1. SNR-Dependent Mixture of PLDA for Noise Robust Speaker Verification
Man-Wai Mak
Interspeech 2014
Department of Electronic and Information Engineering
The Hong Kong Polytechnic University, Hong Kong SAR, China

2. Contents Motivation of Work Conventional PLDA
Mixture of PLDA for Noise Robust Speaker Verification
Experiments on SRE12
Conclusions 2

3. I-Vector/PLDA Scoring
Motivation
Conventional i-vector/PLDA systems use a single PLDA model to handle all SNR conditions.
I-Vector/PLDA Scoring
PLDA Score
Enrollment
Utterances

4. Motivation
We argue that a PLDA model should focus on a small range of SNR.
PLDA
Model 1
PLDA Score
PLDA
Model 2
PLDA Score
PLDA
Model 3
PLDA Score

5. Distribution of SNR in SRE12
Each SNR region is handled by a PLDA Model

6. 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 Score
SNR
Estimator
PLDA
Model 2
SNR Posterior Estimator
PLDA
Model 3

7. 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.

8. Contents Motivation of Work Conventional PLDA
Mixture of PLDA for Noise Robust Speaker Verification
Experiments on SRE12
Conclusions

9. Probabilistic LDA (PLDA)
In PLDA, the i-vectors x are modeled by a factor analyzer of the form:
Speaker factor
Residual noise with covariance Σ
i-vector extracted from the j-th session of the i-th speaker
Global mean of all i-vectors
Speaker factor loading matrix
Density of x is

10. Probabilistic LDA (PLDA)
The PLDA parameters ω={m, V, Σ} are estimated by maximizing

11. Contents Motivation of Work Conventional PLDA
Mixture of PLDA for Noise Robust Speaker Verification
Experiments on SRE12
Conclusions

12. Mixture of PLDA Model Parameters of mPLDA: For modeling SNR of utts.
For modeling SNR-dependent i-vectors 2

13. Generative Model for mPLDA
: SNR in dB
where the posterior prob of SNR is
Posterior of SNR

14. PLDA vs mPLDA
Generative Model
PLDA
Mixture of PLDA

15. Likelihood-Ratio Scores of mPLDA
Same-speaker likelihood:
SNR of target and test utterances
i-vectors of target and test speakers

16. Likelihood-Ratio Scores of mPLDA
Different-speaker likelihood:
Same-speaker likelihood
Verification Score =
Different-speaker likelihood 16

17. PLDA vs mPLDA PLDA: Mixture of PLDA: Auxiliary Function
Latent indicator variables:
No. of mixtures
Latent speaker factors:
SNR of training utterances:
Speaker indexes
Session indexes

18. PLDA vs mPLDA
E-Step
PLDA
Mixture of PLDA

19. PLDA versus mPLDA
M-Step
PLDA
Mixture of PLDA

20. Contents Motivation of Work Conventional PLDA
Mixture of PLDA for Noise Robust Speaker Verification
Experiments on SRE12
Conclusions

21. 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

22. 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
Babble noise
Utterances from microphone channels
FaNT
From telephone channels

23. 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

24. 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
PLDA
mPLDA
mPLDA

25. 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.

26. Hard-Decision Mixture of PLDA

27. Training of mPLDA Auxiliary function: where
No. of mixtures
where
Latent indicator variables:
Latent speaker factors:
SNR of training utterances:
Speaker indexes
Session indexes

28. xs and xt share the same z
PLDA Scoring
xs and xt share the same z

29. Probabilistic LDA (PLDA)
PLDA example: 2-D data in 1-D subspace z
Take a sample according to p(z)
Source: S. Prince, “Computer vision: models, learning and inference”, 2012