MPE-based discriminative linear transform for speaker adaptation
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MPE-BASEDDISCRIMINATIVELINEARTRANSFORMFORSPEAKERADAPTATIONL.WangandP.C.WoodlandMachineIntelligenceLaboratory,CambridgeUniversityEngineeringDepartment,TrumpingtonStreet,Cambridge,CB21PZ,UK.Email:lw256,pcw@eng.cam.ac.uk
ABSTRACTInthispaper,wepresentadiscriminativemethodforspeakeradap-tation,wheretheminimumphoneerror(MPE)criterionisusedtoestimatethediscriminativelineartransform(DLT),includingmeananddiagonalvariancetransforms.TheI-smoothingtech-niqueisessentialtoimprovethegeneralizationofDLTs.Exper-imentsonsupervisedadaptationfornon-nativespeakersontheNorthAmericanBusiness(NAB)Spoke3taskshowthatMPE-basedDLToutperformsbothMLLRandpreviouslyproposeddis-criminativemethodfortransformestimation.Preliminaryexper-imentsonunsupervisedDLTestimationareplottedonconversa-tionaltelephonespeechtranscription.
1.INTRODUCTIONSpeakeradaptationiscrucialtoproduceaspeaker-specificsys-tembaseduponthespeaker-independentHMMsets,givenasmallamountofadaptationutterances.Foravarietyofadaptationtasks,maximumlikelihoodlinearregression(MLLR)formodel-spacetransformationisaneffectiveandefficientapproach.MLLRcanuseaso-calledregression-classtreetoadjustthenumberofgener-atedtransforms,accordingtotheamountofadaptationdataavail-able.Usingthemaximumlikelihood(ML)criteriontoestimatethetransformparameters,MLLRcanbeusedtoestimatemean,diago-nalvariance,orfullvariancetransforms,fortheHMMparameters.MLLRcanbeoperatedineithersupervisedorunsupervisedmode.Sincediscriminativetrainingcriteria[5]suchasmaximummutualinformation(MMI)andminimumphoneerror(MPE)[6,7]havebeensuccessfullyusedtotrainHMM-basedacousticmodels,itisthenexpectedthatthesamediscriminativecriteriacanbenefittheestimationofthelineartransformsforbothadaptivetraining[10]andadaptation.Inrelatedwork[3],theH-criterionwasusedtoestimatediscriminativelineartransform(DLT),wheretheob-jectivefunctionwasdesignedtobeaninterpolationofMLandMMI.Theconditionalmaximumlikelihoodlinearregression[4],anotherderivationoftheMMIcriterion,wasalsoproposedfortransformgeneration.Recently,usingtheminimumclassificationerror(MCE)toestimatethediagonalvariancetransformhasalsobeenexploredandreportedin[9].WealsoinvestigatedtheuseoftheMPEcriterionforconstrainedDLT,whichwasthenappliedtothefeaturesfordiscriminativespeakeradaptivetraining[10].Experimentsonconversationaltelephonespeech(CTS)tran-scriptionforthedirectestimationofHMMparametershavedemon-
(1)whereisthecompositemodelcorrespondingtothewordse-quence,istheprobabilityofthewordsequenceandistheacousticscale.Themeasuresthenumberofphonescorrectlyrecognizedinthesentence.IntheimplementationofMPEtraining,latticesmarkedwithtimeinformationatHMMlevelareusedtorepresentthecorrecttranscriptionsandconfusablehypothesesfromrecognition,asinMMItraining.Usinglatticescanreducethecomputationalloadforgeneratingthestatisticsneededforparameterestimation[5].2.1.TheoptimizationofobjectivefunctionFortheoptimizationofdiscriminativecriteria,theweak-senseaux-iliaryfunctionwasproposed[8,7],incontrasttotheuseofthestandardstrong-senseauxiliaryfunction[7]forMLtraining.Giventheobjectivefunction,theweak-senseauxiliaryfunctionisdefinedtosatisfythefollowingcondition:wherereferstotheoriginalparametersetandrepresentsthenewlyestimatedone.Thisequationimpliesthatifthereisalocalmaximumintheobjectivefunction,itmustalsobealocalmax-imumoftheauxiliaryfunction.Althoughoptimizingtheweak-senseauxiliaryfunctiondoesn’tguaranteeanincreaseintheob-jectivefunction,itcanstilloffertheminimumconditionfortheoptimizationof.Fordiscriminativetraining,theweak-senseauxiliaryfunctionprovidesafeasibleapproachtooptimizetheob-jectivefunctionswithnegativeterms.ConcerningthephoneaccuracyintheMPEobjectivefunction,theauxiliaryfunctionproposedin[8,7]isthenbasedontheloglikelihoodofphonearctomaketheoptimizationtractable,,whichareanalogoustothenumeratoranddenominatortermsintheMMIauxiliaryfunc-tion.Moreimportant,itisproventhatthemodelparameterupdat-ingformulationshavethesimilarformsasthatinMMItraining,providedthatthenumerator/denominatorstatisticshavedifferentdefinitions[7].WhenusingtheMPEcriteriontoestimatelineartransforms,aweak-senseauxiliaryfunctionisthuspresentedfortheoptimiza-tion.AsstandardMLLR[2],MPE-basedDLTisappliedtotrans-formGaussianmeanswithamatrixandabias,where,.WiththequantitydefinedforMPEtraining,,theauxiliaryfunctionconsistsofthreeindividualparts,eachofwhichhasaGaussianexpression,MPEMPE(3)whereistheposteriorprobabilityovertime,atstate,mixturecomponentonconditionofarc.Thefunctiondefinedasbelowdeterminesthatthearcswithpositivewillbeusedtoaccumulatethenumeratorstatistics,whilethosewithnegativevalueswillbeusedtogetdenominatorstatistics.