SNR-Dependent Mixture of PLDA for Noise Robust Speaker Verification

Man-Wai Mak

Department of Electronic and Information EngineeringThe Hong Kong Polytechnic University, Hong Kong SAR, China

Interspeech 2014

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Contents1. Motivation of Work

2. Conventional PLDA

3. Mixture of PLDA for Noise Robust Speaker Verification

4. Experiments on SRE12

5. Conclusions

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3

Motivation• Conventional i-vector/PLDA systems use a single PLDA

model to handle all SNR conditions.

I-Vector/PLDA Scoring

I-Vector/PLDA Scoring

EnrollmentUtterances

PLDA Score

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Motivation• We argue that a PLDA model should focus on a small

range of SNR.

PLDA Model 1

PLDA Model 1

PLDA Score

PLDA Model 2

PLDA Model 2

PLDAModel 3

PLDAModel 3

PLDA Score

PLDA Score

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Distribution of SNR in SRE12

Each SNR region is handled by a PLDA Model

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Proposed Solution• The full spectrum of SNRs is handled by a mixture of

PLDA in which the posteriors of the indicator variables depend on the utterance’s SNR.

PLDA Model 1

PLDA Model 1

PLDA Score

PLDA Model 2

PLDA Model 2

PLDA Model 3

PLDA Model 3

SNR Estimator

SNR Estimator

SN

R P

oste

rior

Est

imat

or

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Key Features of Proposed Solution• Verification scores depend not only on the same-

speaker and different-speaker likelihoods but also on the posterior probabilities of SNR.

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Contents1. Motivation of Work

2. Conventional PLDA

3. Mixture of PLDA for Noise Robust Speaker Verification

4. Experiments on SRE12

5. Conclusions

Probabilistic LDA (PLDA)

• In PLDA, the i-vectors x are modeled by a factor analyzer of the form:

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i-vector extracted from the j-th session of the i-th speaker

Global mean of all i-vectors Speaker factor

loading matrix

Speaker factor

Residual noise with covariance Σ

• Density of x is

Probabilistic LDA (PLDA)

• The PLDA parameters ω={m, V, Σ} are estimated by maximizing

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Contents1. Motivation of Work

2. Conventional PLDA

3. Mixture of PLDA for Noise Robust Speaker Verification

4. Experiments on SRE12

5. Conclusions

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Mixture of PLDA

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For modeling SNR of utts.

For modeling SNR-dependent

i-vectors

• Model Parameters of mPLDA:

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Generative Model for mPLDA

where the posterior prob of SNR is

Po

ste

rior

of

SN

R

: SNR in dB

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PLDA vs mPLDAGenerative Model

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Likelihood-Ratio Scores of mPLDA• Same-speaker likelihood:

i-vectors of target and test speakers

SNR of target and test utterances

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Likelihood-Ratio Scores of mPLDA• Different-speaker likelihood:

• Verification Score = Same-speaker likelihood

Different-speaker likelihood

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PLDA vs mPLDAAuxiliary Function

PLDA:

Mixture of PLDA:

Latent indicator variables:

SNR of training utterances:

Speaker indexes

Session indexes

No. of mixtures

Latent speaker factors:

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PLDA vs mPLDAE-Step

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PLDA versus mPLDAM-Step

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Contents1. Motivation of Work

2. Conventional PLDA

3. Mixture of PLDA for Noise Robust Speaker Verification

4. Experiments on SRE12

5. Conclusions

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Experiments

• Evaluation dataset: Common evaluation condition 2 of NIST SRE 2012 core set.

• Parameterization: 19 MFCCs together with energy plus their 1st and 2nd derivatives 60-Dim

• UBM: gender-dependent, 1024 mixtures • Total Variability Matrix: gender-dependent, 500 total factors• I-Vector Preprocessing:

Whitening by WCCN then length normalization Followed by LDA (500-dim 200-dim) and WCCN

Experiments• In NIST 2012 SRE, training utterances from telephone channels are clean,

but some of the test utterances are noisy.

• We used the FaNT tool to add babble noise to the clean training utterances

Utterances from microphone

channelsFaNTFaNT

Babble noise

From telephone channels 22

Performance on SRE12• Train on tel+mic speech and test on noisy tel speech (CC4)

• Train on tel+mic speech and test on tel speech recorded in noisy environments (CC5)

• Use FaNT and a VAD to determine the SNR of test utts.

See our ISCSLP14

paper

Performance on SRE12• Train on tel+mic speech and test on noisy tel speech (CC4)

• Use FaNT and a VAD to determine the SNR of test utts.Male Female

PLDA

mPLDA

PLDA

mPLDA

Conclusions• Mixture of SNR-dependent PLDA is a flexible model

that can handle noisy speech with a wide range of SNR

• The contribution of the mixtures are probabilistically combined based on the SNR of the test utterances and the target-speaker’s utterances

• Results show that the mixture PLDA performs better than conventional PLDA whenever the SNR of test utterances varies widely.

Hard-Decision Mixture of PLDA

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Training of mPLDA• Auxiliary function:

where

Latent indicator variables:

SNR of training utterances:

Speaker indexes

Session indexes

No. of mixtures

Latent speaker factors:

PLDA Scoring

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xs and xt share the same z

Probabilistic LDA (PLDA)

• PLDA example: 2-D data in 1-D subspace

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Source: S. Prince, “Computer vision: models, learning and inference”, 2012

Take a sample according to p(z)

z