Hidden Markov Models for Speech Recognition

Transcription

1 Hdden Marv Mdel fr Speech Recgnn Reference: Berln Chen Deparmen f Cmpuer Scence & Infrman Engneerng anal awan rmal Unvery. Raner and Juang. Fundamenal f Speech Recgnn. Chaper 6. Huang e. al. Spen Language rceng. Chaper Raner. A ural n Hdden Marv Mdel and Seleced Applcan n Speech Recgnn. rceedng f he IEEE vl. 77. Feruary Gale and Yung. he Applcan f Hdden Marv Mdel n Speech Recgnn Chaper Yung. HMM and Relaed Speech Recgnn echnlge. Chaper 7 Sprnger Hand f Speech rceng Sprnger J.A. Blme A Genle ural f he EM Algrhm and Applcan arameer Eman fr Gauan Mxure and Hdden Marv Mdel U.C. Bereley R-97-0

2 Hry Hdden Marv Mdel (HMM): A Bref Overvew ulhed n paper f Baum n lae 960 and early 970 Inrduced peech prceng y Baer (CMU) and Jelne (IBM) n he 970 (dcree HMM) hen exended cnnuu HMM y Bell La Aumpn Speech gnal can e characerzed a a paramerc randm (chac) prce arameer can e emaed n a prece well-defned manner hree fundamenal prlem Evaluan f praly (lelhd) f a equence f ervan gven a pecfc HMM Deermnan f a e equence f mdel ae Adumen f mdel parameer a e accun fr erved gnal (r dcrmnan purpe) S - Berln Chen

3 Schac rce A chac prce a mahemacal mdel f a pralc expermen ha evlve n me and generae a equence f numerc value Each numerc value n he equence mdeled y a randm varale A chac prce u a (fne/nfne) equence f randm varale Example (a) he equence f recrded value f a peech uerance () he equence f daly prce f a c (c) he equence f hurly raffc lad a a nde f a cmmuncan newr (d) he equence f radar meauremen f he pn f an arplane S - Berln Chen 3

4 Oervale Marv Mdel Oervale Marv Mdel (Marv Chan) Fr-rder Marv chan f ae a rple (SA) S a e f ae A he marx f rann prale eween ae ( = - = - = ) ( = - =) A he vecr f nal ae prale =( =) he upu f he prce he e f ae a each nan f me when each ae crrepnd an ervale even he upu n any gven ae n randm (deermnc!) mple decre he peech gnal characerc Fr-rder and me-nvaran aumpn S - Berln Chen 4

5 Oervale Marv Mdel (cn.) S S SS SS S S S S S S S S S S S S S SS S S S SS (rev. Sae Cur. Sae) S S S S S S S SS S S SS S SS Fr-rder Marv chan f ae Secnd-rder Marv chan f ae S - Berln Chen 5

6 Oervale Marv Mdel (cn.) Example : A 3-ae Marv Chan Sae generae yml A nly Sae generae yml B nly and Sae 3 generae yml C nly 0.6 A B C Gven a equence f erved yml O={CABBCABC} he nly ne crrepndng ae equence {S 3 S S S S 3 S S S 3 } and he crrepndng praly A 0.5 (O ) =(S 3 )(S S 3 )(S S )(S S )(S 3 S )(S S 3 )(S S )(S 3 S ) = = S - Berln Chen 6

7 Oervale Marv Mdel (cn.) Example : A hree-ae Marv chan fr he Dw Jne Indural average he praly f 5 cnecuve up day 5 cnecuve up day a a a a π S - Berln Chen 7

8 Oervale Marv Mdel (cn.) Example 3: Gven a Marv mdel wha he mean ccupancy duran f each ae d d = d = a praly ma funcn f d a a Expeced numer f d d d da a a a a d a duran n a ae a duran d a gemerc drun raly a n ae d d me (Duran) S - Berln Chen 8

9 Hdden Marv Mdel S - Berln Chen 9

10 Hdden Marv Mdel (cn.) HMM an exended vern f Oervale Marv Mdel he ervan urned e a pralc funcn (dcree r cnnuu) f a ae nead f an ne--ne crrepndence f a ae he mdel a duly emedded chac prce wh an underlyng chac prce ha n drecly ervale (hdden) Wha hdden? he Sae Sequence! Accrdng he ervan equence we are n ure whch ae equence generae! Elemen f an HMM (he Sae-Oupu HMM) ={SAB} S a e f ae A he marx f rann prale eween ae B a e f praly funcn each decrng he ervan praly wh repec a ae he vecr f nal ae prale S - Berln Chen 0

11 Hdden Marv Mdel (cn.) w mar aumpn Fr rder (Marv) aumpn he ae rann depend nly n he rgn and denan me-nvaran A Oupu-ndependen aumpn All ervan are dependen n he ae ha generaed hem n n neghrng ervan S - Berln Chen

12 Hdden Marv Mdel (cn.) w mar ype f HMM accrdng he ervan Dcree and fne ervan: he ervan ha all dnc ae generae are fne n numer V={v v v 3 v M } v R L In h cae he e f ervan praly drun B={ (v )} defned a (v )=( =v =) M : ervan a me : ae a me fr ae (v ) cn f nly M praly value A lef--rgh HMM S - Berln Chen

13 Hdden Marv Mdel (cn.) w mar ype f HMM accrdng he ervan Cnnuu and nfne ervan: he ervan ha all dnc ae generae are nfne and cnnuu ha V={v vr d } In h cae he e f ervan praly drun B={ (v)} defned a (v)=f O S ( =v =) (v) a cnnuu praly deny funcn (pdf) and fen a mxure f Mulvarae Gauan (rmal) Drun v M Mxure Wegh w π d Σ Cvarance Marx exp v μ Σ v μ Mean Vecr Oervan Vecr S - Berln Chen 3

14 Hdden Marv Mdel (cn.) Mulvarae Gauan Drun When X=(x x x d ) a d-dmennal randm vecr he mulvarae Gauan pdf ha he frm: f X x μ Σ x; μ Σ Σ he cverance marx Σ and he - elevmen f Σ π where μ he L - dmennal mean vecr h E Σ he he deermnan f d exp x μ Σ x μ Σ μ E x x μx μ Exx μμ Σ E x μ x μ Ex x μ μ If x x x d are ndependen he cvarance marx reduced dagnal cvarance Vewed a d ndependen calar Gauan drun Mdel cmplexy gnfcanly reduced S - Berln Chen 4

15 Hdden Marv Mdel (cn.) Mulvarae Gauan Drun S - Berln Chen 5

16 Hdden Marv Mdel (cn.) Cvarance marx f he crrelaed feaure vecr (Mel-frequency fler an upu) Cvarance marx f he parally de-crrelaed feaure vecr (MFCC whu C 0 ) MFCC: Mel-frequency cepral ceffcen S - Berln Chen 6

17 Hdden Marv Mdel (cn.) Mulvarae Mxure Gauan Drun (cn.) Mre cmplex drun wh mulple lcal maxma can e apprxmaed y Gauan (a unmdal drun) mxure f M M x w x; μ Σ w Gauan mxure wh enugh mxure cmpnen can apprxmae any drun S - Berln Chen 7

18 Hdden Marv Mdel (cn.) Example 4: a 3-ae dcree HMM E 0.6 A A 0.3 B 0. C A 0.7 B 0. C A B C Gven a equence f ervan O={ABC} here are 7 ple crrepndng ae equence and herefre he crrepndng praly {A:.7B:.C:.} 7 7 O λ O S λ O S λs λ S : ae. g. when S 3 O S λ A B C 3 S λ 0.5*0.7 * equence Ergdc HMM {A:.3B:.C:.5} {A:.3B:.6C:.} 0.7 *0.* S - Berln Chen 8

19 Hdden Marv Mdel (cn.) an: O={ 3 }: he ervan (feaure) equence S= { 3 } : he ae equence : mdel fr HMM ={AB} (O ) : he praly f ervng O gven he mdel (O S) : he praly f ervng O gven and a ae equence S f (OS ) : he praly f ervng O and S gven (S O) : he praly f ervng S gven O and Ueful frmula Baye Rule : A B AB B A B B A A B B AA A BB A B λ λ λa λ B λ B A λ : mdel decrng he praly chan rule AB B λ S - Berln Chen 9

20 Hdden Marv Mdel (cn.) Ueful frmula (Cn.): al raly herem A margnal praly all B B f A B A BB all B A BdB f A Bf B B f db B dree and dn f B cnnuu f x x...x n x x... x x x...x are ndependen n n B B 3 A B B 5 B 4 E z q z fz z z q z q z dz z z : dcree : cnnuu Venn Dagram Expecan S - Berln Chen 0

21 hree Bac rlem fr HMM Gven an ervan equence O=(.. ) and an HMM =(SAB) rlem : Hw effcenly cmpue (O )? Evaluan prlem rlem : Hw che an pmal ae equence S=( )? Decdng rlem rlem 3: Hw adu he mdel parameer =(AB) maxmze (O )? Learnng / ranng rlem S - Berln Chen

22 S - Berln Chen Bac rlem f HMM (cn.) Gven O and fnd (O )= r[ervng O gven ] Drec Evaluan Evaluang all ple ae equence f lengh ha generang ervan equence O : he praly f each pah S By Marv aumpn (Fr-rder HMM) S all all S S O S O O S a a a 3... S S By Marv aumpn By chan rule

23 S - Berln Chen 3 Bac rlem f HMM (cn.) Drec Evaluan (cn.) : he n upu praly alng he pah S By upu-ndependen aumpn he praly ha a parcular ervan yml/vecr emed a me depend nly n he ae and cndnally ndependen f he pa ervan S O S O By upu-ndependen aumpn

24 S - Berln Chen 4 Bac rlem f HMM (cn.) Drec Evaluan (Cn.) Huge Cmpuan Requremen: O( ) Expnenal cmpuanal cmplexy A mre effcen algrhm can e ued evaluae Frward/Bacward rcedure/algrhm.. all all a a a a a S O S O S ADD : - MUL - Cmplexy O

25 Bac rlem f HMM (cn.) Drec Evaluan (Cn.) 3 Sae-me rell Dagram Sae me O O O 3 O - O dene ha ( ) ha een cmpued a dene ha a ha een cmpued S - Berln Chen 5

26 Bac rlem f HMM - he Frward rcedure Baed n he HMM aumpn he calculan f and nvlve nly and ple cmpue he lelhd wh recurn n Frward varale :... λ he praly ha he HMM n ae a me havng generang paral ervan S - Berln Chen 6

27 Algrhm. Inalzan. Inducn α 3.ermnan Bac rlem f HMM - he Frward rcedure (cn.) α Cmplexy: O( ) MUL ADD : : π α a O λ α Baed n he lace (rell) rucure Cmpued n a me-ynchrnu fahn frm lef--rgh where each cell fr me cmpleely cmpued efre prceedng me + All ae equence regardle hw lng prevuly merge nde (ae) a each me nance S - Berln Chen 7

28 S - Berln Chen 8 Bac rlem f HMM - he Frward rcedure (cn.) a λ λ λ λ λ λ λ λ λ λ λ λ λ λ fr-rder Marv aumpn B A A B A λ B all B A A A B A B A upu ndependen aumpn

29 Bac rlem f HMM - he Frward rcedure (cn.) 3 (3)=( 3 3 =3 ) =[ ()*a 3 + ()*a 3 + (3)*a 33 ] 3 ( 3 ) Sae me O O O 3 O - O dene ha ( ) ha een cmpued a dene a ha een cmpued S - Berln Chen 9

30 Bac rlem f HMM - he Frward rcedure (cn.) A hree-ae Hdden Marv Mdel fr he Dw Jne Indural average (0.6* * *0.009)*0.7 = S - Berln Chen 30

31 Bac rlem f HMM - he Bacward rcedure Bacward varale : ()=( = ). Inalzan :. Inducn: a - 3. ermnan : Cmplexy MUL: O - ; ADD: - - S - Berln Chen 3

32 S - Berln Chen 3 Bac rlem f HMM - Bacward rcedure (cn.) Why? O O O O

33 Bac rlem f HMM - he Bacward rcedure (cn.) (3)=( 3 4 =3) =a 3 * ( 3 )* 3 () +a 3 * ( 3 )* 3 ()+a 33 * ( 3 )* 3 (3) 3 Sae me O O O 3 O - O S - Berln Chen 33

34 HMM a Knd f Bayean ewr S S S3 S O O O3 O S - Berln Chen 34

35 Bac rlem f HMM Hw che an pmal ae equence S=( )? he fr pmal crern: Che he ae are ndvdually m lely a each me Defne a perr praly varale O λ O λ O λ m O λ m O λ m m m ae ccupan praly (cun) a f algnmen f HMM ae he ervan (feaure) Slun : * = arg max [ ()] rlem: maxmzng he praly a each me ndvdually S*= * * * may n e a vald equence (e.g. a * + * = 0) S - Berln Chen 35

36 Bac rlem f HMM (cn.) ( 3 = 3 O )= 3 (3)* 3 (3) 3 Sae 3 (3) 3 (3) a 3 = me O O O 3 O - O S - Berln Chen 36

37 Bac rlem f HMM - he Ver Algrhm he ecnd pmal crern: he Ver algrhm can e regarded a he dynamc prgrammng algrhm appled he HMM r a a mdfed frward algrhm Inead f ummng up prale frm dfferen pah cmng he ame denan ae he Ver algrhm pc and rememer he e pah Fnd a ngle pmal ae equence S=( ) Hw fnd he ecnd hrd ec. pmal ae equence (dffcul?) he Ver algrhm al can e lluraed n a rell framewr mlar he ne fr he frward algrhm Sae-me rell dagram. R. Bellman On he hery f Dynamc rgrammng rceedng f he anal Academy f Scence 95. A.J. Ver "Errr und fr cnvlunal cde and an aympcally pmum decdng algrhm IEEE ranacn n Infrman hery 3 () 967. S - Berln Chen 37

38 Algrhm By nducn Bac rlem f HMM - he Ver Algrhm (cn.) Fnd a e ae equence S= ervan O Defne a max.... We can acrace frm new varale.. max a arg max a... * arg max δ = he e cre alng a ngle pah a me whch accun....? fr he fr ervan and end n ae fr a gven Fr acracng Cmplexy: O( ) S - Berln Chen 38

39 Bac rlem f HMM - he Ver Algrhm (cn.) 3 Sae 3 (3) me O O O 3 O - O S - Berln Chen 39

40 Bac rlem f HMM - he Ver Algrhm (cn.) A hree-ae Hdden Marv Mdel fr he Dw Jne Indural average (0.6*0.35)*0.7 = S - Berln Chen 40

41 Bac rlem f HMM - he Ver Algrhm (cn.) Algrhm n he lgarhmc frm Fnd a e ae equence S= ervan O Defne a By nducn max lg.... We can acracefrm.. fr hefr ervan and end n ae = he e crealng a ngle pah a me whch accun new varale.... max lga lg arg max lga * arg maxδ? fr a gven...fr acracng S - Berln Chen 4

42 Hmewr A hree-ae Hdden Marv Mdel fr he Dw Jne Indural average Fnd he praly: (up up unchanged dwn unchanged dwn up ) Fnd he pmal ae equence f he mdel whch generae he ervan equence: (up up unchanged dwn unchanged dwn up) S - Berln Chen 4

43 raly Addn n F-B Algrhm In Frward-acward algrhm peran uually mplemened n lgarhmc dman lg + Aume ha we wan add and lg lg( + ) f ele lg lg lg lg lg lg lg lg lg lg x he value f lg can e aved n n a ale peedup he peran S - Berln Chen 43

44 raly Addn n F-B Algrhm (cn.) An example cde #defne LZERO (-.0E0) // ~lg(0) #defne LSMALL (-0.5E0) // lg value < LSMALL are e LZERO #defne mnlgexp -lg(-lzero) // ~=-3 dule LgAdd(dule x dule y) { dule empdffz; f (x<y) { emp = x; x = y; y = emp; } dff = y-x; //nce ha dff <= 0 f (dff<mnlgexp) // f y far maller han x reurn (x<lsmall)? LZERO:x; ele { z = exp(dff); reurn x+lg(.0+z); } } S - Berln Chen 44

45 Bac rlem 3 f HMM Inuve Vew Hw adu (re-emae) he mdel parameer =(AB) maxmze (O OL ) r lg(o OL )? Belngng a ypcal prlem f nferenal ac he m dffcul f he hree prlem ecaue here n nwn analycal mehd ha maxmze he n praly f he ranng daa n a cle frm L lg O O... OL lg O l L l lg R O l lgs O l S l l all S - Suppe ha we have L ranng uerance fr he HMM -S :a ple ae equence f he HMM he lg f um frm dffcul deal wh he daa ncmplee ecaue f he hdden ae equence Well-lved y he Baum-Welch (nwn a frward-acward) algrhm and EM (Expecan-Maxmzan) algrhm Ierave updae and mprvemen Baed n Maxmum Lelhd (ML) crern S - Berln Chen 45

46 Maxmum Lelhd (ML) Eman: A Schemac Depcn (/) Hard Agnmen Gven he daa fllw a mulnmal drun Sae S (B S )=/4=0.5 (W S )=/4=0.5 S - Berln Chen 46

47 Maxmum Lelhd (ML) Eman: A Schemac Depcn (/) Sf Agnmen Gven he daa fllw a mulnmal drun Maxmze he lelhd f he daa gven he algnmen Sae S O O Sae S (B S )=( )/ ( ) =.6/.5=0.64 (W S )=( )/ ( ) =0.9/.5= (B S )=(0.3+0.)/ ( ) =0.4/.5=0.7 (W S )=( )/ ( ) =0./.5=0.73 S - Berln Chen 47

48 S - Berln Chen 48 Bac rlem 3 f HMM Inuve Vew (cn.) Relanhp eween he frward and acward varale a... a... O O

49 S - Berln Chen 49 Bac rlem 3 f HMM Inuve Vew (cn.) Defne a new varale: raly eng a ae a me and a ae a me + Recall he perr praly varale: m n n mn n m a a a O λ O λ O λ ) (fr Ο λ O O m m m a d repreene can e al : e B B A p B A p +

50 Bac rlem 3 f HMM Inuve Vew (cn.) ( 3 = 3 4 = O )= 3 (3)*a 3 * ( 4 )* (4) 3 Sae me O O O 3 O - O S - Berln Chen 50

51 Bac rlem 3 f HMM Inuve Vew (cn.) O λ expeced numer f rann frm ae ae n O O expeced numer f rann frm ae n A e f reanale re-eman frmula fr {A} O expeced freqency (numer f me) n ae expeced numer f ran n frm ae ae expeced numer f ran n frm ae a me a - Frmulae fr Sngle ranng Uerance - ξ γ S - Berln Chen 5

52 Bac rlem 3 f HMM Inuve Vew (cn.) A e f reanale re-eman frmula fr {B} Fr dcree and fne ervan (v )=( =v =) v v expeced numer f me n ae and ervng expeced numer f me n ae yml v uch ha v Fr cnnuu and nfne ervan (v)=f O S ( =v =) M v c v μ Σ M ; c exp μ L / Σ v μ v Mdeled a a mxure f mulvarae Gauan drun S - Berln Chen 5

53 S - Berln Chen 53 Bac rlem 3 f HMM Inuve Vew (cn.) Fr cnnuu and nfne ervan (Cn.) Defne a new varale he praly f eng n ae a me wh he -h mxure cmpnen accunng fr M m m m m c c p m p m p m p m p m p m m m ; ; (ervan - ndependen aumpn appled)... Σ μ Σ μ λ λ λ λ O λ O λ λ O λ O O λ O λ O λ O λ c c c 3 3 Drun fr Sae M m m : e B B A p B A p

54 Bac rlem 3 f HMM Inuve Vew (cn.) Fr cnnuu and nfne ervan (Cn.) c expeced numer f me n ae and mxure expeced numer f me n ae M γ m γ m μ weghed average (mean) f erva n a ae and mxure Σ weghed cvarancef ervan a ae μ μ and mxure Frmulae fr Sngle ranng Uerance S - Berln Chen 54

55 Bac rlem 3 f HMM Inuve Vew (cn.) Mulple ranng Uerance F/B F/B F/B 台師大 3 S - Berln Chen 55

56 Bac rlem 3 f HMM Inuve Vew (cn.) Fr cnnuu and nfne ervan (Cn.) expeced freqency (numer f me) n ae a me ( ) L L l l a expeced numer f rann frm ae ae expeced numer f rann frm ae L l - l ξ l L l - l γ l c expeced numer f me n ae and mxure expeced numer f me n ae L l l γ l L l M l γ l m m μ weghed average (mean) f ervana ae and mxure L l l l L l l l Σ weghed cvarance f ervana ae and mxure L l l l μ μ L l l l Frmulae fr Mulple (L) ranng Uerance S - Berln Chen 56

57 Bac rlem 3 f HMM Inuve Vew (cn.) Fr dcree and fne ervan (cn.) expeced freqency (numer f me) n ae a me ( ) L L l l a expeced numer f rann frm ae ae expeced numer f rann frm ae L - l ξ l L - l l l γ l v v expeced numer f me n ae and ervng ymlv expeced numer f me n ae L l l l uch ha v L l l l Frmulae fr Mulple (L) ranng Uerance S - Berln Chen 57

58 Semcnnuu HMM he HMM ae mxure deny funcn are ed geher acr all he mdel frm a e f hared ernel he emcnnuu r ed-mxure HMM ae upu raly f ae M M f v μ Σ -h mxure wegh -h mxure deny funcn r -h cdewrd f ae (hared acr HMM M very large) (dcree mdel-dependen) A cmnan f he dcree HMM and he cnnuu HMM A cmnan f dcree mdel-dependen wegh ceffcen and cnnuu mdel-ndependen cde praly deny funcn Becaue M large we can mply ue he L m gnfcan value f v Experence hwed ha L ~3% f M adequae aral yng f f fr dfferen phnec cla v S - Berln Chen 58

59 S - Berln Chen 59 Semcnnuu HMM (cn.) 3 3 M.... M.... M μ Σ μ Σ M M Σ μ Σ μ

60 HMM plgy Speech me-evlvng nn-anary gnal Each HMM ae ha he aly capure me qua-anary egmen n he nn-anary peech gnal A lef--rgh plgy a naural canddae mdel he peech gnal (al called he ead-n-a-rng mdel) I general repreen a phne ung 3~5 ae (Englh) and a yllale ung 6~8 ae (Mandarn Chnee) S - Berln Chen 60

61 Inalzan f HMM A gd nalzan f HMM ranng : Segmenal K-Mean Segmenan n Sae Aume ha we have a ranng e f ervan and an nal emae f all mdel parameer Sep : he e f ranng ervan equence egmened n ae aed n he nal mdel (fndng he pmal ae equence y Ver Algrhm) Sep : Fr dcree deny HMM (ung M-cdewrd cde) he numer f vecr wh cde ndex n ae he numer f vecr n ae Fr cnnuu deny HMM (M Gauan mxure per ae) cluer he ervan vecr w m m whn each ae numer f vecr clafed n cluer m f ae dvded y he numer f vecr n ae n a e f ample mean f he vecr clafed n cluer m f ae m ample cvarance marx f he vecr clafed n cluer m f ae Sep 3: Evaluae he mdel cre If he dfference eween he prevu and curren mdel cre greaer han a hrehld g ac Sep herwe p he nal mdel generaed M 3 cluer S - Berln Chen 6

62 Inalzan f HMM (cn.) ranng Daa Mdel Reeman Emae parameer f Oervan va Segmenal K-mean SaeSequence Segmeman Inal Mdel Mdel Cnvergence? O YES Mdel arameer S - Berln Chen 6

63 Inalzan f HMM (cn.) An example fr dcree HMM 3 ae and cdewrd 3 Sae O O O 3 O 4 O 5 O 6 O 7 O 8 O 9 O 0 (v )=3/4 (v )=/4 (v )=/3 (v )=/3 3 (v )=/3 3 (v )=/3 v v S - Berln Chen 63

64 Inalzan f HMM (cn.) An example fr Cnnuu HMM 3 ae and 4 Gauan mxure per ae 3 Sae O O O K-mean { } { } Glal mean Cluer mean Cluer mean { } { } S - Berln Chen 64

65 Knwn Lman f HMM (/3) he aumpn f cnvennal HMM n Speech rceng he ae duran fllw an expnenal drun Dn prvde adequae repreenan f he empral rucure f peech d a a Fr-rder (Marv) aumpn: he ae rann depend nly n he rgn and denan Oupu-ndependen aumpn: all ervan frame are dependen n he ae ha generaed hem n n neghrng ervan frame Reearcher have prped a numer f echnque addre hee lman ale hee lun have n gnfcanly mprved peech recgnn accuracy fr praccal applcan. S - Berln Chen 65

66 Knwn Lman f HMM (/3) Duran mdelng gemerc/ expnenal drun emprcal drun Gamma drun Gauan drun S - Berln Chen 66

67 Knwn Lman f HMM (3/3) he HMM parameer raned y he Baum-Welch algrhm (r EM algrhm) were nly lcally pmzed Lelhd Curren Mdel Cnfguran Mdel Cnfguran Space S - Berln Chen 67

68 Hmewr- (/) 0.34 {A:.34B:.33C:.33} {A:.33B:.34C:.33} {A:.33B:.33C:.34} ranse :. ABBCABCAABC. ABCABC 3. ABCA ABC 4. BBABCAB 5. BCAABCCAB 6. CACCABCA 7. CABCABCA 8. CABCA 9. CABCA ranse :. BBBCCBC. CCBABB 3. AACCBBB 4. BBABBAC 5. CCA ABBAB 6. BBBCCBAA 7. ABBBBABA 8. CCCCC 9. BBAAA S - Berln Chen 68

69 Hmewr- (/). leae pecfy he mdel parameer afer he fr and 50h eran f Baum-Welch ranng. leae hw he recgnn reul y ung he ave ranng equence a he eng daa (he -called nde eng). *Yu have perfrm he recgnn a wh he HMM raned frm he fr and 50h eran f Baum-Welch ranng repecvely 3. Whch cla d he fllwng eng equence elng? ABCABCCAB AABABCCCCBBB 4. Wha are he reul f Oervale Marv Mdel were nead ued n and 3? S - Berln Chen 69

70 Ilaed Wrd Recgnn Wrd Mdel M p X M Lelhd f M Wrd Mdel M Speech Sgnal Feaure Exracn Feaure Sequence X p X M Wrd Mdel M V p X M V Lelhd f M Lelhd f M V M Le Wrd Selecr Lael X arg max px M M ML Ver Apprxman Lael X arg max max px S M S Wrd Mdel M Sl p X M Sl Lelhd f M Sl S - Berln Chen 70

71 Meaure f ASR erfrmance (/) Evaluang he perfrmance f aumac peech recgnn (ASR) yem crcal and he Wrd Recgnn Errr Rae (WER) ne f he m mpran meaure here are ypcally hree ype f wrd recgnn errr Suun An ncrrec wrd wa uued fr he crrec wrd Delen A crrec wrd wa med n he recgnzed enence Inern An exra wrd wa added n he recgnzed enence Hw deermne he mnmum errr rae? S - Berln Chen 7

72 Meaure f ASR erfrmance (/) Calculae he WER y algnng he crrec wrd rng agan he recgnzed wrd rng A maxmum urng machng prlem Can e handled y dynamc prgrammng Example: deleed Crrec : he effec clear Recgnzed: effec n clear WER+ WAR =00% Errr analy: ne delen and ne nern Meaure: wrd errr rae (WER) wrd crrecn rae (WCR) wrd accuracy rae (WAR) Wrd Wrd Wrd mached nered mached Mgh e hgher han 00% Su. Del. In. wrd Errr Rae 00% 50%. f wrd n he crrec enence 4 Mached wrd 3 Crrecn Rae 00% 75%. f wrd n he crrec enence 4 Mached - In. wrd 3 Accuracy Rae 00% 50%. f wrd n he crrec enence 4 Mgh e negave S - Berln Chen 7