Operazioni dell'Associazione per la Linguistica Computazionale, 1 (2013) 231–242. Redattore di azioni: Noah Smith.
Submitted 11/2012; Revised 2/2013; Pubblicato 5/2013. C
(cid:13)
2013 Associazione per la Linguistica Computazionale.
ModelingSemanticRelationsExpressedbyPrepositionsVivekSrikumarandDanRothUniversityofIllinois,Urbana-ChampaignUrbana,IL.61801.{vsrikum2,danr}@illinois.eduAbstractThispaperintroducestheproblemofpredict-ingsemanticrelationsexpressedbypreposi-tionsanddevelopsstatisticallearningmodelsforpredictingtherelations,theirargumentsandthesemantictypesofthearguments.Wedefineaninventoryof32relations,build-ingonthewordsensedisambiguationtaskforprepositionsandcollapsingrelatedsensesacrossprepositions.Givenaprepositioninasentence,ourcomputationaltasktojointlymodeltheprepositionrelationanditsargu-mentsalongwiththeirsemantictypes,asawaytosupporttherelationprediction.Thean-notateddata,Tuttavia,onlyprovideslabelsfortherelationlabel,andnottheargumentsandtypes.Weaddressthisbypresentingtwomod-elsforprepositionrelationlabeling.Ourgen-eralizationoflatentstructureSVMgivescloseto90%accuracyonrelationlabeling.Further,byjointlypredictingtherelation,arguments,andtheirtypesalongwithprepositionsense,weshowthatwecannotonlyimprovethere-lationaccuracy,butalsosignificantlyimprovesensepredictionaccuracy.1IntroductionThispaperaddressestheproblemofpredictingse-manticrelationsconveyedbyprepositionsintext.Prepositionsexpressmanysemanticrelationsbe-tweentheirgovernorandobject.Predictingthesecanhelpadvancingtextunderstandingtaskslikequestionansweringandtextualentailment.Considerthesentence:(1)ThebookofProf.Alexanderonprimaryschoolmethodsisavaluableteachingresource.Here,theprepositiononindicatesthatthebookandprimaryschoolmethodsareconnectedbytherelationTopicandofindicatestheCreator-CreationrelationbetweenProf.Alexanderandthebook.Predictingtheserelationscanhelpanswerquestionsaboutthesubjectofthebookandalsorec-ognizetheentailmentofsentenceslikeProf.Alexan-derhaswrittenaboutprimaryschoolmethods.Beinghighlypolysemous,thesameprepositioncanindicatedifferentkindsofrelations,dependingonitsgovernorandobject.Furthermore,severalprepositionscanindicatethesamesemanticrelation.Forexample,considerthesentence:(2)Poorcareledtoherdeathfrompneumonia.TheprepositionfrominthissentenceexpressestherelationCause(death,pneumonia).Inadiffer-entcontext,itcandenoteotherrelations,asinthephrasescopiedfromthefilm(Fonte)andrecog-nizedfromthestart(Temporal).Ontheotherhand,therelationCausecanbeexpressedbysev-eralprepositions;forexample,thefollowingphrasesexpressaCauserelation:diedofpneumoniaandtiredafterthesurgery.Wecharacterizesemanticrelationsexpressedbytransitiveprepositionsanddevelopaccuratemodelsforpredictingtherelations,identifyingtheirargu-mentsandrecognizingthesemantictypesofthear-guments.Buildingonthewordsensedisambigua-tiontaskforprepositions,wecollapsesemanticallyrelatedsensesacrossprepositionstoderiveourre-lationinventory.Theserelationsactaspredicatesinapredicate-argumentrepresentation,wheretheargumentsarethegovernorandtheobjectofthe
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preposition.Whileascertainingtheargumentsisalargelysyntacticdecision,wepointoutthatsyn-tacticparsersdonotalwaysmakethispredictioncorrectly.However,asillustratedintheexamplesabove,identifyingtherelationdependsonthegov-ernorandobjectofthepreposition.Givenasentenceandapreposition,ourgoalistomodelthepredicate(i.e.theprepositionrela-tion)anditsarguments(i.e.thegovernorandob-ject).Veryoften,therelationlabelisnotinfluencedbythesurfaceformoftheargumentsbutratherbytheirsemantictypes.Insentence(2)above,wewantthepredicatetobeCausewhentheobjectoftheprepositionisanyillness.Wethussuggesttomodeltheargumenttypesalongwiththepreposi-tionrelationsandarguments,usingdifferentnotionsoftypes.Thesethreerelatedaspectsoftherela-tionpredictiontaskarefurtherexplainedinSection3leadinguptotheproblemdefinition.Thoughwewishtopredictrelations,argumentsandtypes,thereisnocorpuswhichannotatesallthree.TheSemEval2007sharedtaskofwordsensedisambiguationforprepositionsprovidessensean-notationsforprepositions.Weusethisdatatogen-eratetrainingandtestcorporafortherelationla-bels.InSection4,wepresenttwomodelsfortheprepositionalrelationidentificationproblem.Thefirstmodelconsidersallpossibleargumentcandi-datesfromvarioussourcesalongwithallargumenttypestopredicttheprepositionrelationlabel.Thesecondmodeltreatstheargumentsandtypesasla-tentvariablesduringlearningusingageneralizationofthelatentstructuralSVMof(YuandJoachims,2009).WeshowinSection5thatthismodelnotonlypredictstheargumentsandtypes,butalsoim-provesrelationpredictionperformance.Theprimarycontributionsofthispaperare:1.Weintroduceanewinventoryofprepositionrelationsthatcoversthe34prepositionsthatformedthebasisoftheSemEval2007taskofprepositionsensedisambiguation.2.Wemodelprepositionrelations,argumentsandtheirtypesjointlyandproposealearningalgo-rithmthatlearnstopredictallthreeusingtrain-ingdatathatannotatesonlyrelationlabels.3.Weshowthatjointlypredictingrelationswithwordsensenotonlyimprovestherelationpre-dictor,butalsogivesasignificantimprovementinsenseprediction.2Prepositions&Predicate-ArgumentSemanticsSemanticrolelabeling(cf.(GildeaandJurafsky,2002;Palmeretal.,2010;Punyakanoketal.,2008)andothers)isthetaskofconvertingtextintoapredicate-argumentrepresentation.Givenatriggerwordorphraseinasentence,thistasksolvestworelatedpredictionproblems:(UN)identifyingtherela-tionlabel,E(B)identifyingandlabelingtheargu-mentsoftherelation.Thisproblemhasbeenstudiedinthecon-textofverbandnominaltriggersusingtheProp-Bank(Palmeretal.,2005)andNomBank(Meyersetal.,2004)annotationsoverthePennTreebank,andalsousingtheFrameNetlexicon(Fillmoreetal.,2003),whichallowsarbitrarywordstotriggersemanticframes.Thispaperfocusesonsemanticrelationsex-pressedbytransitiveprepositions1.Wecandefinethetwopredictiontasksforprepositionsasfollows:identifyingtherelationlabelforapreposition,andpredictingtheargumentsoftherelation.Preposi-tionscanmarkarguments(bothcoreandadjunct)forverbalandnominalpredicates.Inaddition,theycanalsotriggerrelationsthatarenotpartofotherpredicates.Forexample,insentence(3)below,theprepositionalphrasestartingwithtoisanargumentoftheverbvisit,buttheintriggersanindependentrelationindicatingthelocationoftheaquarium.(3)ThechildrenenjoyedthevisittotheaquariuminConeyIsland.FrameNetcoverssomeprepositionalrelations,butallowsonlytemporal,locativeanddirectionalsensesofprepositionstoevokeframes,accountingforonly3%ofthetargetsintheSemEval2007sharedtaskofFrameNetparsing.Infact,thestate-of-the-artFrameNetparserof(Dasetal.,2010)doesnotcon-sideranyframeinducingprepositions.(Baldwinetal.,2009)highlightstheimportanceofstudyingprepositionsforacompletelinguistic1Bytransitiveprepositionswerefertothestandardusageofprepositionsthattakeanobject.Inparticular,wedonotcon-siderprepositionalparticlesinouranalysis.
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analysisofsentencesandsurveysworkintheNLPliteraturethataddressesthesyntaxandsemanticsofprepositions.Onelineofwork(YeandBald-win,2006)addressedtheproblemofprepositionsemanticrolelabelingbyconsideringprepositionalphrasesthatactasargumentsofverbsaccordingtothePropBankannotation.Theybuiltasystemthatpredictsthelabelsoftheseprepositionalphrasesalone.However,bydefinition,thiscoveredonlyverb-attachedprepositions.(Zapirainetal.,2012)studiedtheimpactofautomaticallylearnedselec-tionalpreferencesforpredictingargumentsofverbsandshowedthatmodelingprepositionalphrasessep-aratelyimprovestheperformanceofargumentpre-diction.PrepositionsemanticshasalsobeenstudiedviathePrepositionProject(LitkowskiandHar-graves,2005)andtherelatedSemEval2007sharedtaskofwordsensedisambiguationofprepositions(LitkowskiandHargraves,2007).ThePreposi-tionProjectidentifiesprepositionsensesbasedontheirdefinitionsintheOxfordDictionaryofEnglish.Thereare332differentlabelstobepredictedwithawidevarianceinthenumberofsensesperpreposi-tionrangingfrom2(duringandas)to25(SU).Forexample,accordingtotheprepositionsenseinven-tory,theprepositionfrominsentence(2)abovewillbelabeledwiththesensefrom:12(9)toindicateacause.(Dahlmeieretal.,2009)addedsenseanno-tationtosevenprepositionsinfoursectionsofthePennTreebankwiththegoalofstudyingtheirinter-actionwithverbarguments.UsingtheSemEvaldata,(TratzandHovy,2009)E(Hovyetal.,2010)showedthattheargumentsofferanimportantcuetoidentifythesenseoftheprepositionand(Tratz,2011)showedfurtherim-provementsbyrefiningthesenseinventory.How-ever,thoughtheseworksusedadependencyparsertoidentifyarguments,inordertoovercomeparsingerrors,theyaugmenttheparser’spredictionsusingpart-of-speechbasedheuristics.Wearguethat,whiledisambiguatingthesenseofaprepositiondoesindeedrevealnuancesofitsmeaning,itleadstoaproliferationoflabelstobepredicted.Mostimportantly,senselabelsdonottransfertootherprepositionsthatexpressthesamemeaning.Forexample,bothfinishlunchbeforenoonandfinishlunchbynoonexpressaTemporalrelation.AccordingtothePrepositionProject,thesenselabelforthefirstprepositionisbefore:1(1),andthatforthesecondisby:17(4).Thisbothde-featsthepurposeofidentifyingtherelationstoaidnaturallanguageunderstandingandmakesthepre-dictiontaskharderthanitshouldbe:usingthestan-dardwordsenseclassificationapproach,weneedtotrainaseparateclassifierforeachwordbecausethelabelsaredefinedper-preposition.Inotherwords,wecannotsharefeaturesacrossthedifferentprepo-sitions.Thismotivatestheneedtocombinesuchsensesofprepositionsintothesameclasslabel.Inthisdirection,(O’HaraandWiebe,2009)de-scribesaninventoryofprepositionrelationsob-tainedusingPennTreebankfunctiontagsandframeelementsfromFrameNet.(SrikumarandRoth,2011)mergedprepositionsensesofsevenpreposi-tionsintorelationlabels.(Litkowski,2012)alsosuggestscollapsingthedefinitionsofprepositionsintoasmallersetofsemanticclasses.Toaidbet-tergeneralizationandtoreducethelabelcomplex-ity,wefollowthislineofworktodefineasetofrela-tionlabelswhichabstractwordsensesacrossprepo-sitions2.3Preposition-triggeredRelationsThissectiondescribestheinventoryofprepositionrelationsintroducedinthispaper,andthenidentifiesthecomponentsoftheprepositionrelationextractionproblem.3.1PrepositionRelationInventoryWebuildourrelationinventoryusingthesensean-notationinthePrepositionProject,focusingonthe34prepositions3annotatedfortheSemEval-2007sharedtaskofprepositionsensedisambiguation.AsdiscussedinSection2,weconstructthein-ventoryofprepositionrelationsbycollapsingse-manticallyrelatedprepositionsensesacrossdiffer-2SincetheprepositionsensedataisannotatedoverFrameNetsentences,senseannotationcanbeusedtoextendFrameNet(Litkowski,2012).Webelievethattheabstractla-belsproposedinthispapercanfurtherhelpinthiseffort.3Weconsiderthefollowingprepositions:Di,above,across,after,against,along,among,around,COME,at,before,be-hind,beneath,beside,between,by,down,during,for,from,In,inside,into,like,Di,off,SU,onto,Sopra,round,through,A,to-wards,andwith.Thisdoesnotincludemulti-wordprepositionssuchasbecauseofanddueto.
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entprepositions.Foreachsensethatisdefined,thePrepositionProjectalsospecifiesrelatedprepo-sitions.Thesedefinitionsandrelatedprepositionsprovideastartingpointtoidentifysensesthatcanbemergedacrossprepositions.Wefollowedthiswithamanualcleanupphase.Somesensesdonotcleanlyalignwithasinglerelationbecausethedef-initionsincludeidiomaticorfigurativeusage.Forexample,thesensein:7(5)oftheprepositionin,ac-cordingtothedefinition,includesbothspatialandfigurativenotionsofthespatialsense(thatis,bothinLondonandinafilm).Insuchcases,wesam-pled20examplesfromtheSemEval2007trainingsetandassignedtherelationlabelbasedonmajority.Ifsufficientexamplescouldnotbesampled,thesesenseswereaddedtothelabelOther,whichisnotasemanticallycoherentcategoryandrepresentsthe‘overflow’case.Overall,wehave32labels,whicharelistedinTable14.Acompanionpublication(availableontheauthors’website)providesdetaileddefinitionsofeachrelationandthesensesthatweremergedtocreateeachlabel.Sincewedefinerelationstobegroupsofprepositionsenselabels,eachsensecanbeuniquelymappedtoarelationlabel.Hence,wecanusetheannotatedsensedatafromSemEval2007toobtainacorpusofrelation-labeledsentences.Tovalidatethelabelingscheme,twonativespeak-ersofEnglishannotated200sentencesfromtheSemEvaltrainingcorpususingonlythedefinitionsofthelabelsastheannotationguidelines.Wemea-suredCohen’skappacoefficient(Cohen,1960)be-tweentheannotatorstobe0.75andalsobetweeneachannotatorandtheoriginalcorpustobe0.76and0.74respectively.3.2PrepositionRelationExtractionTheinputtothepredictionproblemconsistsofaprepositioninasentenceandthegoalistojointlymodelthefollowing:(io)Therelationexpressedbythepreposition,E(ii)Theargumentsoftherela-tion,namelythegovernorandtheobject.Weusesentence(2)intheintroductionasourrun-ningexamplethefollowingdiscussion.Inourrun-4Notethat,eventhoughwedonotconsiderintransitiveprepositions,thedefinitionsofsomerelationsinTable1couldbeextendedapplytoprepositionalparticlessuchdrivedown(Direction)andrunabout(Manner).RelationNameExampleActivitygoodatboxingAgentopenedbyAnnieAttributewallsofstoneBeneficiaryfightforNapoleonCausediedofcancerCo-ParticipantspickoneamongtheseDestinationleavingforLondonDirectiondrovetowardstheborderEndStatedriventotearsExperiencerwarmtowardsherInstrumentcutwithaknifeJourneytravelbyroadLocationlivinginLondonMannerscreamlikeananimalMediumOfCommunicationnewshowonTVNumericincreaseby10%ObjectOfVerbmurderoftheboysOpponent/ContrastfightwithhimOtherallothersParticipant/AccompaniersteakwithwinePartWholememberofgangPhysicalSupportleanagainstthewallPossessorsonofafriendProfessionalAspectworksinpublishingPurposetoolsformakingitRecipientunkindtoherSeparationoustedfrompowerSourcepurchasedfromtheshopSpeciescityofPragueStartStaterecoverfromillnessTemporalarrivedonMondayTopicbooksonShakespeareTable1:Listofprepositionrelationsningexample,therelationlabelisCause.Werep-resentthepredictedrelationlabelbyr.ArgumentsTherelationlabelcruciallydependsoncorrectlyidentifyingtheargumentsoftheprepo-sition,whicharedeathandpneumoniainourrun-ningexample.Whileaparsercanidentifytheargu-mentsofapreposition,simplyrelyingontheparsermayimposeanupperlimitontheaccuracyofrela-tionprediction.Webuildanoracleexperimenttohighlightthislimitation.Table2showstherecalloftheeasy-firstdependencyparserof(GoldbergandElhadad,2010)onSection23ofthePennTreebankforidentifyingthegovernorandobjectofprepositions.Wedefineheuristicsthatgenerateacandidategovernorsandobjectsforapreposition.Forthegov-
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ernor,thissetincludesthepreviousverbornounandfortheobject,itincludesonlythenextnoun.TherowlabeledBest(Parser,Heuristics)showstheperformanceofanoraclepredictorwhichselectsthetruegovernor/objectifpresentamongtheparser’spredictionandtheheuristics.Weseethat,evenforthein-domaincase,ifweareabletore-rankthecan-didates,wecouldachieveabigimprovementinar-gumentidentification.RecallGovernorObjectParser88.8892.37Best(Parser,Heuristics)92.5093.06Table2:IdentifyinggovernorandobjectofprepositionsinthePennTreebankdata.Here,Best(Parser,Heuris-tics)reportstheperformanceofanoraclethatpicksthetruegovernorandobject,ifpresentamongthecandidatespresentedbytheparserandtheheuristic.Thispresentsanin-domainupperboundforgovernorandobjectdetec-tion.Seetextforfurtherdetails.Toovercomeerroneousparserdecisions,ween-tertaingovernorandobjectcandidatesproposedbothbytheparserandtheheuristics.Inthefollow-ingdiscussion,wedenotethechosengovernorandobjectbygandorespectively.ArgumenttypesWhiletheprimarypurposeofthisworkistomodelprepositionrelationsandtheirarguments,therelationpredictionisstronglydepen-dentonthesemantictypeofthearguments.Toil-lustratethis,considerthefollowingincompletesen-tence:Themessagewasdeliveredat···.ThisprepositioncanexpressbothaTemporaloraLocationrelationdependingontheobject(forex-ample,noonvs.thedoorstep).(Agirreetal.,2008)showsthatmodelingthese-mantictypeoftheargumentsjointlywithattachmentcanimprovePPattachmentaccuracy.Inthiswork,wepointoutthatargumenttypesshouldbemodeledjointlywithbothaspectsoftheproblemofpreposi-tionrelationlabeling.Typesareanabstractionthatcapturecommonpropertiesofgroupsofentities.Forexample,Word-Netprovidesgeneralizationsofwordsintheformoftheirhypernyms.Inourrunningexample,wewishtogeneralizetherelationlabelfordeathfrompneu-moniatoincludecasessuchassufferingfromflu.Figure1showsthehypernymhierarchyforthewordpneumonia.Inthiscase,synsetsinthehypernymhierarchy,likepathologicalstateorphysicalcondi-tion,wouldalsoincludeailmentslikeflu.pneumonia=>respiratorydisease=>disease=>illness=>illhealth=>pathologicalstate=>physicalcondition=>condition=>state=>attribute=>abstraction=>entityFigure1:HypernymhierarchyforthewordpneumoniaWedefineasemantictypetobeaclusterofwords.InadditiontoWordNethypernyms,wealsoclusterverbs,nounsandadjectivesusingthedependency-basedwordsimilarityof(Lin,1998)andtreatclustermembershipastypes.ThesearedescribedindetailinSection5.1.Relationpredictioninvolvesnotonlyidentifyingthearguments,butalsoselectingtherightsemantictypeforthem,whichtogether,helppredictingtherelationlabel.Givenanargumentcandidateandacollectionofpossibletypes(givenbyWordNetorthesimilaritybasedclusters),weneedtoselectoneofthetypes.Forexample,intheWordNetcase,weneedtopickoneofthehypernymsinthehypernymhierarchy.Thus,forthegovernorandobject,wehaveasetoftypelabels,comprisedofoneelementforeachtypecategory.Wedenotethisbytg(gover-nortype)andto(objecttype)respectively.3.3ProblemdefinitionTheinputtoourpredictiontaskisaprepositioninasentence.Ourgoalistojointlymodeltherelationitexpresses,thegovernorandtheobjectoftherela-tionandthetypesofeachargument(bothWordNethypernymsandclustermembership).Wedenotetheinputbyx,whichconsistsnotonlyoftheprepo-sitionbutalsoasetofcandidatesforthegovernorandtheobjectand,foreachtypecategory,thelistoftypesforthegovernorandcandidate.
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Theprediction,whichwedenotebyy,consistsoftherelationr,whichcanbeoneofthevalidre-lationlabelsinTable1andthegovernorandobject,denotedbygando,eachofwhichisoneoftextseg-mentsproposedbytheparserortheheuristics.Ad-ditionally,yalsoconsistsoftypepredictionsforthegovernorandobject,denotedbytgandtorespec-tively,eachofwhichisavectoroflabels,oneforeachtypecategory.Table3summarizesthenota-tiondescribedabove.Werefertotheithelementofvectorsusingsubscriptsandusethesuperscript∗todenotegoldlabels.Recallthatwehavegoldlabelsonlyfortherelationlabelsandnotforargumentsandtheirtypes.SymbolMeaningxInput(pre-processedsentenceandpreposition)rrelationlabelfortheprepositiong,ogovernorandobjectoftherelationtg,tovectorsoftypeassignmentsforgovernorandobjectrespectivelyyFullstructure(R,G,o,tg,A)Table3:Summaryofnotation4LearningprepositionrelationsAkeychallengeinmodelingprepositionrelationsisthatourtrainingdataonlyannotatestherelationla-belsandnottheargumentsandtypes.Inthissection,weintroducetwoapproachesforpredictingpreposi-tionrelationsusingthisdata.4.1FeatureRepresentationWeusethenotationΦ(X,sì)toindicatethefeaturefunctionforaninputxandthefulloutputy.WebuildΦusingthefeaturesofthecomponentsofy:1.Arguments:Forgando,whichrepresentanassignmenttothegovernorandobject,wede-notethefeaturesextractedfromtheargumentsasφA(X,G)andφA(X,o)respectively.2.Types:Givenatypeassignmenttgitotheithtypecategoryofthegovernor,wedefinefea-turesφT(X,G,tgi).Allo stesso modo,wedefinefeaturesφT(X,o,toi)forthetypesoftheobject.Wecombinetheargumentandtheirtypefeaturestodefinethefeaturesforclassifyingtherelation,whichwedenotebyφ(X,G,o,tg,A):φ=Xa∈{G,o} φA(X,UN)+XiφT(X,UN,tai)!(1)Section5describestheactualfeaturesusedinourexperiments.Observethatgiventheargumentsandtheirtypes,thetaskofpredictingrelationsissimplyamulticlassclassificationproblem.Thus,followingthestandardconventionformulticlassclassification,theoverallfeaturerepresentationfortherelationandargumentpredictionisdefinedbyconjoiningtherelationrwithfeaturesforthecorrespondingargumentsandtypes,φ.Thisgivesusthefullfeaturerepresenta-tion,Φ(X,sì).4.2Model1:PredictingonlyrelationsThefirstmodelaimsatpredictingonlytherela-tionlabelsandnottheargumentsandtypes.Thisfallsintothestandardmulticlassclassificationset-ting,wherewewishtopredictoneof32labels.Todoso,wesumoverallthepossibleassignmentstotherestofthestructureanddefinefeaturesfortheinputsasˆφ(X)=Xg,o,tg,toφ(X,G,o,tg,A)(2)Effectively,doingsousesallthegovernorandob-jectcandidatesandalltheirsemantictypestogetafeaturerepresentationfortherelationclassifica-tionproblem.Onceagain,forarelationlabelr,theoverallfeaturerepresentationisdefinedbyconjoin-ingtherelationrwiththefeaturesforthatrelationˆφ,whichwewriteasφR(X,R).Notethatthissum-mationiscomputationallyinexpensiveinourcasebecausethesumdecomposesaccordingtoequation(1).Withalearnedweightvectorw,therelationlabelispredictedasr=argmaxr0wTφR(X,r0)(3)WeuseastructuralSVM(Tsochantaridisetal.,2004)totrainaweightvectorwthatpredictsthere-lationlabelasabove.ThetrainingisparameterizedbyC,whichrepresentsthetradeoffbetweengener-alizationandthehingeloss.
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4.3Model2:LearningfrompartialannotationsInthesecondmodel,eventhoughourannotationdoesnotprovidegoldlabelsforargumentsandtypes,ourgoalistopredictthem.Atinferencetime,ifwehadaweightvectorw,wecouldpredictthefullstructureusinginferenceasfollows:y=argmaxy0wTΦ(X,sì)(4)Weproposeaniterativelearningalgorithmtolearnthisweightvector.Inthefollowingdiscussion,foralabeledexample(X,y∗),werefertothemissingpartofitsstructureash(y∗).Thatis,H(y∗)istheassignmenttotheargumentsoftherelationandtheirtypes.Weusethenotationr(sì)todenotetherelationlabelspecifiedbyastructurey.Ourlearningalgorithmiscloselyrelatedtore-centlydevelopedlatentvariablebasedframeworks(YuandJoachims,2009;Changetal.,2010a;Changetal.,2010b),wherethesupervisionprovidesonlypartialannotation.Webeginbydefiningtwoaddi-tionalinferenceprocedures:1.LatentInference:Givenaweightvectorwandapartiallylabeledexample(X,y∗),wecan‘complete’therestofthestructurebyinfer-ringthehighestscoringassignmenttothemiss-ingparts.Inthealgorithm,wecallthispro-cedureLatentInf(w,X,y∗),whichsolvesthefollowingmaximizationproblem:ˆy=argmaxywTΦ(X,sì),(5)s.t.r(sì)=r(y∗).2.Lossaugmentedinference:ThisisavariantofthethestandardlossaugmentedinferenceforstructuralSVMs,whichsolvesthefollow-ingmaximizationproblemforagivenxandfullylabeledy∗:argmaxywTΦ(X,sì)+∆(sì,y∗)(6)Here,∆(sì,y∗)denotesthelossfunction.InthestandardstructuralSVMs,thelossisovertheentirestructure.IntheLatentStructuralSVMformulationof(YuandJoachims,2009),thelossisdefinedonlyoverthepartofthestructurewiththegoldlabel.Inthiswork,weusethestandardHamminglossovertheentirestructure,butscalethelossfortheelementsofh(sì)byaparameterα<1.Thisisagen-eralizationofthelatentstructuralSVM,whichcorrespondstothesettingα=0.Theintu-itionbehindhavinganon-zeroαisthatinad-ditiontopenalizingthelearningalgorithmifitviolatestheannotatedpartofthestructure,wealsoincorporateasmallpenaltyfortherestofthestructure.Usingthesetwoinferenceprocedures,wedefinethelearningalgorithmasAlgorithm1.TheweightvectorisinitializedusingModel1.Thealgorithmthenfindsthebestargumentsandtypesforallex-amplesinthetrainingset(steps3-5).Doingsogivesanestimateoftheargumentsandtypesforeachexample,givingus‘fullylabeled’structureddata.Thealgorithmthenproceedstousethisdatatotrainanewweightvectorusingthestandardstruc-turalSVMwiththelossaugmentedinferencelistedabove(step6).Thesetwostepsarerepeatedseveraltimes.NotethataswiththesummationinModel1,solvingtheinferenceproblemsdescribedaboveiscomputationallyinexpensive.Algorithm1AlgorithmforlearningModel2Input:ExamplesD={xi,r(y∗i)},whereexam-plesarelabeledonlywiththerelationlabels.1:InitializeweightvectorwusingModel12:fort=1,2,···do3:for(xi,y∗i)∈Ddo4:ˆyi←LatentInf(w,xi,y∗i)(Eq.5)5:endfor6:w←LearnSSVM({xi,ˆyi})withthelossaugmentedinferenceofEq.67:endfor8:returnwAlgorithm1isparameterizedbyCandα.Theparameterαcontrolstheextenttowhichthehypoth-esizedlabelsaccordingtothepreviousiteration’sweightvectorinfluencethelearning.
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4.4JointinferencebetweenprepositionsensesandrelationsBydefiningprepositionrelationsasdisjointsetsofprepositionsenses,weeffectivelyhaveahierarchi-calrelationshipbetweensensesandrelations.Thissuggeststhatjointinferencecanbeemployedbe-tweensenseandrelationpredictionswithavalidityconstraintconnectingthetwo.Theideaofemploy-inginferencetocombineindependentlytrainedpre-dictorstoobtainacoherentoutputstructurehasbeenusedforvariousNLPtasksinrecentyears,startingwiththeworkof(RothandYih,2004;RothandYih,2007).Weusethefeaturesdefinedby(Hovyetal.,2010),whichwewriteasφs(x,s)foragiveninputxandsenselabels,andtrainaseparateprepositionsensemodelontheSemEvaldatawithfeaturesφs(x,s)usingthestructuralSVMalgorithm.Thus,wehavetwoweightvectors–theoneforpredictingpreposi-tionrelationsdescribedearlier,andtheprepositionsenseweightvector.Atpredictiontime,foragiveninput,wefindthehighestscoringjointassignmenttotherelation,argumentsandtypesandthesense,sub-jecttotheconstraintthatthesenseandtherelationagreeaccordingtothedefinitionoftherelations.5ExperimentsandResultsTheprimaryresearchgoalofourexperimentsistoevaluatethedifferentmodels(Model1,Model2andjointrelation-senseinference)forpredictingprepo-sitionrelations.Inadditionalanalysisexperiments,wealsoshowthatthedefinitionofprepositionrela-tionsindeedcapturescross-prepositionsemanticsbytakingadvantageofsharedfeaturesandalsohigh-lighttheneedforgoingbeyondthesyntacticparser.5.1TypesandFeaturesTypesAsdescribedinSection3,weuseWordNethypernymsasoneofthetypecategories.Weuseallhypernymswithinfourlevelsinthehypernymhier-archyforallsenses.Thesecondtypecategoryisdefinedbyword-similaritydrivenclusters.Webrieflydescribetheclusteringprocesshere.Thethesaurusof(Lin,1998)specifiessimilarlexicalitemsforagivenwordalongwithasimilarityscorefrom0to1.Ittreatsnouns,verbsandadjectivesseparately.Weusethescoretoclustergroupsofsimilarwordsus-ingagreedyset-coveringapproach.Specifically,werandomlyselectawordwhichisnotyetinaclusterasthecenterofanewclusterandaddallwordswhosescoreisgreaterthanσtoit.Were-peatthisprocesstillallwordsareinsomeclus-ter.Awordcanappearinmorethanoneclusterbecauseallwordssimilartotheclustercenterareaddedtothecluster.Werepeatthisprocessforσ∈{0.1,0.125,0.15,0.175,0.2,0.25}.Byincreas-ingthevalueofσ,theclustersbecomemoreselec-tiveandhencesmaller.Table4showsexamplenounclusterscreatedusingσ=0.15.Foragivenword,identifiersforclusterstowhichthewordbelongsserveastypelabelcandidatesforthistypecategory5.FeaturesOurargumentfeatures,denotedbyφAinSection4.1,arederivedfromtheprepositionsensefeaturesetof(Hovyetal.,2010)andextractthefollowingfromtheargument:1.Word,part-of-speech,lemmaandcapitalizationindicator,2.Con-flatedpart-of-speech(oneofNoun,Verb,Adjective,Adverb,andOther),3.IndicatorforexistenceinWordNet,4.WordNetsynsetsforthefirstandallsenses,5.WordNetlemma,lexicographerfilenamesandpart,memberandsubstanceholonyms,6.Rogetthesaurusdivisionsfortheword,7.Thefirstandlasttwoandthreeletters,and8.Indicatorsforknownaf-fixes.Ourtypefeatures(φT)aresimplyindicatorsforthetypelabel,conjoinedwiththetypecategory.Oneadvantageofabstractingwordsensesintore-lationsisthatwecansharefeaturesacrossdifferentprepositions.Thebasefeatureset(forbothtypesandarguments)definedabovedoesnotencodein-formationabouttheprepositiontobeclassified.Wedosobyconjoiningthefeatureswiththepreposi-tion.Inaddition,sincetherelationlabelsaresharedacrossallprepositions,weincludethebasefeaturesasasharedrepresentationbetweenprepositions.Weconsidertwovariantsofourfeaturesets.Werefertothefeaturesdescribedaboveasthetypedfeatures.Inaddition,wedefinethetyped+genfeaturesbyconjoiningargumentandtypefeaturesoftypedwiththenameofthegenera-torthatproposestheargument.Recallthatgovernorcandidatesareproposedbythedependencyparser,orbytheheuristicsdescribedearlier.Hence,for5Theclusterscanbedownloadedfromtheauthors’website.
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JimmyCarter;RonaldReagan;richardnixon;GeorgeBush;LyndonJohnson;RichardM.Nixon;GeraldFordmetalwork;porcelain;handicraft;jade;bronzeware;carving;pottery;ceramic;earthenware;jewelry;stoneware;lacquerwaredegradation;erosion;pollution;logging;desertification;siltation;urbanization;felling;poaching;soilerosion;depletion;waterpollution;deforestationexpert;WallStreetanalyst;analyst;economist;telecommunicationsanalyst;strategist;mediaanalystfoxnewschannel;NBCNews;MSNBC;FoxNews;CNBC;CNNfn;C-SpanTuesdays;Wednesdays;weekday;Mondays;Fridays;Thursdays;sundays;SaturdaysTable4:Examplesofnounclustersgeneratedusingtheset-coveringapproachforσ=0.15agovernor,thetyped+genfeatureswouldconjointhecorrespondingtypedfeatureswithoneofparser,previous-verb,previous-noun,previous-adjective,orprevious-word.5.2ExperimentalsetupanddataAllourexperimentsarebasedontheSem-Eval2007dataforprepositionsensedisambigua-tion(LitkowskiandHargraves,2007)comprisingwordsenseannotationover16176trainingand8058examplesofprepositionslabeledwiththeirsenses.Wepre-processedsentenceswithpart-of-speechtagsusingtheIllinoisPOStaggerandde-pendencygraphsusingtheparserof(GoldbergandElhadad,2010)6.Fortheexperimentsdescribedbe-low,weusedtherelation-annotatedtrainingsettotrainthemodelsandevaluateaccuracyofpredictiononthetestset.WechosethestructuralSVMparameterCusingfive-foldcross-validationona1000randomexam-pleschosenfromthetrainingset.ForModel2,wepickedα=0.1usingavalidationsetconsistingofaseparatesetof1000trainingexamples.WeranAlgorithm1for20rounds.Predictingthemostfrequentrelationforaprepo-sitiongivesanaccuracyof21.18%.Eventhoughtheperformanceofthemost-frequentrelationlabelispoor,itdoesnotrepresenttheproblem’sdifficultyandisnotagoodbaseline.Tocompare,forprepo-sitionsenses,usingfeaturesfromtheneighboringwords,(YeandBaldwin,2007)obtainedanaccuracyof69.3%,andwithfeaturesdesignedfortheprepo-sitionsensetask,(Hovyetal.,2010)getupto84.8%accuracyforthetask.Ourre-implementationofthelattersystemusingadifferentsetofpre-processingtoolsgetsanaccuracyof83.53%.Forprepositionrelations,ourbaselinesystemfor6WeusedtheCurator(Clarkeetal.,2012)forallpre-processing.relationlabelingusesthetypedfeatureset,butwith-outanytypeinformation.Thisproducesanaccuracyof88.01%withModel1and88.64%withModel2.WereportstatisticalsignificanceofresultsusingourimplementationofDanBikel’sstratified-shufflingbasedstatisticalsignificancetester7.5.3Mainresults:RelationpredictionOurmainresult,presentedinTable5,comparesthebaselinemodel(withouttypes)againstothersys-tems,usingbothmodelsdescribedinSection4.First,weseethataddingtypeinformation(typed)improvesperformanceoverthebaseline.Expand-ingthefeaturespace(typed+gen)givesfurtherim-provements.Finally,jointlypredictingtherelationswithprepositionsensesgivesanotherimprovement.SettingAccuracyModel1Model2Notypes88.0188.64typed88.7789.14typed+gen89.90∗89.43∗Jointtyped+gen&sense89.99∗90.26∗†Table5:Mainresults:Accuracyofrelationlabeling.Resultsinboldarestatisticallysignificant(p<0.01)improvementsoverthesystemthatisunawareoftypes.Superscripts∗and†indicatesignificantimprovementsovertypedandtyped+genrespectivelyatp<0.01.ForModel2,theimprovementoftypedoverthemodelwith-outtypesissignificantatp<0.05.Ourobjectiveisnotpredictingprepositionsense.However,weobservethatwithModel2,jointlypre-dictingthesenseandrelationsimprovesnotonlytheperformanceofrelationidentification,butviajointinferencebetweenrelationsandsensesalsoleadstoalargeimprovementinsensepredictionaccuracy.Table6showstheaccuracyforsenseprediction.We7http://www.cis.upenn.edu/∼dbikel/software.html
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seethatwhileModel1doesnotleadtoasignificantimprovementintheaccuracy,Model2givesanab-soluteimprovementofover1%.SettingSenseaccuracyHovy(re-implementation)83.53Joint+Model183.78Joint+Model284.78∗Table6:Sensepredictionperformance.JointinferencewithModel1,whileimprovingrelationperformance,doesnothelpsenseaccuracyincomparisontoourre-implementationoftheHovysensedisambiguationsys-tem.However,withModel2,theimprovementisstatis-ticallysignificantatp<0.01.5.4AblationexperimentsFeaturesharingacrossprepositionsInourfirstanalysisexperiment,weseektohighlighttheutilityofsharingfeaturesbetweendifferentprepositions.Todoso,wecomparetheperformanceofasys-temtrainedwithoutsharedfeaturesagainstthetype-independentsystem,whichusessharedfeatures.Todiscounttheinfluenceofotherfactors,weuseModel1inthetypedsettingwithoutanytypes.Table7reportstheaccuracyofrelationpredictionforthesetwofeaturesets.Weobservedasimilarimprove-mentinperformanceevenwhentypefeaturesareaddedorthesettingischangedtotyped+genorwithModel2.SettingAccuracyIndependent87.17+Shared88.01Table7:Comparingtheeffectoffeaturesharingacrossprepositions.Weseethathavingasharedrepresentationthatgoesacrossprepositionsimprovesaccuracyofrela-tionprediction(p<0.01).DifferentargumentcandidategeneratorsOursecondablationstudylooksattheeffectofthevar-iousargumentcandidategenerators.Recallthatinadditiontothedependencygovernorandobject,ourmodelsalsousethepreviousword,thepreviousnoun,adjectiveandverbasgovernorcandidatesandthenextnounasobjectcandidate.WerefertothecandidatesgeneratedbytheparserasParseronlyandtheothersasHeuristicsonly.Table8comparestheperformanceofthesetwoargumentcandidategeneratorsagainstthefullsetusingModel1inboththetypedandtyped+gensettings.Weseethattheheuristicsgiveabetteraccu-racythantheparserbasedsystem.Thisisbecausetheheuristicsoftencontainthegovernor/objectpre-dictedbythedependency.Thisisnotalwaysthecase,Anche se,becauseusingallgeneratorsgivesaslightlybetterperformingsystem(notstatisticallysignificant).Intheoverallsystem,weretainthede-pendencyparserasoneofthegeneratorsinordertocapturelong-rangegovernor/objectcandidatesthatmaynotbeinthesetselectedbytheheuristics.FeaturesetsGeneratortypedtyped+genParseronly87.1287.12Heuristicsonly87.6388.84All88.0189.12Table8:Theperformanceofdifferentargumentcandi-dategenerators.Weseethatconsideringalargersetofcandidategeneratorsgivesabigaccuracyimprovement.6DiscussionTherearetwokeydifferencesbetweenModel1and2.First,theformerpredictsonlytherelationlabel,whilethelatterpredictstheentirestructure.Table9showsexamplepredictionsofModel2forrelationlabelandWordNetargumenttypes.Theseexamplesshowhowtheargumenttypescanbethoughtofasanexplanationforthechoiceofrelationlabel.InputRelationHypernymsgovernorobjectdiedofpneumoniaCauseexperiencediseasesufferedfromfluCauseexperiencediseaserecoveredfromfluStartStatechangediseaseTable9:ExamplepredictionsaccordingtoModel2.ThehypernymscolumnshowsarepresentativeofthesynsetchosenfortheWordNettypes.Weseethatinthecom-binationofexperienceanddiseasesuggeststherelationCausewhilethechangeanddiseaseindicatetherela-tionStartState.Themaindifferencebetweenthetwomodelsisinthetreatmentoftheunlabeled(orlatent)partsofthestructure(namely,theargumentsandthetypes)duringtrainingandinference.Duringtraining,for
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eachexample,Model1aggregatesfeaturesfromallgovernorsandobjectseveniftheyarepossiblyir-relevant,whichmayleadtoamuchbiggermodelintermsofthenumberofactiveweights.Ontheotherhand,forModel2,Algorithm1usesthesinglehigh-estscoringpredictionofthelatentvariables,accord-ingtothecurrentparameters,torefinetheparame-ters.Indeed,inourexperiments,weobservedthatthenumberofnon-zeroweightsintheweightvec-torofModel2ismuchsmallerthanthatofModel1.Forinstance,inthetypedsetting,theweightvec-torforModel1had2.57millionelementswhilethatforModel2hadonly1.0millionweights.Similarly,forthetyped+gensetting,Model1had5.41millionnon-zeroelementsintheweightvectorwhileModel2hadonly2.21millionnon-zeroelements.ThelearningalgorithmitselfisageneralizationofthelatentstructuralSVMof(YuandJoachims,2009).Bysettingαtozero,wegetthelatentstruc-tureSVM.However,wefoundviacross-validationthatthisisnotthebestsettingoftheparameter.Atheoreticalunderstandingofthesparsityofweightslearnedbythealgorithmandastudyofitsconver-gencepropertiesisanavenueoffutureresearch.7ConclusionWeaddressedtheproblemofmodelingsemanticre-lationsexpressedbyprepositions.Weapproachedthistaskbydefiningasetofprepositionrelationsthatcombineprepositionsensesacrossprepositions.Doingsoallowedustoleverageexistingannotatedprepositionsensedatatoinduceacorpusforprepo-sitionlabels.Wemodeledprepositionrelationsintermsofitsarguments,namelythegovernorandob-jectofthepreposition,andthesemantictypesofthearguments.UsingageneralizationofthelatentstructuralSVM,wetrainedarelation,argumentandtypepredictorusingonlyannotatedrelationlabels.Thisallowedustogetanaccuracyof89.43%onre-lationprediction.Byemployingjointinferencewithaprepositionsensepredictor,wefurtherimprovedtherelationaccuracyto90.23%.AcknowledgmentsTheauthorswishtothankMarthaPalmer,NathanSchneider,theanonymousreviewersandtheeditorfortheirvaluablefeed-back.TheauthorsgratefullyacknowledgethesupportoftheDefenseAdvancedResearchProjectsAgency(DARPA)Ma-chineReadingProgramunderAirForceResearchLaboratory(AFRL)primecontractno.FA8750-09-C-0181.ThismaterialisalsobasedonresearchsponsoredbyDARPAunderagree-mentnumberFA8750-13-2-0008.TheU.S.Governmentisau-thorizedtoreproduceanddistributereprintsforGovernmentalpurposesnotwithstandinganycopyrightnotationthereon.Theviewsandconclusionscontainedhereinarethoseoftheauthorsandshouldnotbeinterpretedasnecessarilyrepresentingtheof-ficialpoliciesorendorsements,eitherexpressedorimplied,ofDARPA,AFRLortheU.S.Government.ReferencesE.Agirre,T.Baldwin,andD.Martinez.2008.Improv-ingparsingandPPattachmentperformancewithsenseinformation.InProceedingsoftheAnnualMeetingoftheAssociationforComputationalLinguistics(ACL),pages317–325,Columbus,USA.T.Baldwin,V.Kordoni,andA.Villavicencio.2009.Prepositionsinapplications:Asurveyandintroduc-tiontothespecialissue.ComputationalLinguistics,35(2):119–149.M.Chang,D.Goldwasser,D.Roth,andV.Srikumar.2010a.Discriminativelearningoverconstrainedlatentrepresentations.InProceedingsoftheAnnualMeet-ingoftheNorthAmericanAssociationofComputa-tionalLinguistics(NAACL),pages429–437,LosAn-geles,USA.M.Chang,V.Srikumar,D.Goldwasser,andD.Roth.2010b.Structuredoutputlearningwithindirectsuper-vision.InProceedingsoftheInternationalConferenceonMachineLearning(ICML),pages199–206,Haifa,Israel.J.Clarke,V.Srikumar,M.Sammons,andD.Roth.2012.AnNLPCurator(O:HowILearnedtoStopWor-ryingandLoveNLPPipelines).InProceedingsoftheInternationalConferenceonLanguageResourcesandEvaluation(LREC),pages3276–3283,Istanbul,Turkey.J.Cohen.1960.Acoefficientofagreementfornominalscales.EducationalandPsychologicalMeasurement,20:37–46.D.Dahlmeier,H.T.Ng,andT.Schultz.2009.Jointlearningofprepositionsensesandsemanticrolesofprepositionalphrases.InProceedingsoftheConfer-enceonEmpiricalMethodsforNaturalLanguagePro-cessing(EMNLP),pages450–458,Singapore.D.Das,N.Schneider,D.Chen,andN.Smith.2010.Probabilisticframe-semanticparsing.InProceedingsofHumanLanguageTechnologies:The2010Annual
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