xiA*5Ú'èÃêbE:I êbďĒ{wÎÙé¯ÒÄ_uĊz¤§éªO
PRMU 2013 2Â 22¼ÿÀ! êbďĒ"êb}&%^#¬%ďĒē'Ēl# ç]ďĎİOCRİsêbďĒ³ă"6,FH9)İÎèÍÉİ+L7N9*DL;
ÐiĞĪćq! øċìÓÌüêbďĒ

:37IÓ¿v"$ñÐāêb " ċôÓë"$êb'įĘgæxĀ øċìÓÌü êbďĒ²Ú Ûí" PCAİ<FNGI=8;KN-İSVM²Ú"# ÕĈt& ĠÔcA-;I'Y To^ìs%ÕĈtgæ ¨ć# êbÃá©'ý®y êbÃá©'ý®ØèìêbďĒ²Ú¨ćíì! x"ÃêbE:I [Nankaku, et al.; ’06]

ïäìR°iiÇMiÇ# ĉÜ:N7ġfi¹!îĢ'E:It"iĨÊHMM [Kurata, et al.; ’06]

2E:I'øy# ďĒē^ìs'E:It"

ĆħE:IÏę%

ĚüĬ! ïäøċE:IüÝ"¡Át (ML) Ý# ¡'Á%ïìº'ß¶ ü:N7"ğyĚü

A*5Ý
# Toi'mèE:I?GDN7T¥i'¶ ØtĀpįE:I'¶

A*5Ý'xÃêbE:IěèïäìÃêbE:I! R°iiÇ'ïäøċE:I¢t!

Ãêb'ïäìR°iiÇ (PPCA) !iÇ (FA)"$Ąåv
wGxG: T9wv

v: !VPQ wg : 4C (')

: !{tx: ysu{txv

wGxG; : wv\k 1mE]r?Dj}wO6; :  j&"D j#fq7S@d+Rïäì

ÃêbE:I! R°iiÇ'ïäøċE:I¢t!

Ãêb'ïäìR°iiÇ (PPCA) !iÇ (FA)"$ĄåvwGxG>*5A-;Ii¹: !{tx: T9wv
MĊói¹
PPCA: !VPQ  v : ysu{txMĊfi¹FA

wg : 4C (')

v

wGxG; : wv\k 1mE]r?Dj}wO6; :  j&"D j#fq7S@d+R

ĥ&BI0@E:I (HMM)
=/ZHG? a111G?

a23a33

a12

a22

23%

b1 (ot )b2 (ot )b3 (ot )ĉÜõkO : o1 o2 o3 o4 o5â­õkz : 1

1

1

12oT
2223

333¾ġ"s%ĉÜõk'E:It2ÔcHMM
! 1ÔcHMMÞº'µâ­ĜðE:I" ¾õkE:Itěj"! 2ÔcHMM

2ÔcĉÜ:N7 (êb) 'E:It" êb^ìs'E:ItxĀ" ċôğā"ÏęìnöÅZ iĨÊHMMiĨÊHMM (SL-HMM)
! 2Ôc´£HMMÏęìnöÅZ"Ñ»|ú»|â­Ĝðãò
53k=/z (1)<*[l#,fqG? %np z (2)=/hCrF(_j=/kG?

%; : &"D r}w
6; : T9wvl#,fqHMMk=/co>JegA0iĨÊHMM (SL-HMM)
! 2Ôc´£HMMÏęìnöÅZ"Ñ»|ú»|â­Ĝðãò
53k=/z (1)<*[l#,fqG? %np 
z (2)=/hCrF(_j=/kG?

%; : &"D r}w
6; : T9wvl#,fqHMMk=/co>JegA0

x

ÃêbE:I (HMEM)

ÃêbE:IiĨÊHMM'øyÃêb>*5A-;I iĨÊHMM#ç°! ïäì!

v
wGxG: T9wv

v: !VPQ wg : 4C (')

: !{tx: ysu{txv

wGxG; : =/\k

1mE]i&"Dr}wx

ÃêbE:I'èêbďĒ! xÃêbE:I"êbÃá©'E:It# à½ÅZ!ďĒēt (ïäìÃêbE:I)# ďĒē^ìs (iĨÊHMM)"ĆħE:IÏę%

ĚüĬ

ü:N7#ØtĀpįE:I'ü%¨ć! ïäøċE:IüÝ"¡Át (ML) Ý# ¦ÆıMLÝ"%x"

ÃêbE:IüA*5Ý
# ·ËıA*5Ý"%x

ÃêbE:Iü¡Át (ML) Ý! ¡Á%E:I?GDN7'ß¶ü:N7

94;:N7YSÜiP (Y | ⇤ML )ü:N7ğÖĦğü:N7
¶E:I

6; : "Nwv[d$[kjY"Nk`ğ

A*5Ý! E:I?GDN7T¥i'¶To«Toiü:N7T¥i

94;:N7YSÜiP (Y | O) =Z

P (Y | ⇤)P (⇤ | O)d⇤

A*5Ý! E:I?GDN7T¥i'¶To«ºWĭêbToi

A*5Ý! E:I?GDN7T¥i'¶To«Toiü:N7

T¥i

O{iĭêb

A*5Ý! E:I?GDN7T¥i'¶To«Toiü:N7T¥i

94;:N7Y;:6; : ISÜiP (Y | O) =Z

P (Y | ⇤)P (⇤ | O)d⇤-d BO}wz~|vrWUKd^A*5Ý! E:I?GDN7T¥i'¶To«Toi

ü:N7T¥i

94;:N7Y;:6; : ISÜiP (Y | O) =Z

P (Y | ⇤)P (⇤ | O)d⇤-d BO}wz~|vrW
X ZZ
UKd^
P (O) =z

P (O, x, z | ⇤)P (⇤)dxd⇤

x, z : :

2

A*5Ý! E:I?GDN7T¥i'¶To«Toi

ü:N7T¥i

94;:N7Y;:6; : ISÜiP (Y | O) =Z

P (Y | ⇤)P (⇤ | O)d⇤-d BO}wz~|vrW
UKd^ b aMCMC8a[Gilks, et al.; ’96]b aMAP8 [Gauvain, et al.; ’94]b a{su8 [Attias; ’99]

iA*5 (VB) Ú (1/2)
! T¥i
P (x, z (1) , z (2) , ⇤ | O)ė\i'¶! º~Ė¡Qģ'û
ln P (O)F(Q)

ln P (O)X X ZZ

Q(x, z(1),z(2)z (1) z (2)= F(Q)P (O, z (1) , z (2) , ⇤), ⇤) lndxd⇤(1)(2)
Q(x, z , z , ⇤)x : !{tx z (1) : 53k=/L
Q(x, z (1) , z (2) , ⇤) : .]2 z (2) : M3k=/L! [¬ĢºT¥iQ
P KLĔĨ KL(Q || P )KL(Q || P ) = ln P (O)

F(Q)

F(Q)
QģÁt KLĔĨÁt" [¬ĢºT¥iė\Qln P (O)KL(Q || P )

"F(Q)

Q




iA*5 (VB) Ú (2/2)
! ė\T¥inöÅZP (x, z (1) , z (2) , ⇤ | O) ⇡ Q(x, z (1) , z (2) , ⇤)= Q(x)Q(z (1) )Q(z (2) )Q(⇤)

Q(x, z (1) , z (2) , ⇤) : X) % Q(x), Q(z (1) ), Q(z (2) ), Q(⇤) :)%

! iT¥i'VUÁět QģÁtF(Q)Q̄(z (1) ) = arg max F
Q(z (1) )VB E-step Q̄(z (2) ) = arg max F
Q(z (2) )Q̄(x) = arg max F
Q(x)

max F
VB M-step  Q̄(⇤) = arg Q(⇤)! T¥iė\i'¶"KL(Q|| P)
KL(Q||PPKL(QKL(Q||||P)) )KL(Q || P )ln P (O)

F(Q)

QVBÚA*5Ý'ė\MLÝ"$įØtĀpĭêbďĒĮĮÅZ
:N7AN4

XM2VTSêb2*564 × 64ê÷İ256Ĥđİ.JN4/NI

ąĮþ(-G4)

100{ü:N71{$6È

94;:N7

1{$2È

E:IÏę

PPCA, FA, SL-HMM,HMEM-PPCA, HMEM-FA

HMMâ­º32 × 32â­¶²ÚMLÚ (MLÝ)İVBÚ (A*5Ý)

ToiOÐiİeü:N7#üE:I (UBM)

:N7AN4ĭêb`ü:N7

94;:N7

E:IÏę¶²Ú"%ďĒäMLÚVBÚďĒä×ĕ (ToiOÐi)

Recognition rate (%)80ßùıMLÚùıVBÚĂıE:IÏę75
70

SLHMM-ML
SLHMM-VB

65

HMEM-PPCA-ML
HMEM-PPCA-VB

60

HMEM-FA-ML
HMEM-FA-VB

55
50
1234
Number of factors

5eE:IÏęVBÚMLÚ"$įďĒäE:IÏę¶²Ú"%ďĒäMLÚVBÚďĒä×ĕ (ToiOÐi)

Recognition rate (%)80ßùıMLÚùıVBÚĂıE:IÏę

7570

SLHMM-ML
SLHMM-VB

65

HMEM-PPCA-ML
HMEM-PPCA-VB

60

HMEM-FA-ML
HMEM-FA-VB

5550
1234
Number of factors

5VBÚ"%x ÃêbE:IiĨÊHMM"$įďĒäVBÚ

%HMMÏę"%ďĒä

HMMÏę"%ďĒä×ĕ (ToiOÐi)

Recognition rate (%)75
ĂıE:IÏę65

PPCA55

FA
SLHMM

45

HMEM-PPCA
HMEM-FA

3525
1234
Number of factors

5HMMÏęįďĒä sīaiA*5Ú%Toi

! T¥i¶ToičĝćOÐi (flat)" eü:N7#üE:I (UBM)
"E:IÏęToi
flat

HMEM-PPCA SLUBM

HMEM-FA

OÐi
SL-HMMÏęüUBM

UBM

HMEM-PPCAÏęüUBM

flat

OÐi

SLUBM

SL-HMMÏęüUBM

UBM

HMEM-FAÏęüUBMHMEMToi"%ďĒä
HMEM-FA

8484

82

82

Recognition rate (%)Recognition rate (%)HMEM-PPCA

80
7876
74
72
70
68

80
78
76
74
72
70
68

12345
Number of factors

12345
Number of factorsßùıMLÚùıVBÚĂıToi

ML
VB-flat
VB-SLUBM
HMEM-VB-UBM

HMEMToi"%ďĒä
HMEM-FA

84

84

82

82

Recognition rate (%)Recognition rate (%)HMEM-PPCA

8078767472706880
78
7674
7270
68

12345
Number of factors

12345
Number of factors

PPCAflat SLUBM"$įďĒäßùıMLÚFASLUBM flat"$įďĒäùıVBÚ Ċfi¹'Y%FAÃrĂıToi

ML
VB-flat
VB-SLUBM
HMEM-VB-UBM

HMEMToi"%ďĒä
HMEM-FA

8484

8282

Recognition rate (%)Recognition rate (%)HMEM-PPCA

80
78
76
74
72
70
68

80
78
7674
72
70
68

12345
Number of factors

12345
Number of factorsßùıMLÚflat UBM"$įďĒä%yùıVBÚ  Toi'č% ĩĂıToi

ML
VB-flat
VB-SLUBM
HMEM-VB-UBM

! êbÃá©'ý®Øèì²ÚÍČ! A*5Ý'x ÃêbE:Iěè
iA*5Ú" ĭêbďĒĮ"ü(I1H5C'h# iA*5ÚÁÚ"$įØtĀp"iA*5Ú%Toič# ějToi'è%ďĒä

|P! X¥ĐĬ"$ÁěToiÍČ" ±Áě©Ĭ'¸%ü(I1H5Cd" "$ĆħE:IA*5Ýěè"