Maximun likelihood linear regression for speaker adaptation of

• Consider the case of a continuous density HMM system with Gaussian output distributions.
• A particular distribution s ,is characterized by a mean vector s ,
data, a transformation may still be applied (global transformation)
6
Estimation of MLLR regression matrices
• 1.Definition of auxiliary function
S
– Assume the adaptation data, O, is a series of T observations.
and a covariance matrix C s
• Given a parameterized speech frame vector o , the probability
density of that vector being generated by distribution s is bs o
j 1
T j t log2 n / 2
t 1
log C j
1/ 2
1 2
ot
j
' C j 1
ot
j
S
constant FO |
j 1
T t 1
j
t
1 2
n
log2
1 2
log
C
j
1 2
ot
j
' C j 1
ot
j
constant
1 2
F O
|
S j 1
T t 1
(Maximum - Likelihood)
Q , E log F O, | | O,
E-step
FO, | log F O, |
V
7
Estimation of MLLR regression matrices (cont.)
• 2.Maximization of auxiliary function
FO | T
s tCs1 ot Wss
s'
t1
0
hence
T
T
s t Cs1ots' s t Cs1Wsss'
<= 估測 W s 的general form
(5)
t 1
t 1
11
Estimation of MLLR regression matrices (cont.)
j tnlog2 log Cj
ot
W
j j
' C j 1
ot
W
j j
1 FO | d
2
dW s
S j1
T
j tnlog2 log Cj
t 1
ot W
j j
'
C
1 j
ot
W
j
j
1 2
FO | T s t*2*Cs1 *
t1
ot
W s s
*
s'
X T AX 2 AX X
s [, 1, 2 ,..., n ]'
offset = 1, include an offset in the regression
offset = 0, ignore offsets
若調適語者的錄音環境與初始模型錄音環境不同時， 可以加入的一項參數 [參考資料]
• So the probability density function for the adapted system becomes
s t
F
1
O
|
V
F
O,
t
s |
8
Estimation of MLLR regression matrices (cont.)
• 2.Maximization of auxiliary function (cont.)
已知 s t
F
1
O
|
V
F
O,
t
s |
則
T
Q , constant F O, | log bt ot V t 1
1 1/ 2oWss ' Cs1 oWss
b o e s
n/ 2 1/ 2
2 Cs
(1)
5
MLLR’s adaptation approach (cont.)
• The transformation matrices Ws are calculated to maximize the
likelihood of the adaptation data • The transformation matrices can be implemented using the
where n is the dimension of the observation vector
S
bs o 2
1 1/ 2os ' Cs1 os e n / 2 1/ 2
Cs
speech frame vector
4
MLLR’s adaptation approach (cont.)
– The totallikelihood of the modelset generate the observation sequenceis
FO | FO, |
objective function V
– Define an auxiliary function,and We want tomaximize it
(3)
V t 1
- Defines S as theset of all statedistributions in the system
and s t as the a posterioriprobability of occupyingstate s at timet
given that the observation sequence O is generated
• The other HMM parameters are not adapted since the main differences between speakers are assumed to be characterized by the means
3
MLLR’s adaptation approach (cont.)
Q , E log F O, | | O,
FO, | log F O, | V
F O, | V
log 1 b1
o1
T
a b t 1t t
t2
ot
(2)
only related with mean
T
constant F O, | log bt ot
forward–backward algorithm • A more general approach is adopted in which the same
transformations matrix is used for several distributions. • If some of the distributions are not observed in the adaptation
Present by Hsu Ting-Wei 2006.03.16

Introduction
Speaker
HMM Models
Say: “Hello!”
• Speaker adaptation techniques fall into two main categories:
– Speaker normalization • The input speech is normalized to match the speaker that the system is trained to model
2
MLLR’s adaptation approach
• This method requires an initial speaker independent continuous density HMM system
• MLLR takes some adaptation data from a new speaker and updates the model mean parameters to maximize the likelihood of the adaptation data
j
t n log2
log
C
j
ot
j
' C j 1 ot
j
constant
1 2
F O
|
S j 1
T t 1
j
t n log2
log
C
j
ot
W j j
' C j 1
ot
W
j j
constant 1 FO | S
2
j 1
T
j t n log2 log C j
t 1
hot , j
• We use the following equation
• We can simply it ˆs Ass bs
Original ..
where
ˆs Wss
n*(n+1) (n+1)*1
transformation extended mean vector