A recursive statistical translation model
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ProceedingsoftheACLWorkshoponBuildingandUsingParallelTexts,pages199–207,AnnArbor,June2005.cAssociationforComputationalLinguistics,2005ARecursiveStatisticalTranslationModel∗
JuanMiguelVilar
Dpto.deLenguajesySistemas
Inform´aticos
UniversitatJaumeI
Castell´on(Spain)
jvilar@lsi.uji.esEnriqueVidal
Dpto.deSistemasInform´aticos
yComputaci´on
UniversidadPolit´ecnicadeValencia
InstitutoTecnol´ogicodeInform´atica
Valencia(Spain)
evidal@iti.upv.es
Abstract
Anewmodelforstatisticaltranslationis
presented.Anovelfeatureofthismodel
isthatthealignmentsitproducesarehier-
archicallyarranged.Thegenerativepro-
cessbeginsbysplittingtheinputsen-
tenceintwoparts.Eachofthepartsis
translatedbyarecursiveapplicationof
themodelandtheresultingtranslation
arethenconcatenated.Ifthesentence
issmallenough,asimplermodel(inour
caseIBM’smodel1)isapplied.
Thetrainingofthemodelisexplained.Fi-
nally,themodelisevaluatedusingthecor-
porafromalargevocabularysharedtask.
1Introduction
SupposeyouweretofindanEnglishtranslationfor
aSpanishsentence.Onepossibleapproachistoas-
sumethateveryEnglishsentenceisacandidatebut
thatdifferentEnglishsentenceshavedifferentprob-
abilitiesofbeingthecorrecttranslation.Then,the
translationtaskcanbedividedintwoparts:define
anadequateprobabilitydistributionthatanswersto
thequestion“giventhisEnglishsentence,whichis
theprobabilitythatitisagoodtranslationofthat
Spanishsentence?”;andusethatdistributioninor-
dertofindthemostlikelytranslationofyourinputsentence.
∗WorkpartiallysupportedbyBancaixathroughtheproject“SistemasInductivos,Estad´ısticosyEstructurales,paralaTra-ducci´onAutom´atica(Siesta)”.Thisapproachisreferredtoasthestatisticalap-
proachtomachinetranslation.Theusualapproach
istodefineanstatisticalmodelandtrainitsparame-
tersfromatrainingcorpusconsistinginpairsofsen-
tencesthatareknowntobetranslationofeachother.
Differentmodelshavebeenpresentedinthelitera-
ture,seeforinstance(Brownetal.,1993;Ochand
Ney,2004;Vidaletal.,1993;Vogeletal.,1996).
Mostofthemrelyontheconceptofalignment:a
mappingfromwordsorgroupsofwordsinasen-
tenceintowordsorgroupsintheother(inthecase
of(Vidaletal.,1993)themappinggoesfromrules
inagrammarforalanguageintorulesofagrammar
fortheotherlanguage).Thisconceptofalignment
hasbeenalsousedfortaskslikeauthomaticvocab-
ularyderivationandcorpusalignment(Daganetal.,
1993).
Anewstatisticalmodelisproposedinthispa-
per,whichwasinitiallyintroducedin(VilarTorres,
1998).Thismodelisdesignedsothatthealign-
mentbetweentwosentencescanbeseeninanstruc-
turedmanner:eachsentenceisdividedintwoparts
andtheyareputincorrespondence;theneachof
thosepartsissimilarlydividedandrelatedtoits
translation.Thisway,thealignmentcanbeseenas
atreestructurewhichalignsprogressivelysmaller
segmentsofthesentences.Thisrecursiveprocedure
givesitsnametothemodel:MAR,whichcomes
from“ModelodeAlineamientoRecursivo”,which
isSpanishfor“RecursiveAlignmentModel”.
Therestofthepaperisstructuredasfollows:af-
teracommentonpreviousworks,weintroducethe
notationthatwewillusethroughoutthepaper,then
webrieflyexplainthemodel1fromIBM,nextwe
199introduceourmodel,thenweexplaintheprocess
ofparameterestimation,andhowtousethemodel
totranslatenewtestsentences.Finally,wepresent
someexperimentsandresults,togetherwithconclu-
sions.
2Previousworks
Theinitialformulationoftheproposedmodel,
includingthetrainingprocedures,waspresented
in(VilarTorres,1998),alongwithpreliminaryex-
perimentsinasmalltranslationtaskwhichprovided
encouragingresults.
Thismodelsharessomesimilaritieswiththe
stochasticinversiontransductiongrammars(SITG)
presentedbyWuin(Wu,1997).Themainpoint
incommonisthetypeofpossiblealignmentscon-
sideredinbothmodels.Someoftheproperties
ofthesealignmentsarestudiedin(ZensandNey,
2003).However,theparametrizationsofSITGsand
theMARarecompletelydifferent.Thegenerative
processofSITGsproducessimultaneouslythein-
putandoutputsentencesandtheparametersofthe
modelrefertotherulesofthenonterminals.This
providesasymmetrytobothinputandoutputsen-
tences.Incontrast,ourmodelclearlydistinguishes
theinputandoutputsentencesandtheparameters
arebasedonobservablepropertiesofthestrings
(theirlengthsandthewordscomposingthem).On
theotherhand,theMARideaofsplittingthesen-
tencesuntilasimplestructureisfound,alsoap-
pearsintheDivisiveClusteringapproachpresented
in(Dengetal.,2004).Again,themaindifference
liesintheprobabilisticmodelingofthealignments.
InDivisiveClusteringauniformdistributiononthe
alignmentsisassumedwhileMARusesaexplicit
parametrization.
3Somenotation
Intherestofthepaper,weusethefollowingnota-
tion.Sentencesaretakenasconcatenationsofsym-
bols(words)andrepresentedusingaletteranda
smallbar,likein¯x.Theindividualwordsarede-
signedbythenameofthesentenceandasubindex
indicatingtheposition,so¯x=x1x2...xn.The
lengthofasentenceisindicatedby|¯x|.Segments