論文紹介: How Contextual are Contextualized Word Representations?

)PX$POUFYUVBMBSF $POUFYUVBMJ[FE8PSE 3FQSFTFOUBUJPOT ,BXJO&UIBZBSBKI &./-1     BS9JWUJUMF)PX$POUFYUVBMBSF$POUFYUVBMJ[FE8PSE 3FQSFTFOUBUJPOT $PNQBSJOHUIF(FPNFUSZPG#&35
&-.P BOE(15&NCFEEJOHT 5.6,PNBDIJMBC.4BUPSV,BUTVNBUB

"CTUSBDU w %FFQOFVSBMMBOHVBHFNPEFMTIBWFTVDDFTTGVMMZDSFBUFE DPOUFYUVBMJ[FEXPSESFQSFTFOUBUJPOT  &-.P 1FUFSTFUBM MBZFSCJ-45.  #&35 %FWMJOFUBM
MBZFSUSBOTGPSNFS&ODPEFS  (15 3BEGPSEFUBM MBZFSUSBOTGPSNFS%FDPEFS w 5IFTFSFQSFTFOUBUJPOTSFNBJOQPPSMZVOEFSTUPPE  )PXDPOUFYUVBMBSFUIFTFDPOUFYUVBMJ[FEXPSESFQSFTFOUBUJPOT   "SFUIFSFJOpOJUFMZNBOZDPOUFYUTQFDJpDSFQSFTFOUBUJPOTUIBU #&35BOE&-.PDBOBTTJHOUPFBDIXPSE w 5IJTQBQFSBOTXFSUIFTFRVFTUJPOCZTUVEZJOHUIFHFPNFUSZPGUIF SFQSFTFOUBUJPOTQBDFGPSFBDIMBZFSPG&-.P #&35 BOE(15 !2

&YQFSJNFOU4FUUJOH w 5IFDPOUFYUVBMJ[JOHNPEFMT  &-.P#&35(15 JOQVUMBZFSUIMBZFS w %BUB  454 w
.FBTVSFTPG$POUFYUVBMJUZ  4FMGTJNJMBSJUZ  *OUSBTFOUFODFTJNJMBSJUZ  .BYJNVNFYQMBJOBCMFWBSJBODF !3

4FMGTJNJMBSJUZ w -FUCFBXPSEUIBUBQQFBSTJOTFOUFODFT  BUJOEJDFTSFTQFDUJWFMZ  ˠ w -FUCFBGVODUJPOUIBUNBQTUPJUTSFQSFTFOUBUJPO JOMBZFS w 4FMGTJNJMBSJUZ
w 4FMGTJNJMBSJUZJTUIFBWFSBHFDPTJOFTJNJMBSJUZCFUXFFOJUT DPOUFYUVBMJ[FESFQSFTFOUBUJPOTBDSPTTJUTOVOJRVFDPOUFYUT !4 w {s1 , . . . , sn } {i1 , . . . , in } w = s1 [i1 ] = . . . = sn [in ] fl (s, i) s[i] l SelfSiml (w) = 1 n2 − n ∑ j ∑ k≠j cos (fl (sj , ij), fl (sk , ik))

*OUSBTFOUFODFTJNJMBSJUZ w -FUCFBTFOUFODFUIBUJTBTFRVFODFPGOXPSET w -FUCFBGVODUJPOUIBUNBQTUPJUTSFQSFTFOUBUJPOJO MBZFS w *OUSBTFOUFODFTJNJMBSJUZ  w *OUSBTFOUFODFTJNJMBSJUZPGBTFOUFODFJTUIFBWFSBHFDPTJOF
TJNJMBSJUZCFUXFFOJUTXPSESFQSFTFOUBUJPOTBOEUIFTFOUFODF WFDUPS  ˠ5IJTNFBTVSFDBQUVSFTIPXDPOUFYUTQFDJpDJUZNBOJGFTUT  JOUIFWFDUPSTQBDF !5 s ⟨w1 , . . . , wn ⟩ fl (s, i) s[i] l IntraSiml (s) = 1 n ∑ i cos ( ⃗ sl , fl (s, i)) where ⃗ sl = 1 n ∑ i fl (s, i)

.BYJNVNFYQMBJOBCMF WBSJBODF w -FUCFBXPSEUIBUBQQFBSTJOTFOUFODFT  BUJOEJDFTSFTQFDUJWFMZ  ˠ w -FUCFBGVODUJPOUIBUNBQTUPJUTSFQSFTFOUBUJPOJOMBZFS w JTUIFPDDVSSFODFNBUSJYPGXPSEX 
BSFUIFpSTUNTJOHVMBSWBMVFTPGUIJTNBUSJY w .BYJNVNFYQMBJOBCMFWBSJBODF w .&7JTUIFQSPQPSUJPOPGWBSJBODFJOX`TDPOUFYUVBMJ[FESFQSFTFOUBUJPOT GPSBHJWFOMBZFSUIBUDBOCFFYQMBJOFECZUIFJSpSTUQSJODJQBMDPNQPOFOU w *UHJWFTVTBOVQQFSCPVOEPOIPXXFMMBTUBUJDFNCFEEJOHDPVME SFQMBDFBXPSE`TDPOUFYUVBMJ[FESFQSFTFOUBUJPOT !6 w {s1 , . . . , sn } {i1 , . . . , in } w = s1 [i1 ] = . . . = sn [in ] fl (s, i) s[i] l MEVl (w) = σ2 1 ∑ i σ2 i [fl (s1 , i1 ) . . . fl (sn , in )] σ1 . . . σm

"EKVTUJOHGPS"OJTPUSPQZ w &YBNQMF4FMGTJNJMBSJUZ  5IJTQBQFSJOEVDF#BTFMJOF w JTUIFTFUPGBMMXPSEPDDVSSFODF  NBQTBXPSEPDDVSSFODFUPJUTSFQSFTFOUBUJPOJO MBZFS w #BTFMJOFJTUIFBWFSBHFDPTJOFTJNJMBSJUZCFUXFFO
UIFSFQSFTFOUBUJPOTPGVOJGPSNMZSBOEPNMZ TBNQMFEXPSETGSPNEJ⒎FSFOUDPOUFYUT !7 Baseline (fl) = 𝔼x,y∼U(𝒪) [cos (fl (x), fl (y))] 𝒪 fl ( ⋅ ) l

UIFSFQSFTFOUBUJPOTPGVOJGPSNMZSBOEPNMZ TBNQMFEXPSETGSPNEJ⒎FSFOUDPOUFYUT !8 Baseline (fl) = 𝔼x,y∼U(𝒪) [cos (fl (x), fl (y))] 𝒪 fl ( ⋅ ) 8IZJTUIFCBTFMJOFJOEVDFE FH JG  ˠ8PSEX`TSFQSFTFOUBUJPOTXFSFQPPSMZDPOUFYUVBMJ[FE JG  ˠ8PSEX`TSFQSFTFOUBUJPOTXFSFXFMMDPOUFYUVBMJ[FE  5IJTJTCFDBVTFSFQSFTFOUBUJPOTPGXJOEJ⒎FSFOUDPOUFYUTXPVMEPOBWFSBHFCFNPSFEJTTJNJMBSUP FBDIPUIFSUIBOUXPSBOEPNMZDIPTFOXPSET 5IFDBTFPG  ˠ8PSEWFDUPSTBSFQSFUUZVOJGPSNMZEJTUSJCVUFEJO TQBDF *TPUSPQZ PUIFSXJTF   UIFDBTFPGJTBOJTPUSPQZ SelfSiml (w) = 0.95 Baseline(fl ) = 0.00 Baseline(fl ) = 0.99 Baseline(fl ) = 0.00 Baseline(fl ) = 0.99

UIFSFQSFTFOUBUJPOTPGVOJGPSNMZSBOEPNMZ TBNQMFEXPSETGSPNEJ⒎FSFOUDPOUFYUT !9 Baseline (fl) = 𝔼x,y∼U(𝒪) [cos (fl (x), fl (y))] 𝒪 fl ( ⋅ ) 8IZJTUIFCBTFMJOFJOEVDFE FH JG  ˠ8PSEX`TSFQSFTFOUBUJPOTXFSFQPPSMZDPOUFYUVBMJ[FE JG  ˠ8PSEX`TSFQSFTFOUBUJPOTXFSFXFMMDPOUFYUVBMJ[FE  5IJTJTCFDBVTFSFQSFTFOUBUJPOTPGXJOEJ⒎FSFOUDPOUFYUTXPVMEPOBWFSBHFCFNPSFEJTTJNJMBSUP FBDIPUIFSUIBOUXPSBOEPNMZDIPTFOXPSET 5IFDBTFPG  ˠ8PSEWFDUPSTBSFQSFUUZVOJGPSNMZEJTUSJCVUFEJO TQBDF *TPUSPQZ PUIFSXJTF   UIFDBTFPGJTBOJTPUSPQZ SelfSiml (w) = 0.95 Baseline(fl ) = 0.00 Baseline(fl ) = 0.99 Baseline(fl ) = 0.00 Baseline(fl ) = 0.99 4FF"SPSBFUBM "SPSBFUBM .VBOE7JTXBOBUI   GPSEFUBJMT

UIFSFQSFTFOUBUJPOTPGVOJGPSNMZSBOEPNMZ TBNQMFEXPSETGSPNEJ⒎FSFOUDPOUFYUT !10 Baseline (fl) = 𝔼x,y∼U(𝒪) [cos (fl (x), fl (y))] 𝒪 fl ( ⋅ ) 5PBEKVTUGPSUIFF⒎FDUPGBOJTPUSPQZ TFMGTJNJMBSJUZBOEJOUSBTFOUFODFTJNJMBSJUZ  #BTFMJOFJTUIFBWFSBHFDPTJOFTJNJMBSJUZCFUXFFOUIFSFQSFTFOUBUJPOTPG VOJGPSNMZSBOEPNMZTBNQMFEXPSET NBYJNVNFYQMBJOBCMFWBSJBODF  #BTFMJOFJTUIFQSPQPSUJPOPGWBSJBODFJOVOJGPSNMZSBOEPNMZTBNQMFEXPSE SFQSFTFOUBUJPOTUIBUJTFYQMBJOFECZUIFJSpSTUQSJODJQBMDPNQPOFOU UIFOTVCUSBDUGSPNFBDINFBTVSFJUTSFTQFDUJWF CBTFMJOFUPHFUUIFBOJTPUSPQZBEKVTUFEDPOUFYVBMJUZ NFBTVSF Baseline (fl) = 𝔼x,y∼U(𝒪) [cos (fl (x), fl (y))] SelfSim* l (w) = SelfSiml (w) − Baseline (fl)

'JOEJOHT*TPUSPQZ w !11 Baseline (fl) = 𝔼x,y∼U(𝒪) [cos (fl
(x), fl (y))]

'JOEJOHT*TPUSPQZ !12 Baseline (fl) = 𝔼x,y∼U(𝒪) [cos (fl (x), fl
(y))] $POUFYUVBMJ[FESFQSFTFOUBUJPOTBSFBOJTPUSPQJDJO BMMOPOJOQVUMBZFST $POUFYUVBMJ[FESFQSFTFOUBUJPOTBSFHFOFSBMMZNPSF BOJTPUSPQJDJOIJHIFSMBZFST

'JOEJOHT*TPUSPQZ !13 Baseline (fl) = 𝔼x,y∼U(𝒪) [cos (fl (x), fl
(y))] $POUFYUVBMJ[FESFQSFTFOUBUJPOTBSFBOJTPUSPQJDJO BMMOPOJOQVUMBZFST $POUFYUVBMJ[FESFQSFTFOUBUJPOTBSFHFOFSBMMZNPSF BOJTPUSPQJDJOIJHIFSMBZFST *TPUSPQZIBTCPUIUIFPSFUJDBMBOEFNQJSJDBM CFOFpUTGPSTUBUJDXPSEFNCFEEJOHT ˠ5IFFYUSFNFEFHSFFPGBOJTPUSPQZTFFOJO DPOUFYUVBMJ[FEXPSESFQSFTFOUBUJPOTJT TVSQSJTJOH

'JOEJOHT  $POUFYUTQFDJpDJUZ !14 SelfSiml (w) = 1 n2 − n
∑ j ∑ k≠j cos (fl (sj , ij), fl (sk , ik))

∑ j ∑ k≠j cos (fl (sj , ij), fl (sk , ik)) $POUFYUVBMJ[FEXPSESFQSFTFOUBUJPOTBSFNPSF DPOUFYUTQFDJpDJOIJHIFSMBZFST 4UPQXPSET FH bUIF` bPG` bUP` IBWFBNPOHUIF NPTUDPOUFYUTQFDJpDSFQSFTFOUBUJPOT -PXFS

∑ j ∑ k≠j cos (fl (sj , ij), fl (sk , ik)) $POUFYUVBMJ[FEXPSESFQSFTFOUBUJPOTBSFNPSF DPOUFYUTQFDJpDJOIJHIFSMBZFST 4UPQXPSET FH bUIF` bPG` bUP` IBWFBNPOHUIF NPTUDPOUFYUTQFDJpDSFQSFTFOUBUJPOT -PXFS "DSPTTBMMMBZFST   TUPQXPSETIBWFBNPOHUIFMPXFTUTFMGTJNJMBSJUZPGBMMXPSET  ˠ5IJTJTSFMBUJWFMZTVSQSJTJOH HJWFOUIBUUIFTFXPSETBSFOPU QPMZTFNPVT 5IJTBOTXFSTPOFPGUIFRVFTUJPOTUIJTQBQFSQPTFE  &-.P #&35 BOE(15BSFOPUTJNQMZBTTJHOJOHPOFPGB pOJUFOVNCFSPGXPSETFOTFSFQSFTFOUBUJPOTUPFBDIXPSE

'JOEJOHT  IPXDPOUFYUTQFDJpDJUZNBOJGFTUT !17 IntraSiml (s) = 1 n ∑ i
cos ( ⃗ sl , fl (s, i)) where ⃗ sl = 1 n ∑ i fl (s, i) )PXEPFTUIJTJODSFBTFEDPOUFYUTQFDJpDJUZNBOJGFTU JOUIFWFDUPSTQBDF %PXPSESFQSFTFOUBUJPOTJOUIFTBNFTFOUFODF DPOWFSHFUPBTJOHMFQPJOU %PUIFZSFNBJOEJTUJODUGSPNPOFBOPUIFSXIJMFTUJMM CFJOHEJTUJODUGSPNUIFJSSFQSFTFOUBUJPOTJOPUIFS DPOUFYUT

'JOEJOHT  IPXDPOUFYUTQFDJpDJUZNBOJGFTUT !18 IntraSiml (s) = 1 n ∑ i
cos ( ⃗ sl , fl (s, i)) where ⃗ sl = 1 n ∑ i fl (s, i) &-.P  8PSETJOUIFTBNFTFOUFODFBSFNPSFTJNJMBSUPPOFBOPUIFSJOVQQFSMBZFST #&35  8PSETJOUIFTBNFTFOUFODFBSFNPSFEJTTJNJMBSUPPOFBOPUIFSJOVQQFSMBZFST (15  8PSESFQSFTFOUBUJPOTJOUIFTBNFTFOUFODFBSFOPNPSFTJNJMBSUPFBDIPUIFSUIBO SBOEPNMZTBNQMFEXPSET $POUFYUVBMJ[FESFQSFTFOUBUJPOTBSF  NPSFDPOUFYUTQFDJpDJOVQQFSMBZFST

'JOEJOHT  TUBUJD DPOUFYUVBMJ[FE !19 MEVl (w) = σ2 1 ∑
i σ2 i

i σ2 i 0OBWFSBHF MFTTUIBOPGUIFWBSJBODFJOBXPSE`TDPOUFYUVBMJ[FE SFQSFTFOUBUJPOTDBOCFFYQMBJOFECZBTUBUJDFNCFEEJOH 5IFSBX.&7PGNBOZXPSETJTBDUVBMMZCFMPXUIFBOJTPUSPQZCBTFMJOF  JF BHSFBUFSQSPQPSUJPOPGUIFWBSJBODFBDSPTTBMMXPSETDBOCFFYQMBJOFE CZBTJOHMFWFDUPSUIBODBOUIFWBSJBODFBDSPTTBMMSFQSFTFOUBUJPOTPGB TJOHMFXPSE

i σ2 i 0OBWFSBHF MFTTUIBOPGUIFWBSJBODFJOBXPSE`TDPOUFYUVBMJ[FE SFQSFTFOUBUJPOTDBOCFFYQMBJOFECZBTUBUJDFNCFEEJOH 5IFSBX.&7PGNBOZXPSETJTBDUVBMMZCFMPXUIFBOJTPUSPQZCBTFMJOF  JF BHSFBUFSQSPQPSUJPOPGUIFWBSJBODFBDSPTTBMMXPSETDBOCFFYQMBJOFE CZBTJOHMFWFDUPSUIBODBOUIFWBSJBODFBDSPTTBMMSFQSFTFOUBUJPOTPGB TJOHMFXPSE 5IJTTVHHFTUTUIBUDPOUFYUVBMJ[JOHNPEFMTBSF OPUTJNQMZBTTJHOJOHPOFPGBpOJUFOVNCFSPG XPSETFOTFSFQSFTFOUBUJPOTUPFBDIXPSE  rPUIFSXJTF UIFQSPQPSUJPOPGWBSJBODF FYQMBJOFEXPVMECFNVDIIJHIFS

1SJODJQBMDPNQPOFOUT  WT(MP7F !22 5IJTQBQFSDSFBUFTUBUJDFNCFEEJOHTGPSFBDIXPSECZUBLJOHUIFpSTU QSJODJQBMDPNQPOFOU 1$ PGJUTDPOUFYUVBMJ[FESFQSFTFOUBUJPOTJOB HJWFOMBZFS
5IF1$TPGIJHIMZDPOUFYUTQFDJpDSFQSFTFOUBUJPOTBSFMFTTF⒎FDUJWFPO USBEJUJPOBMCFODINBSLT

$PODMVTJPO w 5IJTQBQFSJOWFTUJHBUFEIPXDPOUFYUVBMDPOUFYUVBMJ[FEXPSESFQSFTFOUBUJPOTUSVMZ BSF w 5IFZGPVOEUIBUVQQFSMBZFSTPG&-.P #&35 BOE(15QSPEVDFNPSFDPOUFYU TQFDJpDSFQSFTFOUBUJPOTUIBOMPXFSMBZFST w
5IJTJODSFBTFEDPOUFYUTQFDJpDJUZJTBMXBZTBDDPNQBOJFECZJODSFBTFE BOJTPUSPQZ w )PXFWFS DPOUFYUTQFDJpDJUZBMTPNBOJGFTUTEJ⒎FSFOUMZBDSPTTUIFUISFFNPEFMT  FHUIFBOJTPUSPQZBEKVTUFETJNJMBSJUZCFUXFFOXPSETJOUIFTBNFTFOUFODFJT IJHIFTUJO&-.PCVUBMNPTUOPOFYJTUFOUJO(15 w 5IFZGPVOEUIBUTUBUJDXPSEFNCFEEJOHTXPVMECFBQPPSSFQMBDFNFOUGPS DPOUFYUVBMJ[FEPOFT !23

3FMBUFEXPSLT w "SPSBFUBM "4*.1-&#65506()50#&"5#"4&-*/&'034&/5&/$& &.#&%%*/(4*$-3 w "SPSBFUBM "-BUFOU7BSJBCMF.PEFM"QQSPBDIUP1.*CBTFE8PSE&NCFEEJOHT 5"$- w
.VBOE7JTXBOBUI "--#655)&5014*.1-&"/%&''&$5*7& 1045130$&44*/('03803%3&13&4&/5"5*0/4*$-3 w 1FUFSTFUBM %FFQ$POUFYUVBMJ[FE8PSE3FQSFTFOUBUJPOT/""$- w %FWMJOFUBM #&351SFUSBJOJOHPG%FFQ#JEJSFDUJPOBM5SBOTGPSNFSTGPS-BOHVBHF 6OEFSTUBOEJOH/""$- w 3BEGPSEFUBM -BOHVBHF.PEFMTBSF6OTVQFSWJTFE.VMUJUBTL-FBSOFST0QFO"* CMPHQPTU !24

論文紹介: How Contextual are Contextualized Word Representations?

論文紹介: How Contextual are Contextualized Word Representations?

Satoru Katsumata

More Decks by Satoru Katsumata

Other Decks in Research

Featured

Transcript

)PX$POUFYUVBMBSF $POUFYUVBMJ[FE8PSE 3FQSFTFOUBUJPOT ,BXJO&UIBZBSBKI &./-1     BS9JWUJUMF)PX$POUFYUVBMBSF$POUFYUVBMJ[FE8PSE 3FQSFTFOUBUJPOT $PNQBSJOHUIF(FPNFUSZPG#&35

"CTUSBDU w %FFQOFVSBMMBOHVBHFNPEFMTIBWFTVDDFTTGVMMZDSFBUFE DPOUFYUVBMJ[FEXPSESFQSFTFOUBUJPOT  &-.P 1FUFSTFUBM MBZFSCJ-45.  #&35 %FWMJOFUBM

&YQFSJNFOU4FUUJOH w 5IFDPOUFYUVBMJ[JOHNPEFMT  &-.P#&35(15 JOQVUMBZFSUIMBZFS w %BUB  454 w

4FMGTJNJMBSJUZ w -FUCFBXPSEUIBUBQQFBSTJOTFOUFODFT  BUJOEJDFTSFTQFDUJWFMZ  ˠ w -FUCFBGVODUJPOUIBUNBQTUPJUTSFQSFTFOUBUJPO JOMBZFS w 4FMGTJNJMBSJUZ

OUSBTFOUFODFTJNJMBSJUZ w -FUCFBTFOUFODFUIBUJTBTFRVFODFPGOXPSET w -FUCFBGVODUJPOUIBUNBQTUPJUTSFQSFTFOUBUJPOJO MBZFS w OUSBTFOUFODFTJNJMBSJUZ  w *OUSBTFOUFODFTJNJMBSJUZPGBTFOUFODFJTUIFBWFSBHFDPTJOF

.BYJNVNFYQMBJOBCMF WBSJBODF w -FUCFBXPSEUIBUBQQFBSTJOTFOUFODFT  BUJOEJDFTSFTQFDUJWFMZ  ˠ w -FUCFBGVODUJPOUIBUNBQTUPJUTSFQSFTFOUBUJPOJOMBZFS w JTUIFPDDVSSFODFNBUSJYPGXPSEX

"EKVTUJOHGPS"OJTPUSPQZ w &YBNQMF4FMGTJNJMBSJUZ  5IJTQBQFSJOEVDF#BTFMJOF w JTUIFTFUPGBMMXPSEPDDVSSFODF  NBQTBXPSEPDDVSSFODFUPJUTSFQSFTFOUBUJPOJO MBZFS w #BTFMJOFJTUIFBWFSBHFDPTJOFTJNJMBSJUZCFUXFFO

"EKVTUJOHGPS"OJTPUSPQZ w &YBNQMF4FMGTJNJMBSJUZ  5IJTQBQFSJOEVDF#BTFMJOF w JTUIFTFUPGBMMXPSEPDDVSSFODF  NBQTBXPSEPDDVSSFODFUPJUTSFQSFTFOUBUJPOJO MBZFS w #BTFMJOFJTUIFBWFSBHFDPTJOFTJNJMBSJUZCFUXFFO

"EKVTUJOHGPS"OJTPUSPQZ w &YBNQMF4FMGTJNJMBSJUZ  5IJTQBQFSJOEVDF#BTFMJOF w JTUIFTFUPGBMMXPSEPDDVSSFODF  NBQTBXPSEPDDVSSFODFUPJUTSFQSFTFOUBUJPOJO MBZFS w #BTFMJOFJTUIFBWFSBHFDPTJOFTJNJMBSJUZCFUXFFO

"EKVTUJOHGPS"OJTPUSPQZ w &YBNQMF4FMGTJNJMBSJUZ  5IJTQBQFSJOEVDF#BTFMJOF w JTUIFTFUPGBMMXPSEPDDVSSFODF  NBQTBXPSEPDDVSSFODFUPJUTSFQSFTFOUBUJPOJO MBZFS w #BTFMJOFJTUIFBWFSBHFDPTJOFTJNJMBSJUZCFUXFFO

'JOEJOHT*TPUSPQZ w !11 Baseline (fl) = 𝔼x,y∼U(𝒪) [cos (fl

'JOEJOHT*TPUSPQZ !12 Baseline (fl) = 𝔼x,y∼U(𝒪) [cos (fl (x), fl

'JOEJOHT*TPUSPQZ !13 Baseline (fl) = 𝔼x,y∼U(𝒪) [cos (fl (x), fl

'JOEJOHT  $POUFYUTQFDJpDJUZ !14 SelfSiml (w) = 1 n2 − n

'JOEJOHT  $POUFYUTQFDJpDJUZ !15 SelfSiml (w) = 1 n2 − n

'JOEJOHT  $POUFYUTQFDJpDJUZ !16 SelfSiml (w) = 1 n2 − n

'JOEJOHT  IPXDPOUFYUTQFDJpDJUZNBOJGFTUT !17 IntraSiml (s) = 1 n ∑ i

'JOEJOHT  IPXDPOUFYUTQFDJpDJUZNBOJGFTUT !18 IntraSiml (s) = 1 n ∑ i

'JOEJOHT  TUBUJD DPOUFYUVBMJ[FE !19 MEVl (w) = σ2 1 ∑

'JOEJOHT  TUBUJD DPOUFYUVBMJ[FE !20 MEVl (w) = σ2 1 ∑

'JOEJOHT  TUBUJD DPOUFYUVBMJ[FE !21 MEVl (w) = σ2 1 ∑

1SJODJQBMDPNQPOFOUT  WT(MP7F !22 5IJTQBQFSDSFBUFTUBUJDFNCFEEJOHTGPSFBDIXPSECZUBLJOHUIFpSTU QSJODJQBMDPNQPOFOU 1$ PGJUTDPOUFYUVBMJ[FESFQSFTFOUBUJPOTJOB HJWFOMBZFS

$PODMVTJPO w 5IJTQBQFSJOWFTUJHBUFEIPXDPOUFYUVBMDPOUFYUVBMJ[FEXPSESFQSFTFOUBUJPOTUSVMZ BSF w 5IFZGPVOEUIBUVQQFSMBZFSTPG&-.P #&35 BOE(15QSPEVDFNPSFDPOUFYU TQFDJpDSFQSFTFOUBUJPOTUIBOMPXFSMBZFST w

3FMBUFEXPSLT w "SPSBFUBM "4.1-&#65506()50#&"5#"4&-/&'034&/5&/$& &.#&%%/(4$-3 w "SPSBFUBM "-BUFOU7BSJBCMF.PEFM"QQSPBDIUP1.*CBTFE8PSE&NCFEEJOHT 5"$- w