balloons blue big like I

Challenges: Double Translations

1 2 3 5 6 4 I (3) like (3) big (1) kites (1) balloons (2) blue (2) ε (1) ε (1) ε (1)

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Silja Hildebrand – MT System Combination

I like big blue balloons I like blue kites I like balloons balloons NULL NULL like I NULL blue kites like I balloons blue big like I

I like kites blue balloons

Challenges: Double Translations

1 2 3 5 6 4 I (3) like (3) big (1) kites (1) balloons (2) blue (2) ε (1) ε (1) ε (1)

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Silja Hildebrand – MT System Combination

I like blue balloons I like my blue I like blue kites

Challenges: Dropped Words

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Silja Hildebrand – MT System Combination

I like blue balloons I like my blue I like blue kites NULL blue blue kites NULL like I NULL my like I balloons NULL like I

Challenges: Dropped Words

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Silja Hildebrand – MT System Combination

I like blue balloons I like my blue I like blue kites NULL blue blue kites NULL like I NULL my like I balloons NULL like I

Challenges: Dropped Words

1 2 3 5 6 4 I (3) like (3) my (1) ε (2) balloons (1) blue (3) ε (1) kites (1)

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Silja Hildebrand – MT System Combination

I like blue balloons I like my blue I like blue kites NULL blue blue kites NULL like I NULL my like I balloons NULL like I

I like blue

Challenges: Dropped Words

1 2 3 5 6 4 I (3) like (3) my (1) ε (2) balloons (1) blue (3) ε (1) kites (1)

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Silja Hildebrand – MT System Combination

I like balloons I like big blue balloons I like blue kites

pairwise incremental

Pairwise vs. Incremental Alignment: Example

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Silja Hildebrand – MT System Combination

I like balloons I like big blue balloons I like blue kites

pairwise incremental

Pairwise vs. Incremental Alignment: Example

balloons big blue like I balloons NULL like I

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Silja Hildebrand – MT System Combination

I like balloons I like big blue balloons I like blue kites

pairwise incremental

Pairwise vs. Incremental Alignment: Example

balloons big blue like I balloons NULL like I NULL balloons like I kites blue like I

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Silja Hildebrand – MT System Combination

I like balloons I like big blue balloons I like blue kites

pairwise incremental

Pairwise vs. Incremental Alignment: Example

kites blue NULL like I NULL balloons big blue like I NULL balloons NULL like I

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Silja Hildebrand – MT System Combination

I like balloons I like big blue balloons I like blue kites

pairwise incremental

1 2 3 5 6 4 I (3) like (3) big blue (1) ε (2) balloons (2) blue (1) ε (2) kites (1)

Pairwise vs. Incremental Alignment: Example

kites blue NULL like I NULL balloons big blue like I NULL balloons NULL like I

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Silja Hildebrand – MT System Combination

I like balloons I like big blue balloons I like blue kites

pairwise incremental

1 2 3 5 6 4 I (3) like (3) big blue (1) ε (2) balloons (2) blue (1) ε (2) kites (1)

I like balloons

Pairwise vs. Incremental Alignment: Example

kites blue NULL like I NULL balloons big blue like I NULL balloons NULL like I

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Silja Hildebrand – MT System Combination

I like balloons I like big blue balloons I like blue kites

kites blue NULL like I balloons blue big like I balloons NULL NULL like I

pairwise incremental

1 2 3 5 6 4 I (3) like (3) big blue (1) ε (2) balloons (2) blue (1) ε (2) kites (1)

I like balloons

Pairwise vs. Incremental Alignment: Example

kites blue NULL like I NULL balloons big blue like I NULL balloons NULL like I

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Silja Hildebrand – MT System Combination

I like balloons I like big blue balloons I like blue kites

kites blue NULL like I balloons blue big like I balloons NULL NULL like I

pairwise incremental

1 2 3 5 6 4 I (3) like (3) big blue (1) ε (2) balloons (2) blue (1) ε (2) kites (1)

I like balloons

Pairwise vs. Incremental Alignment: Example

kites blue NULL like I NULL balloons big blue like I NULL balloons NULL like I

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Silja Hildebrand – MT System Combination

I like balloons I like big blue balloons I like blue kites

kites blue NULL like I balloons blue big like I balloons NULL NULL like I

pairwise incremental

1 2 3 5 6 4 I (3) like (3) big blue (1) ε (2) balloons (2) blue (1) ε (2) kites (1) 1 2 3 5 6 4 I (3) like (3) big (1) ε (2) balloons (2) blue (2) ε (1) kites (1)

I like balloons

Pairwise vs. Incremental Alignment: Example

kites blue NULL like I NULL balloons big blue like I NULL balloons NULL like I

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Silja Hildebrand – MT System Combination

I like balloons I like big blue balloons I like blue kites

kites blue NULL like I balloons blue big like I balloons NULL NULL like I

pairwise incremental

1 2 3 5 6 4 I (3) like (3) big blue (1) ε (2) balloons (2) blue (1) ε (2) kites (1) 1 2 3 5 6 4 I (3) like (3) big (1) ε (2) balloons (2) blue (2) ε (1) kites (1)

I like balloons I like blue balloons

Pairwise vs. Incremental Alignment: Example

kites blue NULL like I NULL balloons big blue like I NULL balloons NULL like I