Hidden Markov Model and Its Applications in Speech Recognition A Tutorial
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1 Reogo ehes Hdde ov odel d Is Alos Reogo A ol seeh Fee Alyss seeh e eeseo e Reogo oly eogo deso B.H. Jg Geog Ise of ehology Rles ees odels d Jg BIRS l 0/0/007 Ssl e Reogo ole ole See: o eogze/lssfy ow osevo X s oe of lsses of eves o sees wh oly of eo Defo of eo d eo oly - Codol Eo: gve X he s ssoed wh dedg h s lss eve R C X e C X Eeed Eo: C X oly h X he gve osevo s lss eve e s he os of lssfyg lss eve s lss eveslly e 0 e 0 E R C X X X dx whee C X s he deso sed o oly de o How shold C X e de o heve eo oly? X Byes Deso heoy oe: R C X If we se he oly: e C X d sose C A he R C X X R C X Why? A R C f X So he es oly s C e e 0 X C g C X I s he so-lled A oseo A deso. Cve: How do we ow ll C X L fo y X? e C X > R C C X C X < C X C X C g C X C e C X 3 Jg BIRS l 0/0/007 4 Jg BIRS l 0/0/007
2 Reeseo of & Sgl G & Sy How he oee of wods seee s goveed Leo/Doy How wod s sosed o e ooed s seee of y sods Aos-hoes How y sod d/o seee of y sods e sosed o e oded wh he loy s odels fo odo of essge Soe W S W A S X A Lgs Chel W S A essge elzed s wod seee W Aloy Chel wods elzed s seee of sods S Aos Chel sods eeved y sde hogh os e A ssso Chel X sgl oveed fo os o ele sed dsoed d eeved fo oessg s X 5 Jg BIRS l 0/0/007 6 Jg BIRS l 0/0/007 Lgge s Fe Se he Leo & hoology lso s FS o FS ees: ls se: flgh COOSIE Fe Se ewo eed I go o fo fly flgh h leves dee_y Dlls y_e: Dlls sl sh ow sl w l sl Begg se l e s sl Fl se oe-deede hoee odel eles: φ-sh-ow φ--l -l-e l-e- 7 Jg BIRS l 0/0/007 8 Jg BIRS l 0/0/007
3 eol Vo Vos le fele hese e hee el wvefos fo he wod y hey e vey dffee. How o hese vsly dffee elzos he se sohs odel so s o llow egfl defo of he oess s wod y? A doly sohs oess lled e dso Hdde ov odel 9 Jg BIRS l 0/0/007 0 Jg BIRS l 0/0/007 Hdde ov odel osevo L Se seee 0 L π 0 Eh se eeses oess of esle osevos Ie-oess so s goveed y fe se ov h oesses e sohs d dvdl osevos do o edely defy he se. Hdde ov odels - Sefos L s he seee of osevos L s he seee of ses he syse s 0 e of ses of he ov h Se so oly A [ ] fo ll I-se osevo oly dso fos B { } λ.e. eezed y λ Il se oly dso π [ π π L π ] whee π [ 0 ] he le π A B defes hdde ov odel. π Jg BIRS l 0/0/007 Jg BIRS l 0/0/007
4 hee Bs oles of H Gve he osevo seee L d odel π A B how do we effely oe? Gve he osevo seee L d he odel π A B how do we fd oesodg se seee 0 L h s ol soe sese? Gve osevo seee X o e of seees { } how o ese ees he odel se π A B? Evlo of H oly De evlo wll volve llos. α π 0 π 0 he Fowd oede Defe α { L Is he oly of he l osevo seee L o e d he syse s se e. 3 Jg BIRS l 0/0/007 4 Jg BIRS l 0/0/007 Fowd oede Ilzo: α 0 π L Ido: α+ α + 0 eo: α e α α 3 α 3 α + + L L L ~ llos Le Ol Se Seee Sevel ossles he se seee h zes he o seosevo oly o 0 g g π he se seee h osss of dvdl ses zg he oseo oly gve he osevo γ.e. oly of eg se e gve γ [ ] [ ] 5 Jg BIRS l 0/0/007 6 Jg BIRS l 0/0/007
5 ee Eso Lelhood Eso fd o ze Eso Algohs: s dsee - B & Eg 967 s log-ove oos - B ee Soles d Wess 970 s elllly sye - Loe 98 s e of log-ove o elllly sye Bell Ls 984 Fo ov Ch o Dsee H A 3-se ov Ch δ Rd δ Bl 3 δ B A 4-se dsee hdde ov odel 4 3 Coos e desy hdde ov odel oe y desy fo wh y eso ovded h he e of e ooes s osed. Rd δ Rd Rd δ Rd + Bl δ Bl + B δ B + Bl δ Bl + B δ B Rd δ Rd Rd δ Rd Bl δ Bl 3 + B δ B Bl δ Bl 4 + B δ B 4 7 Jg BIRS l 0/0/007 8 Jg BIRS l 0/0/007 I-Se Lol Osevo Dsos lve e Dso Dsee dsos s } d s { s } { Log-ove oly desy fos s oos- vled d log log f s ove fo Elllly sye oly desy fos f g dµ g Geel e oly desy fos whee f Elllly Sye Dso e of Elllly Sye Dso gl 9 Jg BIRS l 0/0/007 0 Jg BIRS l 0/0/007
6 Jg BIRS l 0/0/007 We sse he soe h odes s oegessve oe wh he followg goveg eo Cosde osevo veo e.g. fe of seeh sgl whee eh s wvefo sle. Aoegessve H 0 K L 0 + K e Rell LC Whee e Gss deede delly dsed do vles wh zeo e d ve d e he oegessve o edo oeffes. As he he df of eoes } { σ d legh of K / / σ δ πσ K e f δ K whee d I sho-e lyss oe eh veo wold y e de. e Jg BIRS l 0/0/007 Eh dso s hezed y ooelo veo whh defes he edo veo. I e-eso he sfoo o ooelo veo fo eh e ooe s o o vege of he ooelo veos eh weghed y he oesodg oly of eg ssoed wh he l e ooe Eh se s ssoed wh e ooes eh e ooe s defed y oegessve df: e Aoegessve H / / K e σ δ πσ whee γ γ β α β α γ Jg BIRS l 0/0/007 3 Re-eso:. Gve defe he ly fo s fo of. ze he ly fo ove d o 3. Rele wh d ee he ove l soy o s ehed. L Re-eso... E log Q Defe Q Aly fo heoe: If he. he ely s s less los eveywhee. Q Q } ˆ { ˆ Ψ Q Q Τ hs s he B-Welh e-eso hll-lg lgoh o heve L sl o he E eeo-zo lgoh. Jg BIRS l 0/0/007 4 Reeso sfoo } ˆ { ˆ Ψ Q Q Τ 0 ] [ π Fo Gss e desy H: Il se oly: Se so oly: e weghs: Σ f µ Gss ees: µ Σ µ µ
7 Ieeo of Re-eso Fol Segel K-es Algoh Σ { π A [ ] B} { π A [ ] B} µ µ µ oly veso of oso fo se o se oso fo se oly veso of oso fo se log e oso fo se Eeed o oly-weghed vege o ove log eh e ooe eh se df. ovo: deve good eses of he deses s eed fo d ovegee of e-eso oede. Illy: g se of lle seees of osevos l odel ese. oede: sege eh osevo seee o ses sg Ve oede. Fo dsee osevo deses ode ll osevos se sg he -odewod odeoo gvg e of veos wh odeoo de se dvded y he e of veos se. fo oos osevo deses lse he osevos se o se of lses gvg g 5 Jg BIRS l 0/0/007 6 Jg BIRS l 0/0/007 Geg he Rgh Sss Beyod Lelhood H wo ovg Qesos Fes. Hve we ee le o hoose he gh odels fo seeh eogo? o we eve gee o he gh seeh eeseo I.e. he osevo se. We e sll wog o he fo-ed he sfoo d y ohe eled sses. Effey s lso l. Fe/se Segel eeseos e dvge of sly ewee de fes o deve sle eeseos e dvge of y oes o deve osse eeseos. If o wh s he leve eogze desg le o follow? We eed o eee he ole d ss of dso eso eogze desg eff he gol of seeh eogo eg o hve he les eogo eos d e-fole he ole d segy so s o o he es efoe os d hghes effey. 7 Jg BIRS l 0/0/007 8 Jg BIRS l 0/0/007
8 efoe Isse yl Wod Eo Res efoe y & oely H A- L few wods solo Bee odels oe g d DW H 980 Adve Dsve H Dsve H 990 s Coley voly sze seg & s oss Deloyle efoe heshold soeos oveso fo of 7 ese dg eo e 9 Jg BIRS l 0/0/ Jg BIRS l 0/0/007 DARA Reogo Beh Reogo ogess WORD ERROR RAE 00% 0% % Red Soeos 0 AIS Resoe gee Swhod Covesol WSJ 5 Ved ohoe osy foeg Bods swhd foeg AB Wh los of g d Coesy IS 999 DARA HUB-4 Reo lle e l. d Swhd elll Seg Syle Soeos Fle Red Coeed Isoled Wod wod sog 980 dg sgs voe ods syse dve dlog e dlg fo fll y voe see vefo -wy dlog ewo ge & ellge essgg deoy ssse l oveso 990 offe do so Voly Sze 3 Jg BIRS l 0/0/007 3 Jg BIRS l 0/0/007
9 H Reogo vs ASR ACHIE ERROR % hes Oefo Hs HUA ERROR % Dgs R-L AB- WSJ R-ll AB-o SWBD WSJ-dB ASR Chlleges Ahed Vly of sods e.g. oo wods hses wh sgle see oss sees oss vos ohoes ssso hels Bgod ose od ose f os ose god oveso doo sl See odo eos hesos eeos seeh eled effes lly ds wods wod/sod o-lo he lgge l eessos seeh oveso Se of odel Rosess & do of odel 33 Jg BIRS l 0/0/ Jg BIRS l 0/0/007 oo Vos I yl Swhod d se sed o DARA eo y Dgo Syses Refeee Doy - osed fo Cll-hoe d Swhod 3 wods g se of 8000 ds wods 3500 of whh hve lle oos. es D Se wod oes 900 ds wods 00 oos odg o hoe so 00 oes 47% ooed oely odg o doy 500 ew oos eege fo olee ovege Ohe es: 650 wods wh sgle oo he hs 36 oos shw s oo of 7 wods 38 oos e hooy wh oe h 5 wods he d o e os ofsle wh 7 oos oo Led Soe Lgge Udesdg Iee he eg of ey wods d hses he eogzed seeh sg d he o os h he seeh desdg syse shold e e desdg ofe e heved who oely eogzg evey wod y led ss ehodology: elo s g sy d s ses o es he ge of eg ssoed wh he eogzed wod sg elo sle wods d hses o hgh foo wod seees o oe eg Alos: oo of ole oeo-sed ss e.g. soe e log odeg fo fllg syses ovsog of ew seves soe hel les e. Chlleges: wh goes eyod sle lssfos syses elow fll l Lgge voe dloge syses 35 Jg BIRS l 0/0/ Jg BIRS l 0/0/007
10 Sy H s he do ehod o seeh eogo Coos e desy H s he evle odel se h heves es esls y Alos of H hve ee odeed o eywod sog seeh desdg d he slo o-seeh eled los e eegg s well. 37 Jg BIRS l 0/0/007
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