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Andrew Rosenberg- Lecture 20: Model Adaptation
Transcript of Andrew Rosenberg- Lecture 20: Model Adaptation
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Lecture20:ModelAdaptaon
MachineLearning
April15,2010
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Today
AdaptaonofGaussianMixtureModelsMaximumAPosteriori(MAP)MaximumLikelihoodLinearRegression(MLLR)
Applicaon:SpeakerRecognionUBM-MAP+SVM
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TheProblem
IhavealiOlebitoflabeleddata,andalotofunlabeleddata.
Icanmodelthetrainingdatafairlywell.
ButwealwaysfittrainingdatabeOerthantesngdata.
CanweusethewealthofunlabeleddatatodobeOer?
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LetsuseaGMM
GMMstomodellabeleddata. Insimplestform,onemixturecomponentperclass.
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LabeledtrainingofGMM
MLEesmatorsofparameters
rthesecanbeusedtoseedEM.
i =
tp(i|xt
)xt
tp(i|xt)
=
xt
x
nkt =
tp(i|xt)N
= niN
i =
xt
(xt )(xt )T
nk
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Adapngthemixturestonewdata
Essenally,letEMstartwithMLEparametersasseeds. ExpandtheavailabledataforEM,proceedunlconvergence
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Adapngthemixturestonewdata
Essenally,letEMstartwithMLEparametersasseeds. ExpandtheavailabledataforEM,proceedunlconvergence
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ProblemwithEMadaptaon
TheiniallabeledseedscouldcontributeveryliOletothefinalmodel
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neProblemwithEMadaptaon
TheiniallabeledseedscouldcontributeveryliOletothefinalmodel
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MAPAdaptaon
Constrainthecontribuonofunlabeleddata.
Letthealphatermsdictatehowmuchweighttogivetothenew,unlabeleddatacomparedtotheexingesmates.
i = i
u p(i|xu)xuu p(i|xu)
+ (1 i )i
i =
i
up(i|xu)
U+ (1
i)i
i =
i
up(i|xu)(xu i)(xu i)
T
U
+ (1 i
)i
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MAPadaptaon
Themovementoftheparametersisconstrained.
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MLLRadaptaon
Anotheridea MaximumLikelihoodLinearRegression. Applyanaffinetransformaontothemeans. Dontchangethecovariancematrices
=W
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MLLRadaptaon
Anotherviewonadaptaon. Applyanaffinetransformaontothemeans. Dontchangethecovariancematrices
=W
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MLLRadaptaon
ThenewmeansaretheMLEofthemeanswiththenewdata.
i = Wii =
x
p(i|x,i, i,i
)xi
xp(i|x,i, i,i)
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MLLRadaptaon
ThenewmeansaretheMLEofthemeanswiththenewdata.
i = Wii =
x
p(i|x,i, i,i
)xi
xp(i|x,i, i,i)
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MLLRadaptaon
ThenewmeansaretheMLEofthemeanswiththenewdata.
i = Wii =
xp(i|x,i, i,i)xi
x p(i|x,
i
, i
,i
)Wi =
xp(i|x,i, i,i)xixp(i|x,i, i,i)
(1)T
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WhyMLLR?
Wecanethetransformaonmatricesofmixturecomponents.
Forexample: Youknowthattheredandgreenclassesaresimilar Assumpon:Theirtransformaonsshouldbesimilar
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WhyMLLR?
Wecanethetransformaonmatricesofmixturecomponents.
Forexample: Youknowthattheredandgreenclassesaresimilar Assumpon:Theirtransformaonsshouldbesimilar
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ApplicaonofModelAdaptaon
SpeakerRecognion. Task:Givenspeechfromaknownsetofspeakers,idenfythespeaker.
Assumethereistrainingdatafromeachspeaker. Approach:
Modelagenericspeaker. Idenfyaspeakerbyitsdifferencefromthegenericspeaker
Measurethisdifferencebyadaptaonparameters
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SpeechRepresentaon
Extractafeaturerepresentaonofspeech. Samplesevery10ms.
MFCC16dims
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Similarityofsounds
MFCC1
MFCC2 /s/
/b/
/o//u/
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UniversalBackgroundModel
Ifwehadlabeledphoneinformaonthatwouldbegreat.
Butitsexpensive,andmeconsuming. SojustfitaGMMtotheMFCCrepresentaonofallofthespeechyouhave.
Generallyallbutoneexample,butwellcomebacktothis.
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MFCCScaOer
MFCC1
MFCC2 /s/
/b/
/o//u/
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UBMfing
MFCC1
MFCC2 /s/
/b/
/o//u/
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MAPadaptaon
Whenwehaveasegmentofspeechtoevaluate,
GenerateMFCCfeatures.
UseMAPadaptaonontheUBMGaussianMixtureModel.
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MAPAdaptaon
MFCC1
MFCC2 /s/
/b/
/o//u/
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MAPAdaptaon
MFCC1
MFCC2 /s/
/b/
/o//u/
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UBM-MAP
Claim:Thedifferencesbetweenspeakerscanberepresentedbythemovementofthemixture
componentsoftheUBM.
Howdowetrainthismodel?
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UBM-MAPtraining
Training
Data
Heldout
SpeakerN
UBM
Training
MAP
Supervector
Supervector Avectorofadaptedmeansofthegaussianmixturecomponents
xi =
0 1 . . . kT
ti = Speaker ID
Trainasupervisedmodelwiththese
labeledvectors.
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UBM-MAPtraining
Training
Data
Heldout
SpeakerN
UBM
Training
MAP
Supervector
xi =
0 1 . . . kT
ti = Speaker ID
Repeatforalltrainingdata
Mulclass
SVM
Training
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UBM-MAPEvaluaon
TestData
UBM
MAP
Supervector Mulclass
SVM
Predicon
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AlternateView
Doweneedallthis? WhatifwejusttrainanSVMonlabeledMFCCdata?
TestData
Mulclass
SVM
Predicon
Labeled
Training
Data
Mulclass
SVM
Training
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Results
UBM-MAP(withsomevariants)isthestate-of-the-artinSpeakerRecognion.
Currentstateoftheartperformanceisabout97%accuracy(~2.5%EER)withafewminutesof
speech.
DirectMFCCmodelingperformsabouthalfaswell~5%EER.
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ModelAdaptaon
AdaptaonallowsGMMstobeseededwithlabeleddata.
Incorporaonofunlabeleddatagivesamorerobustmodel.
Adaptaonprocesscanbeusedtodifferenatemembersofthepopulaon
UBM-MAP
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NextTime
SpectralClustering