A Decision Theoretic Formulation for Robust Automatic Speech Recognition
CONTENTS +PVTQFWEVKQP
3.6 Robust Decision Rules .1 Decision Rule Robustness
3.6.3 Bayesian Predictive Classification Rule
#U + FKUEWUUGF DGHQTG OKPKOCZ ENCUUKſECVKQP VTKGU VQ JCPFNG VJG YQTUV ECUG OKUOCVEJ D[ CUUWOKPI C WPKHQTO FKUVTKDWVKQP KP VJG WPEGTVCKPV[ PGKIJDQTJQQF HQT CNN RQUUKDNG FGXKCVKQPU HTQO VJG PQOKPCN RCTCOGVGTU¼ +PUVGCF QH CUUKIPKPI CPQVJGT RQKPV GU VKOCVG CU FQPG KP VJG OKPKOCZ ENCUUKſECVKQP TWNG FKUEWUUGF CDQXG QPG ECP CNUQ average outVJG GHHGEV QH VJG RQUUKDNG OQFGNKPI CPF GUVKOCVKQP GTTQTU D[ CUUWOKPI C IGPGTCN RTKQT 2&( HQTVQ EJCTCEVGTK\G VJG RCTCOGVGT XCTKCDKNKV[ YJKNG OCMKPI ENCU UKſECVKQP FGEKUKQPU +P VJKU YC[ C PGY TQDWUV FGEKUKQP UVTCVGI[ ECP DG FGTKXGF CPF KU QHVGP TGHGTTGF VQ CU CBayesian predictive classification$2% TWNG = ? .GV WU EQPUKFGT VJG WPEGTVCKPV[ QH VJG OQFGN RCTCOGVGTUD[ VTGCVKPI VJGO CU KH VJG[ YGTG TCPFQO 1WT RTKQT MPQYNGFIG CDQWVKU CUUWOGF VQ DG UWOOCTK\GF KP C MPQYP LQKPVa prioriFGPUKV[´¼µ UGVU QH RCTCOGVGTU QH VJG RTKQT 2&( QHVGP TGHGTTGF VQ CU hyperparameters YJKEJ CTG CUUKIPGF XCNWGU D[ VJG KPXGUVKICVQT 5WEJ RTKQT KPHQTOCVKQP OC[ HQT GZCORNG EQOG HTQO UWDLGEV OCVVGT EQPUKFGTCVKQPU CPFQT HTQO RTGXKQWU GZRGTKGPEGU (QT VJG UKORNKEKV[ QH VJG HQNNQYKPI FKUEWUUKQP NGV WU HWTVJGT CUUWOG VJCV
)KXGP C VTCKPKPI UGV CU FGUETKDGF CV VJG DGIKPPKPI QH 5GEVKQP VJG WPEGT VCKPV[ CDQWVECP DG TGFWEGF D[ GXQNXKPI´¼µ
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#RRCTGPVN[ VJGTG CTG OCP[ YC[U VQ GXQNXGYJKEJ FGRGPF QP VJG RWTRQUG QH VJG OQFGNKPI KP OKPF VJG MPQYNGFIGKPHQTOCVKQP UQWTEGU WUGF CPF VJG RQUUKDNG EQPUVTCKPVU KORQUGF
= ? +V KU CV VJKU RQKPV VJCV QWT RTQRQUCN FGRCTVU HTQO VJG EQPXGPVKQPCN VTGCV OGPV KP UVCVKUVKEU %QPXGPVKQPCNN[´¼µ
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KU GXQNXGF D[ EQPUVTWEVKPI VJG HQNNQYKPI RQUVGTKQT 2&(
6JKU RQUVGTKQT 2&(KPENWFGU CNN QH VJG KPHQTOCVKQP KPJGTKVGF HTQO VJG RTKQT MPQYNGFIG´¼µ
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CPF NGCTPGF HTQO VJG VTCKPKPI FCVC %QPXGPVKQPCNN[
QPG FGTKXGU Cpoint estimate HTQO GI /#2 GUVKOCVG CPF VJGP WUG VJG RNWIKP /#2 FGEKUKQP TWNG HQT TGEQIPKVKQP 6JG EQPXGPVKQPCN RNWIKP /#2 FGEKUKQP TWNG DCUGF QP VJG /. GUVKOCVG QH VJG OQFGN RCTCOGVGTUECP DG VTGCVGF CU C URGEKCN ECUG QH VJG CDQXG /#2 GUVKOCVG YKVJ C PQPKPHQTOCVKXG RTKQT
*QYGXGT KP QWT RTQRQUCN YG FQ PQV WUGOGEJCPKECNN[ +PUVGCF YG CFQRV C OQTG ƀGZKDNGempirical BayesCRRTQCEJ KP YJKEJ C URGEKſE RCTCOGVTKE 2&(
KU WUGF VQ TGRTGUGPV QWT WPEGTVCKPV[ CDQWVCHVGT QDUGTXKPI 6JG KPVTCEVCDKNKV[
QH FKTGEVN[ ECNEWNCVKPIHQT VJG RQRWNCT OQFGNU KP #54 UWEJ CU *//U KU PQV VJG QPN[ TGCUQP HQT VJG CDQXG RTQRQUCN # OQTG KORQTVCPV TGCUQP KU VJCV WUKPI
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KPUVGCF QH VQ TGRTGUGPV VJG prior uncertaintyYKVJ TG URGEV VQ TGEQIPK\KPI RTQXKFGU C ƀGZKDNG YC[ VQ KPEQTRQTCVG CPF OCMG WUG QH QVJGT MPQYNGFIG UQWTEGU YJKEJ OC[ DG CXCKNCDNG KP CFFKVKQP VQCPF´¼µ
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CPFQT GXGP VQ EQPUKFGT VJG OQFGNKPI KPVGPVKQP (QT GZCORNG VJG UGV QH J[RGTRC TCOGVGTU£
EQWNF DG GUVKOCVGF HTQO VTCKPKPI FCVC QT URGEKſGF WUKPI UQOG GORKTKECN TGCUQPKPI QT VJGKT EQODKPCVKQP = ? (WTVJGTOQTG KH VJG VTCKP KPI FCVC KU PQVrepresentative GPQWIJ VJGP UWEJ NGCTPGF OKIJV PQV DG KPHQTOCVKXG GPQWIJ VQ JGNR TGEQIPK\G +P VJKU ECUG DGHQTG KPXQMKPI VJG TGEQIPK VKQP RTQEGUU YG ECP ſTUV KORTQXGD[ WUKPI VJG KPHQTOCVKQP GODGFFGF KP VJG QDUGTXCVKQPKVUGNH +P CP[ ECUG YG WUG£
IGPGTKECNN[ VQ TGRTGUGPV QWT prior uncertaintyCDQWVLWUV DGHQTG OCMKPI VJG FGEKUKQP QP +P VJKU YC[ YG CTG GUUGPVKCNN[ EQPUKFGTKPI VJG HQNNQYKPI CFOKUUKDNG FKUVQTVGF UGV QH FCVC OQFGN£
YJGTG YG ECP XKGY VJGCU C RCTCOGVGT VQ EJCTCEVGTK\G VJG DTQCFPGUU QH VJG FKUVTK DWVKQP£ QT GSWKXCNGPVN[ VJG FGITGG QH VJG FKUVQTVKQP $CUGF QP VJG
CTG ECNNGFpredictive densities= ? DGECWUG YG ECP XKGY£
CU C HWPEVKQP QH VTCKPKPI UCORNGU 6JGP WPFGT VJG NQUU HWPEVKQP VJG RTGFKEVKXG
FGEKUKQP TWNG YJKEJ OKPKOK\GU VJG CDQXGKU CU HQNNQYU 6JKU FGEKUKQP TWNG YKNN DG TGHGTTGF VQ CU VJGBayesian predictive classification (BPC) rule 6JTGG MG[ KUUWGU VJWU CTKUG KP $2% PCOGN[
VJG FGſPKVKQP QH VJG RTKQT FGPUKV[£ HQT OQFGNKPI VJG WPEGTVCKPV[
QH VJG OQFGN RCTCOGVGTU
VJG URGEKſECVKQP QH VJG J[RGTRCTCOGVGTU£ CPF VJG GXCNWCVKQP QH VJG RTGFKEVKXG FGPUKV[
+P VJG RCUV UGXGTCN [GCTU UQOG URGEKſE VGEJPKSWGU JCXG DGGP FGXGNQRGF VQ CFFTGUU VJG CDQXG KUUWGU CPF UQOG GPEQWTCIKPI TGUWNVU JCXG DGGP QDVCKPGF 4GCFGTU CTG TGHGTTGF VQ = ? HQT FGVCKNU
+P GZVGPFKPI VJG CDQXGHQTOWNCVGF $2% CRRTQCEJ VJGTG CTG VYQ QRRQUKVG FKTGEVKQPU YJKEJ ECP DG RWTUWGF 1PG FKTGEVKQP KU VQ WUG C UVTWEVWTG OQFGN HQT OQFGNKPI RCTCO GVGT WPEGTVCKPV[ (QT GZCORNG YG ECP WUG
FGPQVG URGEKſE VTCPUHQTOCVKQPU QH¼CPF¼YKVJ RC TCOGVGTU £ CPF TGURGEVKXGN[ +P VJKU YC[ VJG WPEGTVCKPV[ QHECP DG EJCT CEVGTK\GF D[ VJG WPEGTVCKPV[ QH £ 6JG $2% FGEKUKQP TWNG KP ECP VJGP DG OQFKſGF WUKPI VJG HQNNQYKPI RTGFKEVKXG 2&(U
6JG CDQXG KUUWG QH RTKQT URGEKſECVKQP YKNN VJGP DG VTCPUNCVGF KPVQ VJG URGEKſECVKQP QH
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CPF
4GCFGTU CTG TGHGTTGF VQ =? HQT C TGEGPV YQTM CNQPI VJKU NKPG QH VJQWIJV #PQVJGT RQUUKDNG FKTGEVKQP VQ RWTUWG KU VQ IQ DG[QPF VJGmodel parameter uncertaintyD[ EQPUKFGTKPI VJG CFOKUUKDNG FKUVQTVGF FGPUKVKGU CV VJG FKUVTKDWVKQP NGXGN
6JWU VJG FKUVQTVGF FGPUKV[CPF KU C OKZVWTG QH VJG J[RQVJGVKECN FKUVTKDWVKQP£¼
FGUETKDKPI VJG RQUUKDNG FKUVQTVKQPU 6JKU V[RG QH FKUVQTVKQP OQFGN KU VJG OQUV RQRWNCT QPG KP TQDWUV UVCVKUVKEU = ? *QY VQ FGTKXG VJG TGNGXCPV TQDWUV FGEKUKQP TWNG WPFGT VJKU FKUVQTVKQP OQFGN TGOCKPU CP KPVGTGUVKPI RTQDNGO HQT HWVWTG TGUGCTEJ
3.6.4 Discussion
6JG ETWEKCN FKHHGTGPEG DGVYGGP VJG RNWIKP CPF RTGFKEVKXG ENCUUKſGTU KU VJCV VJG HQTOGT CEVU CU KH VJG GUVKOCVGF OQFGN RCTCOGVGTU YGTG VJG VTWG QPGU YJGTGCU VJG RTGFKEVKXG OGVJQFU CXGTCIG QXGT VJG WPEGTVCKPV[ KP RCTCOGVGTU *QYGXGT KH YG WUG VJG RQUVGTKQT 2&(KP 'S FGTKXGF HTQO VJGtraining set FKTGEVN[ VQ UGTXG CU VJG RTKQT 2&( KP RTGFKEVKXG FGEKUKQP OCMKPI $2% YKNN OCMG NKVVNG FKHHGTGPEG HTQO VJG EQPXGPVKQPCN RNWIKP /#2 TWNG KP OCP[ CRRNKECVKQPU 6JKU KU DGECWUG YJCVGXGT KPKVKCN RTKQT 2&(
KU WUGF YJGP C NCTIG COQWPV QH VTCKPKPI FCVC CTG CXCKNCDNG YG YKNN IGV C RQUVGTKQT 2&(YKVJ C UJCTR RGCM 6JKU OCMGU VJG RTGFKEVKXG 2&(U KP 'SU CPF QH NKVVNG FKHHGTGPEG HTQO
CPF
YKVJ VJG /. GUVKOCVGU +P VJG NKOKV KH VJG RQUVGTKQT RTQDCDKNKV[ OCUU QH
KU EQPEGPVTCVGF CV VJG /. GUVKOCVG QDVCKPGF HTQO KV KU GCU[ VQ UGG HTQO 'SU CPF VJCV VJG $2% FGEKUKQP TWNG EQKPEKFGU YKVJ VJG RNWIKP /#2 FGEKUKQP TWNG
*KUVQTKECNN[ VJG RTGFKEVKXG ENCUUKſECVKQP CRRTQCEJ TGEGKXGU NKVVNG CVVGPVKQP KP OCP[
ENCUUKECN UVCVKUVKEU VGZVDQQMU FGURKVG VJG GZKUVGPEG QH OCP[ IQQF YQTMU = ?
#U RQKPVGF QWV D[ 4KRNG[ =? VJKU OC[ DG DGECWUG KV WUWCNN[ OCMGU NKVVNG FKHHGTGPEG HTQO RNWIKP CRRTQCEJGU YKVJKP VJG RTQDNGOU CPF VJG VKIJVN[EQPUVTCKPGF RCTCOGVTKE HCOKNKGU OCP[ UVCVKUVKEKCPU WUG QT EQPUKFGT 0QPGVJGNGUU KV YKNN DGEQOG KORQTVCPV YJGP YG EQPUKFGT OWEJ NCTIGT HCOKNKGU CPF HQTOWNCVG VJG RTQDNGO CRRTQRTKCVGN[ CU UJQYP DGHQTG 6Q QWT MPQYNGFIG KV YCU 0CFCU YJQ ſTUV
CFQRVGF C $2% HQTOWNCVKQP CPF RQKPVGF QWV KVU RQVGPVKCN KP URGGEJ TGEQIPKVKQP CRRNKECVKQPU =? CPF
GZRNKEKVN[ UVCVGF CPF RTQXGF VJG QRVKOCNKV[ QH $2% KP VJG UGPUG QH OKPKOK\KPI QXGTCNN TKUM 4KRNG[ CNUQ FKUEWUUGF VJG RTGFKEVKXG ENCUUKſECVKQP CRRTQCEJ KP VJKU YC[ KP JKU TGEGPV RCVVGTP TGEQIPKVKQP VGZVDQQM =?
*QYGXGT NKMG QVJGT UVCVKUVKEKCPU 0CFCU YCU FKTGEVN[ WUKPI VJG RQUVGTKQT 2&(
VQ UGTXG CU VJG RTKQT 2&( KP RTGFKEVKXG FGEKUKQP OCMKPI CPF ICXG C UKORNG GZCORNG KP YJKEJ Creproducing densityGZKUVU 0Q GZRGTKOGPVCN TGUWNVU YGTG TGRQTVGF CPF VJG RCRGT ENQUGF D[ DTKGƀ[ FKUEWUUKPI VJG FKHſEWNV[ QH CRRN[KPI VJG VJGQT[ VQ *//
DCUGF URGGEJ TGEQIPKVKQP
5VCTVKPI HTQO 0CFCUŏU HQTOWNCVKQP /GTJCX CPF 'RJTCKO =? UWIIGUVGF C UQECNNGF approximate Bayesian (AB) decision ruleHQT URGGEJ TGEQIPKVKQP YJKEJ YCU DCUGF QP VJG IGPGTCNK\GF NKMGNKJQQF TCVKQU EQORWVGF HTQO VJG CXCKNCDNG VTCKPKPI CPF VGUVKPI FCVC 5WEJ CP #$ TWNG QRGTCVGU CU HQNNQYU
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+V KU ENGCT VJCV KH VJG VTCKPKPI UGSWGPEGU CTG EQPUKFGTCDN[ NQPIGT VJCP VJG VGUV UG SWGPEGYJKEJ KU VJG ECUG KP OQUV URGGEJ TGEQIPKVKQP CRRNKECVKQPU VJG RCTCOGVGT UGVVJCV OCZKOK\GU VJG FGPQOKPCVQT QH 'S KU XGT[ ENQUG VQ VJG RCTCOGVGT
UGV VJCV OCZKOK\GU VJG PWOGTCVQT JGPEG VJG HCEVQTKP DQVJ VJG PWOGT CVQT CPF FGPQOKPCVQT KU GUUGPVKCNN[ ECPEGNGF 6JKU OCMGU VJG #$ FGEKUKQP TWNG QH NKVVNG FKHHGTGPEG HTQO VJG RNWIKP /#2 FGEKUKQP TWNG WUKPI CP /. GUVKOCVG QH 6JG #$ FGEKUKQP TWNG KU CNUQ EQORWVCVKQPCNN[ GZRGPUKXG DGECWUG VJG OCZKOK\CVKQP QHQXGTOWUV DG RGTHQTOGF HQT GXGT[ VGUV UGSWGPEG (WTVJGTOQTG CNN QH VJG VTCKPKPI FCVC OWUV DG UVQTGF #NN QH VJGUG HCEVQTU OCMG VJG
#$ FGEKUKQP TWNG KORTCEVKECN HQT OQUV URGGEJ TGEQIPKVKQP CRRNKECVKQPU
#U FKUEWUUGF RTGXKQWUN[ VJG OKPKOCZ ENCUUKſECVKQP TWNG ECP DG XKGYGF CU C VYQUVGR RTQEGFWTG CPF KORNGOGPVGF KP 'S (KTUV GCEJ VGUVKPI WVVGTCPEG KU VTGCVGF CU RQUUKDN[ DGNQPIKPI VQ CP[ YQTF UGSWGPEG CPF C EQPUVTCKPGF /. GUVKOCVG QH VJG TGNCVGF RCTCOGVGTU KU QDVCKPGF 6JGP C RNWIKP /#2 TWNG KU WUGF HQT URGGEJ TGEQI PKVKQP D[ WUKPI VJG WRFCVGF RCTCOGVGTU 6JKU KPVWKVKXG KPVGTRTGVCVKQP QRGPU WR VJG RQUUKDKNKVKGU VQ WUG QVJGT GUVKOCVKQP CRRTQCEJGU GI VJG /#2 CRRTQCEJ KP VJG ſTUV UVGR 5WEJ C OQFKſGF OKPKOCZ FGEKUKQP TWNG YQTMU CU HQNNQYU
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YJGTG KU VJG /#2 GUVKOCVG QH (QT VJG EQPXGPKGPEG QH TGHGTGPEG YG ECNN VJKU OQFKſGF OKPKOCZ FGEKUKQP TWNG CU C Bayesian minimax ruleVQ GORJCUK\G KVU FKHHGTGPEG HTQO VJG OKPKOCZ CRRTQCEJ KP =?
9G JCXG RTGXKQWUN[ FKUEWUUGF VJG $2% CRRTQCEJ CU C PGY FGEKUKQP TWNG YJKEJ CXGT CIGU QWV VJG UCORNKPI GTTQT KP RCTCOGVGT GUVKOCVKQP # TGNCVGF DWV UKORNGT CRRTQCEJ ECP CNUQ DG WUGF (QT GZCORNG HQT C %&*//DCUGF #54 U[UVGO KPUVGCF QH FKTGEVN[
OQFKH[KPI VJG DCUKE FGEKUKQP TWNG QPG ECP CNUQ CUUWOG VJCV VJG %&*// RCTCOGVGTU CTG WPEGTVCKP 6JGP QPG WUGU VJGBayesian predictive densityQH GCEJ )CWUUKCP OKZ VWTG EQORQPGPV VQ UGTXG CU VJG EQORGPUCVGF FKUVTKDWVKQP QH VJCV EQORQPGPV CPF RNWI VJGUG EQORGPUCVGF FKUVTKDWVKQPU KPVQ VJG RNWIKP /#2 FGEKUKQP TWNG KP 'S 6JG CRRTQCEJ KU VJWU ECNNGFBayesian predictive density based model compensation OGVJQF QT UJQTVN[ $2/% OGVJQF VQ FKHHGTGPVKCVG KV HTQO VJG $2% TWNG FGſPGF KP 'S +P =? UWEJ CP KFGC KU GZRNQTGF KP VJG EQPVGZV QH $C[GUKCP URGCMGT CFCRVCVKQP YJGTG C )CWUUKCP RTKQT 2&( HQT OGCP XGEVQT KU CFQRVGF +P =? C UKO KNCT KFGC KU CRRNKGF VQ PQKU[ URGGEJ TGEQIPKVKQP YJGTG C WPKHQTO RTKQT 2&( QP C RTGURGEKſGF WPEGTVCKPV[ PGKIJDQTJQQF HQT OGCP XGEVQT KU CFQRVGF /QTG TGEGPVN[
UKOKNCT KFGCU CTG CRRNKGF VQ VJG VTCPUHQTOCVKQPDCUGF OQFGN EQORGPUCVKQP D[ WUKPI VJG RTGFKEVKXG 2&( QH VJG VTCPUHQTOCVKQP RCTCOGVGTU = ?
3.7 Summary
+P VJKU EJCRVGT YG JCXG TGXKUKVGF VJG FGEKUKQP VJGQTGVKE HQWPFCVKQP QH VJG OQFGTP
#54 VGEJPQNQI[ 9G JCXG GZRNCKPGF UGXGTCN MG[ EQPEGRVU CDQWV VJG QRVKOCN FGEK UKQP TWNG CFCRVKXG FGEKUKQP TWNG CPF TQDWUV FGEKUKQP TWNG 9G JCXG UJQYP JQY VJGUG FGEKUKQP TWNGU ECP DG FGTKXGF WPFGT FKHHGTGPV CUUWORVKQPU CPF QRVKOCNKV[ ETKVGTKC #
ENGCT WPFGTUVCPFKPI QH VJGUG CUUWORVKQPU CPF ETKVGTKC YKNN IWKFG WU VQ CRRTGEKCVG YJ[
VJG EWTTGPV #54 VGEJPQNQI[ KU UQ UWEEGUUHWN KP EGTVCKP CRRNKECVKQPU CPF OQTG KORQT VCPVN[ YJ[ KV HCKNU KP OCP[ QVJGT UKVWCVKQPU %QPUGSWGPVN[ YG CTG CDNG VQ FKUEWUU VJG TCVKQPCNG QH UGXGTCN YC[U QH KORTQXKPI CFCRVKXG FGEKUKQP TWNGU XKC FGEKUKQP RCTCOG VGT CFCRVCVKQP /QUV QH VJG FKUEWUUKQPU KP VJKU EJCRVGT ECP CNUQ DG CRRNKGF VQ QVJGT RCVVGTP TGEQIPKVKQP RTQDNGOU GORNQ[KPI VJG UCOG FGEKUKQPVJGQTGVKE HQTOWNCVKQP
$GHQTG ENQUKPI VJG EJCRVGT YG FQ YCPV VQ RQKPV QWV QPG KORQTVCPV WPUCVKUHCEVQT[ HCEV 9G CTG VTGCVKPI GCEJÏ CU CclassYJKEJ EQWNF OGCP FKHHGTGPV VJKPIU CU GZRNCKPGF CV VJG DGIKPPKPI QH 5GEVKQP +P VJG ECUG QH EQPVKPWQWU URGGEJ TGEQIPKVKQPÏ VCMGU VJG HQTO QH C UGSWGPEG QH QVJGT UOCNNGT NKPIWKUVKE WPKVU UWEJ CU YQTFU KP PQTOCN UGPUG
#NN QH VJG FGEKUKQP TWNGU FGUETKDGF KP VJKU EJCRVGT CKO CV CEJKGXKPI VJG OKPKOWO ENCUUKſECVKQP GTTQT QHÏ KPUVGCF QH VJG YQTF TGEQIPKVKQP GTTQT TCVG YJKEJ KU WUWCNN[
WUGF CU C OGCUWTG QH RTCEVKECN #54 RGTHQTOCPEG #RRCTGPVN[ VJGTG KU C OKUOCVEJ JGTG VQQ 7PHQTVWPCVGN[ VJG OGVJQF VQ FGTKXG C FGEKUKQP TWNG YJKEJ CEJKGXGU VJG OKPKOWO YQTF TGEQIPKVKQP GTTQT TCVG RQUUKDN[ D[ WUKPI C NQUUHWPEVKQP DG[QPF ő Œ TGOCKPU CP KPVGTGUVKPI QRGP RTQDNGO 4GCFGTU CTG TGHGTTGF VQ UQOG KPVGTGUVKPI TGEGPV YQTMU VJCV VT[ VQ CVVCEM VJKU RTQDNGO = ?
+V KU QWT JQRG VJCV VJG KPFGRVJ FKUEWUUKQPU KP VJKU EJCRVGT OC[ KPURKTG HWTVJGT KPPQ XCVKQPU VJCV YKNN NGCF VQ DGVVGT UQNWVKQPU HQT #54 CPF OCP[ QVJGT RCVVGTP TGEQIPKVKQP CRRNKECVKQPU
Acknowledgement
6JG CWVJQT ITCVGHWNN[ CEMPQYNGFIGU VJG EQPVTKDWVKQPU QH JKU RCUV CPF RTGUGPV EQN NCDQTCVQTU KPENWFKPI % %JCP %* .GG * ,KCPI $ /C CPF , 9W 6JKU YQTM YCU HWPFGF D[ ITCPVU HTQO VJG 4)% QH VJG *QPI -QPI 5#4 2TQLGEV 0WODGTU
*-7' CPF *-7'
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=? #ſH[ / CPF 1 5KQJCP ő5GSWGPVKCN PQKUG GUVKOCVKQP YKVJ QRVKOCN HQTIGVVKPI HQT TQDWUV URGGEJ TGEQIPKVKQPŒProc. of ICASSP-2001
=? #ſH[ / 1 5KQJCP CPF %* .GG ő7RRGT CPF NQYGT DQWPFU QP VJG OGCP QH PQKU[ URGGEJ CRRNKECVKQP VQ OKPKOCZ ENCUUKſECVKQPŒIEEE Trans. on Speech and Audio Processing 8QN 0Q RR
=? #KVEJKUQP , CPF + 4 &WPUOQTGStatistical Prediction Analysis %CODTKFIG 7- %CODTKFIG 7PKXGTUKV[ 2TGUU
=? #OCTK 5 ő# VJGQT[ QH CFCRVKXG RCVVGTP ENCUUKſGTUŒIEEE Trans. on Electronic Computers 8QN '% 0Q RR
=? $CJN . 4 ( ,GNKPGM CPF 4 . /GTEGT ő# OCZKOWO NKMGNKJQQF CRRTQCEJ VQ EQPVKPWQWU URGGEJ TGEQIPKVKQPŒIEEE Trans. on Pattern Analysis and Machine Intelligence 8QN 2#/+ 0Q RR /CTEJ
=? $CJN . 4 2 ( $TQYP 2 8 FG 5QW\C CPF 4 . /GTEGT ő/CZKOWO OW VWCN KPHQTOCVKQP GUVKOCVKQP QH JKFFGP /CTMQX OQFGN RCTCOGVGTU HQT URGGEJ TGEQIPKVKQPŒ KPProc. of ICASSP-86 RR
=? $CJN . 4 2 ( $TQYP 2 8 FG 5QW\C CPF 4 . /GTEGT ő'UVKOCVKPI JKFFGP /CTMQX OQFGN RCTCOGVGTU UQ CU VQ OCZKOK\G URGGEJ TGEQIPKVKQP CEEWTCE[Œ IEEE Trans. Speech and Audio Processing 8QN 0Q RR
=? $CMGT , - ő5VQEJCUVKE OQFGNKPI HQT CWVQOCVKE URGGEJ WPFGTUVCPFKPIŒ KP Speech Recognition& 4 4GFF[ GF 0GY ;QTM #ECFGOKE RR
=? $CMGT , - ő6JG &4#)10 U[UVGO Ō CP QXGTXKGYŒIEEE Trans. on Acoustics, Speech, and Signal Processing 8QN #552 RR
=? $CWO . ' ő#P KPGSWCNKV[ CPF CUUQEKCVGF OCZKOK\CVKQP VGEJPKSWGU KP UVCVKU VKECN GUVKOCVKQP HQT RTQDCDKNKUVKE HWPEVKQPU QH /CTMQX RTQEGUUGUŒInequalities 8QN RR
=? %JGPICNXCTC[CP 4 ő5RGCMGT CFCRVCVKQP WUKPI FKUETKOKPCVKXG NKPGCT TGITGU UKQP QP VKOGXCT[KPI OGCP RCTCOGVGTU KP VTGPFGF *//ŒIEEE Signal Pro-cessing Letters 8QN 0Q RR
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