Bayesian Method in Speaker Verification

Chengyuan Ma and Jinyu Li

School of Electrical and Computer Engineering

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Outline

Speaker Verification System

MAP adaptation of Speaker Model

Experiment Setup, Conclusion and Future Work

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Speaker Verification System

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Speaker Verification SystemFramework

Speaker Verification

Determines whether person is who they claim to be

User makes identity claim (one to one mapping)

Three Main Components

Front-end processing (Feature Extraction)

Speaker and background modeling (Speaker Modeling)

Log-likelihood-ratio score normalization (Decision

Making)

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Speaker Verification SystemFramework (Cont.)

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Speaker and Background Modeling

GMM (Gaussian Mixtures Model) represent static acoustic

event distribution for each speaker

p(ot|Λ) =M∑

m=1

wm

(2π)d

2 |Σm|1

2

· e−1

2(ot−µm)τΣ−1

m (ot−µm)

M∑

m=1

wm = 1 and wm > 0

Λ is used to represent speaker model parameters. wm is the mth weight ofGaussian mixture N (ot; µm, Σm) with mean µm and covariance matrix Σm.

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Speaker Recognition Scoring

p(O|Λ) = p(o1, o2, · · · , oT |Λ) =

T∏

t=1

p(ot|Λ)

The score (average Log-Likelihood Ratio (LLR)) of a given test segment O is

computed as follow,

score =1

T

T∑

t=1

(log p(ot|Λtar) − log p(ot|ΛUBM))

T is the length of the test segment, ot is the feature vector at time t and Λtar and

ΛUBM are parameters of the target model and UBM (Universal Background

Model) respectively.

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Performance Measurement ofSpeaker Verification System

ROC and DET plots are used for performance measurement

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MAP adaptation of Speaker Model

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Speaker Model Adaptation UsingMAP Method

EM training is reliable only when sufficient training data are

available

If only a small amount of training data, adaptation method

will be used for model training.

Background model is regarded as prior information for each

speaker, speaker-specified training data are the observation

samples, these two can be combined in the Bayesian

framework.

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Speaker Model Adaptation UsingMAP Method (Cont.)

Speaker model parameters to be estimated

Λ = (w1, w2, · · · , wM , µ1, µ2, · · · , µM ,Σ1,Σ2, · · · ,ΣM )

MAP estimation of speaker model parameters

θMAP = arg maxθ

p(O|Λ)g(Λ)

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Speaker Model Adaptation UsingMAP Method (Cont.)

Prior distribution of mixture weights is a conjugete density

such as Dirichlet density

g(w1, w2, · · · , wM ) ∝M∏

m=1

wvk−1m

where vk > 0 are the parameters for the Dirichlet density. a

aJ.-L. Gauvain and C.-H. Lee, ”Maximum a Posterior Estimation for Multivariate Gaussian Mixture Ob-

servations of Markov Chains,” IEEE Trans. Speech and Audio Processing, vol. 2, no. 2, pp. 291-298, April

1994.

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Speaker Model Adaptation UsingMAP Method (Cont.)

Prior distribution of (µm,Σm) is a normal_Wishart density

g(µm,Σm) ∝ |γm|(αm−p)/2

exp[

−τm

2(µm − mm)tΣm(µm − mm)

]

exp

[

−1

2tr(umΣm)

]

where (τm, mm, αm, um) are the prior density parameters

such that αm > p − 1, τm > 0, mm is a vector of dimension p,

and um is a p ∗ p positive definite matrix.

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Speaker Model Adaptation UsingMAP Method (Cont.)

Practical method for parameter adaptation only the mean

vectors will be updated

µ̂m = αmEm(O) + (1 − αm)µm

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Experiment Setup, Conclusion and Future Work

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Experiment Setup

1996 NIST(National Institute of Standards and Technology)

dataset was used for experiment,

225 Speakers in the Corpus

1 minutes for training and 15 second for testing for each

speaker

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System Performance using EMTraining

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System Performance using MAPAdaptation

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Future Work

Acoustic features robust against noisy environment and

different channels

Incorporation dynamical acoustic features and prosodic

features

Higher level information

novel probabilistic models for speaker modeling

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Q & A

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