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11-731 Machine Translation Syntax-Based Translation Models

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Title: 11-731 Machine Translation Syntax-Based Translation Models


1
11-731 Machine TranslationSyntax-Based
Translation Models Principles, Approaches,
Acquisition
  • Alon Lavie
  • 16 March 2011

2
Outline
  • Syntax-based Translation Models Rationale and
    Motivation
  • Resource Scenarios and Model Definitions
  • String-to-Tree, Tree-to-String and Tree-to-Tree
  • Hierarchical Phrase-based Models (Chiangs Hiero)
  • Syntax-Augmented Hierarchical Models (Venugopal
    and Zollmann)
  • String-to-Tree Models
  • Phrase-Structure-based Model (Galley et al.,
    2004, 2006)
  • Tree-to-Tree Models
  • Phrase-Structure-based Stat-XFER Model (Lavie et
    al., 2008)
  • DCU Tree-bank Alignment method (Zhachev, Tinsley
    et. al.)
  • Tree-to-String Models
  • Tree Transduction Models (Yamada and Knight,
    Gildea et al.)

3
Syntax-based Models Rationale
  • Phrase-based models model translation at very
    shallow levels
  • Translation equivalence modeled at the multi-word
    lexical level
  • Phrases capture some cross-language local
    reordering, but only for phrases that were seen
    in training No effective generalization
  • Non-local cross-language reordering is modeled
    only by permuting order of phrases during
    decoding
  • No explicit modeling of syntax, structural
    divergences or syntax-to-semantic mapping
    differences
  • Goal Improve translation quality using
    syntax-based models
  • Capture generalizations, reorderings and
    divergences at appropriate levels of abstraction
  • Models direct the search during decoding to more
    accurate translations
  • Still Statistical MT Acquire translation models
    automatically from (annotated) parallel-data and
    model them statistically!

4
Syntax-based Statistical MT
  • Building a syntax-based Statistical MT system
  • Similar in concept to simpler phrase-based SMT
    methods
  • Model Acquisition from bilingual
    sentence-parallel corpora
  • Decoders that given an input string can find the
    best translation according to the models
  • Our focus today will be on the models and their
    acquisition
  • Next week Chris Dyer will cover decoding for
    hierarchical and syntax-based MT

5
Syntax-based Resources vs. Models
  • Important Distinction
  • What structural information for the parallel-data
    is available during model acquisition and
    training?
  • What type of translation models are we acquiring
    from the annotated parallel data?
  • Structure available during Acquisition Main
    Distinctions
  • Syntactic/structural information for the parallel
    training data
  • Given by external components (parsers) or
    inferred from the data?
  • Syntax/Structure available for one language or
    for both?
  • Phrase-Structure or Dependency-Structure?
  • What do we extract from parallel-sentences?
  • Sub-sentential units of translation equivalence
    annotated with structure
  • Rules/structures that determine how these units
    combine into full transductions

6
Syntax-based Translation Models
  • String-to-Tree
  • Models explain how to transduce a string in the
    source language into a structural representation
    in the target language
  • During decoding
  • No separate parsing on source side
  • Decoding results in set of possible translations,
    each annotated with syntactic structure
  • The best-scoring stringstructure can be selected
    as the translation
  • Example

ne VB pas ? (VP (AUX (does) RB (not) x2
7
Syntax-based Translation Models
  • Tree-to-String
  • Models explain how to transduce a structural
    representation of the source language input into
    a string in the target language
  • During decoding
  • Parse the source string to derive its structure
  • Decoding explores various ways of decomposing the
    parse tree into a sequence of composable models,
    each generating a translation string on the
    target side
  • The best-scoring string can be selected as the
    translation
  • Examples

8
Syntax-based Translation Models
  • Tree-to-Tree
  • Models explain how to transduce a structural
    representation of the source language input into
    a structural representation in the target
    language
  • During decoding
  • Decoder synchronously explores alternative ways
    of parsing the source-language input string and
    transduce it into corresponding target-language
    structural output.
  • The best-scoring structurestring can be selected
    as the translation
  • Example

NPNP VP ? CD ? ?? ? one of the CD countries
that VP ( Alignments (X1Y7) (X3Y4) )
9
Structure Available During Acquisition
  • What information/annotations are available for
    the bilingual sentence-parallel training data?
  • (Symerticized) Viterbi Word Alignments (i.e. from
    GIZA)
  • (Non-syntactic) extracted phrases for each
    parallel sentence
  • Parse-trees/dependencies for source language
  • Parse-trees/dependencies for target language
  • Some major potential issues and problems
  • GIZA word alignments are not aware of syntax
    word-alignment errors can have bad consequences
    on the extracted syntactic models
  • Using external monolingual parsers is also
    problematic
  • Using single-best parse for each sentence
    introduces parsing errors
  • Parsers were designed for monolingual parsing,
    not translation
  • Parser design decisions for each language may be
    very different
  • Different notions of constituency and structure
  • Different sets of POS and constituent labels

10
Hierarchical Phrase-Based Models
  • Proposed by David Chiang in 2005
  • Natural hierarchical extension to phrase-based
    models
  • Representation rules in the form of synchronous
    CFGs
  • Formally syntactic, but with no direct
    association to linguistic syntax
  • Single non-terminal X
  • Acquisition Scenario Similar to standard
    phrase-based models
  • No independent syntactic parsing on either side
    of parallel data
  • Uses symetricized bi-directional viterbi word
    alignments
  • Extracts phrases and rules (hierarchical phrases)
    from each parallel sentence
  • Models the extracted phrases statistically using
    MLE scores

11
Hierarchical Phrase-Based Models
  • Extraction Process Overview
  • Start with standard phrase extraction from
    symetricized viterbi word-aligned sentence-pair
  • For each phrase-pair, find all embedded
    phrase-pairs, and create a hierarchical rule for
    each instance
  • Accumulate collection of all such rules from the
    entire corpus along with their counts
  • Model them statistically using maximum likelihood
    estimate (MLE) scores
  • P(targetsource) count(source,target)/count(sour
    ce)
  • P(sourcetarget) count(source,target)/count(targ
    et)
  • Filtering
  • Rules of length lt 5 (terminals and non-terminals)
  • At most two non-terminals X
  • Non-terminals must be separated by a terminal

12
Hierarchical Phrase-Based Models
  • Example
  • Chinese-to-English Rules

13
Syntax-Augmented Hierarchical Model
  • Proposed by CMUs Venugopal and Zollmann in 2006
  • Representation rules in the form of synchronous
    CFGs
  • Main Goal add linguistic syntax to the
    hierarchical rules that are extracted by the
    Hiero method
  • Hieros X labels are completely generic allow
    substituting any sub-phrase into an X-hole (if
    context matches)
  • Linguistic structure has labeled constituents
    the labels determine what sub-structures are
    allowed to combine together
  • Idea use labels that are derived from parse
    structures on one side of parallel data to label
    the X labels in the extracted rules
  • Labels from one language (i.e. English) are
    projected to the other language (i.e. Chinese)
  • Major Issues/Problems
  • How to label X-holes that are not complete
    constituents?
  • What to do about rule fragmentation rules
    that are the same other than the labels inside
    them?

14
Syntax-Augmented Hierarchical Model
  • Extraction Process Overview
  • Parse the strong side of the parallel data
    (i.e. English)
  • Run the Hiero extraction process on the
    parallel-sentence instance and find all
    phrase-pairs and all hierarchical rules for
    parallel-sentence
  • Labeling for each X-hole that corresponds to a
    parse constituent C, label X as C. For all other
    X-holes, assign combination labels
  • Accumulate collection of all such rules from the
    entire corpus along with their counts
  • Model the rules statistically Venagopal
    Zollman use six different rule score features
    instead of just two MLE scores.
  • Filtering similar to Hiero rule filtering
  • Advanced Modeling Preference Grammars
  • Avoid rule fragmentation instead of explicitly
    labeling the X-holes in the rules with different
    labels, keep them as X, with distributions over
    the possible labels that could fill the X.
    These are used as features during decoding

15
Syntax-Augmented Hierarchical Model
  • Example

16
Tree-to-Tree Stat-XFER
  • Developed by Lavie, Ambati and Parlikar in 2007
  • Goal Extract linguistically-supported syntactic
    phrase-pairs and synchronous transfer rules
    automatically from parsed parallel corpora
  • Representation Synchronous CFG rules with
    constituent-labels, POS-tags or lexical items on
    RHS of rules. Syntax-labeled phrases are
    fully-lexicalized S-CFG rules.
  • Acquisition Scenario
  • Parallel corpus is word-aligned using GIZA,
    symetricized.
  • Phrase-structure parses for source and/or target
    language for each parallel-sentence are obtained
    using monolingual parsers

17
Transfer Rule Formalism
SL the old man, TL ha-ish ha-zaqen NPNP
DET ADJ N -gt DET N DET ADJ ( (X1Y1) (X1Y3)
(X2Y4) (X3Y2) ((X1 AGR) 3-SING) ((X1 DEF
DEF) ((X3 AGR) 3-SING) ((X3 COUNT)
) ((Y1 DEF) DEF) ((Y3 DEF) DEF) ((Y2 AGR)
3-SING) ((Y2 GENDER) (Y4 GENDER)) )
  • Type information
  • Part-of-speech/constituent information
  • Alignments
  • x-side constraints
  • y-side constraints
  • xy-constraints,
  • e.g. ((Y1 AGR) (X1 AGR))

18
Translation Lexicon French-to-English Examples
DETDET le" -gt the" ( (X1Y1) ) Prep
Prep dans -gt in ( (X1Y1) ) NN
principes" -gt principles" ( (X1Y1) ) NN
respect" -gt accordance" ( (X1Y1) )
NPNP le respect" -gt accordance" ( ) PP
PP dans le respect" -gt in
accordance" ( ) PPPP des principes" -gt
with the principles" ( )
19
French-English Transfer Grammar Example
Rules(Automatically-acquired)
PP,24691 SL des principes TL with the
principles PPPP des N -gt with the
N ( (X1Y1) )
PP,312 SL dans le respect des
principes TL in accordance with the
principles PPPP Prep NP -gt Prep
NP ( (X1Y1) (X2Y2) )
20
Syntax-driven Acquisition Process
  • Overview of Extraction Process
  • Word-align the parallel corpus (GIZA)
  • Parse the sentences independently for both
    languages
  • Tree-to-tree Constituent Alignment
  • Run our Constituent Aligner over the parsed
    sentence pairs
  • Enhance alignments with additional Constituent
    Projections
  • Extract all aligned constituents from the
    parallel trees
  • Extract all derived synchronous transfer rules
    from the constituent-aligned parallel trees
  • Construct a data-base of all extracted parallel
    constituents and synchronous rules with their
    frequencies and model them statistically (assign
    them MLE maximum-likelihood probabilities)

21
PFA Constituent Node Aligner
  • Input a bilingual pair of parsed and
    word-aligned sentences
  • Goal find all sub-sentential constituent
    alignments between the two trees which are
    translation equivalents of each other
  • Equivalence Constraint a pair of constituents
    ltS,Tgt are considered translation equivalents if
  • All words in yield of ltSgt are aligned only to
    words in yield of ltTgt (and vice-versa)
  • If ltSgt has a sub-constituent ltS1gt that is aligned
    to ltT1gt, then ltT1gt must be a sub-constituent of
    ltTgt (and vice-versa)
  • Algorithm is a bottom-up process starting from
    word-level, marking nodes that satisfy the
    constraints

22
PFA Node Alignment Algorithm Example
  • Words dont have to align one-to-one
  • Constituent labels can be different in each
    language
  • Tree Structures can be highly divergent

23
PFA Node Alignment Algorithm Example
  • Aligner uses a clever arithmetic manipulation to
    enforce equivalence constraints
  • Resulting aligned nodes are highlighted in figure

24
PFA Node Alignment Algorithm Example
  • Extraction of Phrases
  • Get the yields of the aligned nodes and add them
    to a phrase table tagged with syntactic
    categories on both source and target sides
  • Example
  • NP NP
  • ?? Australia

25
PFA Node Alignment Algorithm Example
  • All Phrases from this tree pair
  • IP S ?? ? ? ?? ? ?? ? ?? ?? ?? ? Australia
    is one of the few countries that have diplomatic
    relations with North Korea .
  • VP VP ? ? ?? ? ?? ? ?? ?? ?? is one of the
    few countries that have diplomatic relations with
    North Korea
  • NP NP ? ?? ? ?? ? ?? ?? ?? one of the few
    countries that have diplomatic relations with
    North Korea
  • VP VP ? ?? ? ?? have diplomatic relations
    with North Korea
  • NP NP ?? diplomatic relations
  • NP NP ?? North Korea
  • NP NP ?? Australia

26
Further Improvements
  • The Tree-to-Tree (T2T) method is high precision
    but suffers from low recall
  • Alternative Tree-to-String (T2S) methods (i.e.
    Galley et al., 2006) use trees on ONE side and
    project the nodes based on word alignments
  • High recall, but lower precision
  • Recent work by Vamshi Ambati Ambati and Lavie,
    2008 combine both methods (T2T) by seeding
    with the T2T correspondences and then adding in
    additional consistent projected nodes from the
    T2S method
  • Can be viewed as restructuring target tree to be
    maximally isomorphic to source tree
  • Produces richer and more accurate syntactic
    phrase tables that improve translation quality
    (versus T2T and T2S)

27
Extracted Syntactic Phrases
English French
The principles Principes
With the principles des Principes
Accordance with the.. Respect des principes
Accordance Respect
In accordance with the Dans le respect des principes
Is all in accordance with.. Tout ceci dans le respect
This et
English French
The principles Principes
With the principles Principes
Accordance with the.. Respect des principes
Accordance Respect
In accordance with the Dans le respect des principes
Is all in accordance with.. Tout ceci dans le respect
This et
English French
The principles Principes
With the principles des Principes
Accordance Respect
TnT
TnS
TnT
28
Comparative Results French-to-English
  • MT Experimental Setup
  • Dev Set 600 sents, WMT 2006 data, 1 reference
  • Test Set 2000 sents, WMT 2007 data, 1 reference
  • NO transfer rules, Stat-XFER monotonic decoder
  • SALM Language Model (4M words)

29
Transfer Rule Acquisition
  • Input Constituent-aligned parallel trees
  • Idea Aligned nodes act as possible decomposition
    points of the parallel trees
  • The sub-trees of any aligned pair of nodes can be
    broken apart at any lower-level aligned nodes,
    creating an inventory of tree-fragment
    correspondences
  • Synchronous tree-frags can be converted into
    synchronous rules
  • Algorithm
  • Find all possible tree-frag decompositions from
    the node aligned trees
  • Flatten the tree-frags into synchronous CFG
    rules

30
Rule Extraction Algorithm
Sub-Treelet extraction Extract Sub-tree
segments including synchronous alignment
information in the target tree. All the sub-trees
and the super-tree are extracted.
31
Rule Extraction Algorithm
Flat Rule Creation Each of the treelets pairs
is flattened to create a Rule in the Stat-XFER
Formalism Four major parts to the rule 1.
Type of the rule Source and Target side type
information 2. Constituent sequence of the
synchronous flat rule 3. Alignment information
of the constituents 4. Constraints in the rule
(Currently not extracted)
32
Rule Extraction Algorithm
Flat Rule Creation Sample rule IPS NP
VP . -gt NP VP . ( Alignments (X1Y1) (X2Y
2) Constraints )
33
Rule Extraction Algorithm
  • Flat Rule Creation
  • Sample rule
  • NPNP VP ? CD ? ?? -gt one of the CD
    countries that VP
  • (
  • Alignments
  • (X1Y7)
  • (X3Y4)
  • )
  • Note
  • Any one-to-one aligned words are elevated to
    Part-Of-Speech in flat rule.

34
Rule Extraction Algorithm
All rules extracted VPVP VC NP -gt VBZ
NP ( (score 0.5) Alignments (X1Y1) (X2Y2
) ) VPVP VC NP -gt VBZ NP ( (score
0.5) Alignments (X1Y1) (X2Y2) ) NPNP
NR -gt NNP ( (score 0.5)
Alignments (X1Y1) (X2Y2) ) VPVP ? NP VE
NP -gt VBP NP with NP ( (score 0.5)
Alignments (X2Y4) (X3Y1) (X4Y2) )
All rules extracted NPNP VP ? CD ? ?? -gt
one of the CD countries that VP ( (score
0.5) Alignments (X1Y7) (X3Y4) ) IPS
NP VP -gt NP VP ( (score 0.5)
Alignments (X1Y1) (X2Y2) ) NPNP ?? -gt
North Korea ( Many to one alignment is a
phrase )
34
35
Some Chinese XFER Rules
  • SL(2,4) ? ? ??
  • TL(3,5) trade to taiwan
  • Score22
  • NP,1045537
  • NPNP PP NP -gt NP PP
  • ((score 0.916666666666667)
  • (X2Y1)
  • (X1Y2))
  • SL(2,7) ?? ?? ? ? ? ??
  • TL(1,7) commercials that directly mention the
    name viagra
  • Score5
  • NP,1017929
  • NPNP VP "?" NP -gt NP "that" VP
  • ((score 0.111111111111111)
  • (X3Y1)
  • (X1Y3))
  • SL(4,14) ? ? ? ? ? ? ? ?? ?? ? ??

36
DCU Tree-bank Alignment method
  • Proposed by Tinsley, Zhechev et al. in 2007
  • Main Idea
  • Focus on parallel treebank scenario parallel
    sentences annotated with constituent parse-trees
    for both sides (obtained by parsing)
  • Same notion and idea as Lavie et al. find
    sub-sentential constituent nodes across the two
    trees that are translation equivalents
  • Main difference does not depend on the viterbi
    word alignments
  • Instead, use the lexical probabilities (obtained
    by GIZA) to score all possible node-to-node
    alignments and incrementally grow the set of
    aligned-nodes.
  • Various types of rules can then be extracted
    (i.e. Stat-XFER rules, etc.)
  • Overcomes some of the problems due to incorrect
    and sparse word alignments
  • Produces surprisingly different collections of
    rules than the Stat-XFER method

37
String-to-Tree Galley et al. (GHKM)
  • Proposed by Galley et al. in 2004 and improved in
    2006
  • Idea model full syntactic structure on the
    target-side only in order to produce translations
    that are more grammatical
  • Representation synchronous hierarchical strings
    on the source side and their corresponding tree
    fragments on the target side
  • Example

ne VB pas ? (VP (AUX (does) RB (not) x2
38
String-to-Tree Galley et al. (GHKM)
  • Overview of Extraction Process
  • Obtain symetricized viterbi word-alignments for
    parallel sentences
  • Parse the strong side of the parallel data
    (i.e. English)
  • Find all constituent nodes in the source-language
    tree that have consistent word alignments to
    strings in target-language
  • Treat these as decomposition points extract
    tree-fragments on target-side along with
    corresponding gapped string on source-side
  • Labeling for each gap that corresponds to a
    parse constituent C, label the gap as C.
  • Accumulate collection of all such rules from the
    entire corpus along with their counts
  • Model the rules statistically initially used
    standard P(tgtsrc) MLE scores. Also
    experimented with other scores, similar to SAMT
  • Advanced Modeling Extraction of composed rules,
    not just minimal rules

39
Tree Transduction Models
  • Originally proposed by Yamada and Knight, 2001.
    Influenced later work by Gildea et al. on
    Tree-to-String models
  • Conceptually simpler than most other models
  • Learn finite-state transductions on
    source-language parse-trees in order to map them
    into well-ordered and well-formed target
    sentences, based on the viterbi word alignments
  • Representation simple local transformations on
    tree structure, given contextual structure in the
    tree
  • Transduce leaf words in the tree from source to
    target language
  • Delete a leaf-word or a sub-tree in a given
    context
  • Insert a leaf-word or a sub-tree in a given
    context
  • Transpose (invert order) of two sub-trees in a
    given context
  • Advanced model by Gildea duplicate and insert a
    sub-tree

40
Tree Transduction Models
  • Main Issues/Problems
  • Some complex reorderings and correspondences
    cannot be modeled using these simple tree
    transductions
  • Highly sensitive to errors in the source-language
    parse-tree and to word-alignment errors

41
Summary
  • Variety of structure and syntax based models
    string-to-tree, tree-to-string, tree-to-tree
  • Different models utilize different structural
    annotations on training resources and depend on
    different independent components (parsers, word
    alignments)
  • Different model acquisition processes from
    parallel data, but several recurring themes
  • Finding sub-sentential translation equivalents
    and relating them via hierarchical and/or
    syntax-based structure
  • Statistical modeling of the massive collections
    of rules acquired from the parallel data

42
Major Challenges
  • Sparse Coverage the acquired syntax-based models
    are often much sparser in coverage than
    non-syntactic phrases
  • Because they apply additional hard constraints
    beyond word-alignment as evidence of translation
    equivalence
  • Because the models fragment the data they are
    often observed far fewer times in training data ?
    more difficult to model them statistically
  • Consequently, pure syntactic models often lag
    behind phrase-based models in translation
    performance observed and learned again and
    again by different groups (including our own)
  • This motivates approaches that integrate
    syntax-based models with phrase-based models
  • Overcoming Pipeline Errors
  • Adding independent components (parser output,
    viterbi word alignments) introduces cumulative
    errors that are hard to overcome
  • Various approaches try to get around these
    problems
  • Also recent work on syntax-aware
    word-alignment, bi-lingual-aware parsing

43
Major Challenges
  • Optimizing for Structure Granularity and Labels
  • Syntactic structure in MT heavily based on Penn
    TreeBank structures and labels (POS and
    constituents) are these needed and optimal for
    MT, even for MT into English?
  • Approaches range from single abstract
    hierarchical X label, to fully lexicalized
    constituent labels. What is optimal? How do we
    answer this question?
  • Alternative Approaches (i.e. ITGs) aim to
    overcome this problem by unsupervised inference
    of the structure from the data
  • Direct Contrast and Comparison of alternative
    approaches is extremely difficult
  • Decoding with these syntactic models is highly
    complex and computationally intensive
  • Different groups/approaches develop their own
    decoders
  • Hard to compare anything beyond BLEU (or other
    metric) scores
  • Different groups continue to pursue different
    approaches this is at the forefront of current
    research in Statistical MT

44
References
  • (2008) Vamshi Ambati Alon Lavie Improving
    syntax driven translation models by
    re-structuring divergent and non-isomorphic parse
    tree structures. AMTA-2008. MT at work
    Proceedings of the Eighth Conference of the
    Association for Machine Translation in the
    Americas, Waikiki, Hawaii, 21-25 October 2008
    pp.235-244
  • (2005) David Chiang A hierarchical phrase-based
    model for statistical machine translation.
    ACL-2005 43rd Annual meeting of the Association
    for Computational Linguistics, University of
    Michigan, Ann Arbor, 25-30 June 2005 pp.
    263-270.
  • (2004) Michel Galley, Mark Hopkins, Kevin Knight
    Daniel Marcu Whats in a translation rule?
    HLT-NAACL 2004 Human Language Technology
    conference and North American Chapter of the
    Association for Computational Linguistics annual
    meeting, May 2-7, 2004, The Park Plaza Hotel,
    Boston, USA pp.273-280.
  • (2006) Michel Galley, Jonathan Graehl, Kevin
    Knight, Daniel Marcu, Steve DeNeefe, Wei Wang,
    Ignacio Thayer Scalable inference and training
    of context-rich syntatic translation models.
    Coling-ACL 2006 Proceedings of the 21st
    International Conference on Computational
    Linguistics and 44th Annual Meeting of the
    Association for Computational Linguistics,
    Sydney, 17-21 July 2006 pp.961-968.
  • (2008) Alon Lavie, Alok Parlikar, Vamshi
    Ambati Syntax-driven learning of sub-sentential
    translation equivalents and translation rules
    from parsed parallel corpora. Second ACL Workshop
    on Syntax and Structure in Statistical
    Translation (ACL-08 SSST-2), Proceedings, 20 June
    2008, Columbus, Ohio, USA pp.87-95.
  • (2007) John Tinsley, Ventsislav Zhechev, Mary
    Hearne, Andy Way Robust language
    pair-independent sub-tree alignment. MT Summit
    XI, 10-14 September 2007, Copenhagen, Denmark.
    Proceedings pp.467-474
  • (2007) Ashish Venugopal Andreas Zollmann
    Hierarchical and syntax structured MT. First
    Machine Translation Marathon, Edinburgh, April
    16-20, 2007 52pp.
  • (2001) Kenji Yamada Kevin Knight A
    syntax-based statistical translation model
    ACL-EACL-2001 39th Annual meeting of the
    Association for Computational Linguistics and
    10th Conference of the European Chapter of ACL,
    July 9th - 11th 2001, Toulouse, France
    pp.523-530.
  • (2006) Andreas Zollmann Ashish Venugopal
    Syntax augmented machine translation via chart
    parsing. HLT-NAACL 2006 Proceedings of the
    Workshop on Statistical Machine Translation, New
    York, NY, USA, June 2006 pp. 138-141
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