[PPT] - Adaptation Techniques for Acoustic Adaptation Techniques for PowerPoint Presentation

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Adaptation Techniques for Acoustic Models Adaptation Techniques for Acoustic Adaptation Techniques for Acoustic Models Models

Jen Jen-

Wei

Wei Roger Roger Kuo Kuo

Speech Lab, CSIE, NTNU Speech Lab, CSIE, NTNU rogerkuo@csie.ntnu.edu.tw rogerkuo@csie.ntnu.edu.tw

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Presentation Outline

Background
Maximum a Posterior
Maximum Likelihood Linear Regression
MLLR another approach
Constrained Maximum Likelihood Linear Regression
Maximum a Posterior Linear Regression
Structural Maximum a Posterior
Joint MAP and MLLR
Appendix — Matrix Calculus

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Background Background Background

SLIDE 4

Reference

Adaptive Methods for Speech and

Speaker Recognition – PSTL Jean- Claude Junqua and Roland Kuhn

SLIDE 5

Background

Intra-Speaker Variability

SLIDE 6

Background

Inter-Speaker Variability

SLIDE 7

Background

Adaptive System

SLIDE 8

Background

Goal

– Produce a system with Speaker-Dependent (SD) performance given small amount of data from new speaker.

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Background

Main Speaker Adaptation Methods

– Bayesian – Transformation-based – Based on Clustering and Model selection

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Background

Comparison of Methods

model crazy

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Background

Direct and indirect adaptation

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Approaches

Eigen- MAPLR Eigen- MLLR Indirect Direct MCELR SMAPLR EMAPLR QBLR MAPLR-Mean MAPLR-Covariance MLLR CMLLR Indirect Adaptation (Transformation) SMAP Structural Hierarchy MCE Maximum Classification Error QB MAP Baum- Welch Training Direct Adaptation Maximum a Posterior (MAP) On-Line(QB) EigenVoice Eigen Approach Maximum Likelihood (ML)

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Maximum a Posterior Maximum a Posterior Maximum a Posterior

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Maximum a Posterior

Reference:

– A Study on Speaker Adaptation of the Parameters

f Continuous Density Hidden Markov Models –

SAP’91 C.-H. Lee – Bayesian Adaptive Learning of the Parameters of Hidden Markov Model for Speech Recognition – TR’92 Q. Huo – Maximum a Posteriori Estimation for Multivariate Gaussian Mixture Observations of Markov Chains – SAP’94 J.-L. Gauvain – Bayesian Adaptive Learning of the Parameters of Hidden Markov Model for Speech Recognition – SAP’95 Q. Huo – On Adaptive Decision Rules and Decision Parameter Adaptation for Automatic Speech Recognition – Proceedings of IEEE’00 C.-H. Lee

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Maximum a Posterior

Introduction
MAP estimate for Multinomial

– Prior Dirichlet

MAP estimate for DHMM

– Prior Dirichlet

MAP estimate for SCHMM

– Prior Dirichlet + normal-Wishart

MAP estimate for CDHMM

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Introduction

Estimation Posterior a Maximum ) ( ) | ( max ) ( ) ( ) | ( max ) | ( max Estimation Likelihood Maximum ) | ( max model acoustic d reestimate : model acoustic current : adaptation for data n

bservatio

: ↓ = = = → = λ λ X X λ λ X X λ λ λ X λ λ λ X

λ λ λ λ

p p p p p p p

MAP ML

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Introduction

slow. be will prior from away movement big, s it' if prior, in faith

f

strength is Gaussian. prior

f

mean the is ) ( ) ( MAP Use ) ( ) ( MLE Use : Gaussian particular a

f

mean the estimate To

1 1 1 1

τ γ τ γ τ γ γ

nwi T t T t t nwi MAP T t T t t ML

t t t t µ x µ µ x µ

∑ ∑ ∑ ∑

= = = =

+ + = → = →

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Multinomial

1

e

K

e

M

1

e

K

e

M

1

e

K

e

M

1

x

2

x

T

x

L L L

→

1

w →

K

w

{ } ( ) ( ) ( )

function. indicator the is ) 1( with sequence the in event th the

bserving
ccurrence
f

number the is ) ( 1 where ! ! ! ! ! ! ! ! , , | , ,

n

distributi l multinomia a follows , , ns

bservatio

discrete i.i.d

f

sequence a

bserving
f

y probabilit the Then, . 1 and , , 1 |

utcomes

possible

f

set a among event discrete th the

bserving
f

y probabilit the be Let

1 1 2 1 1 2 1 1 1

⋅ = = = + + = = = =

∑ ∏ ∏ ∑

= = = =

k e x n w n n n T w n n n n n w w p w K k e K e k w

T t k t k K k n k k K k n k k k 1 K T 1 T 1 K k k k k k

k k

L L L L L L L x x x x X

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Multinomial

Many useful random variables used in speech

recognition and language processing, including N- grams, histograms, mixture gains, and discrete HMM probabilities, can be modeled this way.

( ) { }

∏

= − − −

∝ = > Γ Γ + + Γ =

K k k K K k K K K K K K 1

k K

w w w p K k w w w w p w w

1 1 1 1 1 1 1 1 1 1 1

) , | ,..., ( So, eters. hyperparam

f

set the is , , 1 | where ... ) ( )... ( ) ... ( ) , | ,..., ( density. l multinomia a

f

parameters for the prior conjugate a is which density t a Dirichle as assumed be can , ,

f

density prior The

1

ν ν ν

ν ν ν ν ν ν ν ν ν L L L L

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Multinomial

( ) ( )

∑ ∑ ∑ ∑ ∑ ∑ ∏

= = = = = = = − +

− + − + = ∴ − + − = ⇒ = − + − = − + − = ⇒ = + − + × ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ + ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ − + + Ψ = ⇒ ∝

K k k k k k k K k k k K k k k K k k k k k k k k k K j j K k k k k T K K k n k T K

n n w n l l n w l n w l n w w w l w n w w p w w w p

k k

1 1 1 1 1 1 1 1 1 1 1 1

1 1 1 1 1 1 ) 1 ( 1 then w.r.t ate Differenti log ) 1 ( ) ,..., | ,..., ( log ) ,..., | ,..., ( So, ν ν ν ν ν ν ν

ν

Q x x x x

Apply Lagrange Multiplier

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Discrete HMM

( ) { } { } ( )

[ ] [ ]

{ }

K 1 k jk jk ij N T T T t t s s s s s

v v V j v b K k N j b N j i a N s s b a b p p

t t t

, , as denoted is set symbol n

bservatio

The state in symbol

bserving
f

y probabilit the being with , , 1 , , 1, where matrix. y probabilit transition the is , , 1 , where y vector. probabilit state initial the is where , , vector parameter DHMM with state

Consider

, , and , , where , sequence state a is ) ( ) ( | , ) | (

1 1 1 2 1

1 1 1

L L L L M L L = = = = = = ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎣ ⎡ = = = = ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ = =

∑ ∏ ∑

=

−

B A π B A π λ x x X S S x x λ S X λ X

S S

π π π

Definition :

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Discrete HMM

( )

( ) [ ]

( )

( ) [ ]

( ) ( )

( )

( ) ( ) ( )

∑ ∑ ∑ ∑ ∏ ∑ ∏ ∑ ∑ ∑

⎥ ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎢ ⎣ ⎡ ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ + + ′ = ⎥ ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎢ ⎣ ⎡ ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ ′ = ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ = = =

= = ′ = = ′

− − −

S S S S S S

x λ S X x x x x λ S X λ S X λ S X λ X λ S X λ S X λ X S λ X λ S X λ λ λ X

T t t s T t s s s T t t s s s s s T t t s s s s s

t t t t t t t t t

b a P b a b b a b P P P P P P P P E Q p

2 2 2 1 2 1

) ( log log | , ) ( ) ( ) ( ) ( log | , | , , log | | , , log , , | , log | maximize to need

nly

we , ) | ( log maximize

rder to

In

1 1 1 1 1 1 1 1

π π π

Q-function :

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Discrete HMM

1 2 1 2 1 2

4

v

7

v

4

v

statrt

1

π

2

π

11

a

12

a

22

a

21

a

4 , 1 11 7 , 1 11 4 , 1 1

b a b a b ⋅ ⋅ ⋅ ⋅ ⋅ π

1

4 , 1 11 7 , 1 11 4 , 1 1