Ψ΢εࠞ߹Ϟσϧ
 ʹ͓͚Δਪ࿦ #BZFTBJO*OGFSFODFPO (.. UBOJNV

Ψ΢εࠞ߹Ϟσϧʹ͓͚Δਪ࿦ w ࣄલ஌ࣝ w Ψ΢εࠞ߹Ϟσϧ w ΪϒεαϯϓϦϯά w ม෼ਪ࿦ w ่յܕΪϒεαϯϓϦϯά w ؆қ࣮ݧ w ʢϏοΫσʔλͱϕΠζֶशʣ 2

ࢀߟهࣄ w ஶऀͷਢࢁ͞Μͷղઆهࣄ w IUUQNBDIJOFMFBSOJOHIBUFOBCMPHDPNFOUSZ 3

֓ཁ w Ψ΢εࠞ߹Ϟσϧ (BVTTJBO.JYUVSF.PEFM ͷࣄޙ෼෍ ΛαϯϓϦϯάख๏ʹΑͬͯٻΊΔख๏ w ฏۉɼਫ਼౓ߦྻ͕ະ஌Ͱ͋Δଟ࣍ݩΨ΢ε෼෍Ͱɼࠞ߹ ൺ཰΋ະ஌ͷࠞ߹ϞσϧΛߟ͑ɼͦͷࣄޙ෼෍ΛٻΊΔͨ ΊͷαϯϓϦϯάΛಋग़͢Δ 4

લఏ 1SFMJNJOBSJFT

ࠞ߹Ϟσϧ w ࠞ߹ϞσϧͷΠϝʔδ 6 ࠞ߹ൺ཰ Ϋϥελม਺ ֤෼෍ͷύϥϝʔλ ͜͜Ͱ͸࣍ݩΨ΢γΞϯ

Ψ΢εࠞ߹Ϟσϧ w ଟ࣍ݩͷ֬཰෼෍ʹ͓͍ͯɼଟ࣍ݩΨ΢ε෼෍ʹै͏ๆ ͕ෳ਺ଘࡏ͢ΔΑ͏ͳ෼෍ͷ͜ͱ 7

લఏ஌ࣝ w ଟ࣍ݩΨ΢ε෼෍ w ଟ࣍ݩΨ΢ε෼෍ʹ͓͚Δࣄޙ෼෍ w ͦ΋ͦ΋ࣄޙ෼෍ΛٻΊΔ໨తͱ͸ w ࠞ߹ϞσϧͰ͸ɼͳͥαϯϓϦϯά͢Δͷ͔ ʢ͜͜Ͱ͸جຊతʹؾ࣋ͪΛड़΂·͢ʣ 8

ଟ࣍ݩΨ΢ε෼෍ w Ψ΢ε෼෍ͷଟ࣍ݩόʔδϣϯ w ͭͷ࣍ݩʹண໨͢ΔͱɼͨͩͷΨ΢ε෼෍ 9 N(x|µ, ⌃) = 1 p (2⇡)D|⌃| exp{ 1 2 (x µ)T ⌃ 1(x µ)} AAACpnicfVFNbxMxEPUuHw0ppQGOXEZElRKpiXYDUrkgRcABLlWhTVMpToLX8aZW7d3F9qJGrn8af4Ib/wbvNlW/ECNZejPzRm/8JikE1yaK/gThg4ePHm80njQ3n2492249f3Gs81JRNqK5yNVJQjQTPGMjw41gJ4ViRCaCjZOzj1V//JMpzfPsyKwKNpVkmfGUU2J8ad76hSUxp5QIu+86NU5Se+7gAq4SLEu3e50d8qUkrgvvAaeKUBs7i/UPZWxngAvenX2qRmsSXDgH7LwAbHvX5IGDmzq9Wzrd2RFcScxsL/4vF7Cbt9pRP6oD7oN4DdpoHQfz1m+8yGkpWWaoIFpP4qgwU0uU4VQw18SlZgWhZ2TJJh5mRDI9tbXNDnZ8ZQFprvzLDNTVmxOWSK1XMvHMak99t1cV/9WblCZ9N7U8K0rDMnoplJYCTA7VzWDBFaNGrDwgVHG/K9BT4g01/rJNb0J898v3wfGgH7/pR1/ftocf1nY00Cv0GnVQjPbQEH1GB2iEaNAOvgTfgsOwE+6Ho3B8SQ2D9cxLdCvC738BGWvP9Q==

ଟ࣍ݩΨ΢ε෼෍ͷࣄޙ෼෍ w ฏۉͱਫ਼౓ߦྻ͕ͲͪΒ΋ະ஌ͷ৔߹ʹ͸ɼΨ΢εɾ΢Ο γϟʔτ෼෍͕ڞ໾ࣄલ෼෍ͱͳΔ w ฏۉʢΨ΢εଆʣͷࣄޙ෼෍ͷ෼ࢄ͸ɼ΢Ογϟʔτͷࣄ ޙ෼෍ʹґଘ͢ΔͨΊɼฏۉʢΨ΢εଆʣΛઌʹܭࢉ͢Δ 10 p(µ, ⇤) = N(µ|m, ( ⇤) 1)W(⇤|⌫, W) 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

ͦ΋ͦ΋ࣄޙ෼෍ΛٻΊΔ໨త w ϕΠζਪ࿦ͷ໨త w σʔλͷੜ੒աఔΛ֬཰෼෍ΛݩʹϞσϦϯά͢Δ͜ͱͰɼ ະ஌ͷσʔλʹର͢Δ༧ଌΛߦ͏ w ࠷ऴతʹٻΊ͍ͨ΋ͷ w ༧ଌ෼෍ w ༧ଌ෼෍ͱ͸ w ࣄޙ෼෍ʹΑͬͯɼ৚͚݅ͣΒΕͨ؍ଌ෼෍ 11

༧ଌ෼෍ΛٻΊΑ͏ 12 予測分布

w ࣄޙ෼෍ΛٻΊΔ w ༧ଌ෼෍ʹର͢Δڞ໾ࣄલ෼෍Ͱɼࣄલ෼෍ΛԾఆ͢Δͱ ղੳతʹࣄޙ෼෍ͷύϥϝʔλΛٻΊΔ͜ͱ͕Ͱ͖Δ ࣄޙ෼෍ΛٻΊΕ͹͍͍ͷ͔ 13

w ࣄޙ෼෍͕ղੳతʹٻ·Βͳ͍ྫ w ༧ଌ෼෍ʹର͢Δڞ໾ࣄલ෼෍Ͱɼࣄલ෼෍ΛԾఆ͍ͯ͠ͳ ͍ͨΊʹɼࣄޙ෼෍ͷܗ͕ະ஌ʹͳΔͨΊɼϞσϧΤϏσϯ εΛܭࢉ͢Δඞཁੑ͕ੜͯ͡͠·͏ͨΊɼൺྫ͢Δ֬཰ີ౓ ؔ਺͔ΒαϯϓϦϯάͯ͠ɼ෼෍ͷಛ௃ΛಘΔ w ύϥϝʔλͷґଘؔ܎͕ෳࡶͰɼ ಉ࣌ ࣄޙ෼෍ΛٻΊΔ͜ ͱ͕ࠔ೉ w ࠞ߹Ϟσϧ w σʔλ͕؍ଌ͞ΕΔ͜ͱͰɼΫϥελΛܾఆ͢ΔTͱɼ֤Ϋϥ ελ෼෍ͷύϥϝʔλʹґଘؔ܎͕ੜͯ͡͠·͏ ࣄޙ෼෍͕ղੳతʹٻ·Βͳ͍ 14

Ψ΢εࠞ߹Ϟσϧͷґଘؔ܎ w Ψ΢εࠞ߹ϞσϧΛάϥϑΟΧϧϞσϧͰॻ͘ͱɼҎԼͷ Α͏ʹͳΔ w IFBEUPIFBEΑΓɼY͕؍ଌ͞ΕΔ͜ͱͰɼЖ Ͻ Tͷؒ ʹґଘؔ܎͕ੜ͡Δ 15

8IZEPXFTBNQMFGSPNQPTUFSJPS w ґଘؔ܎ʹΑΓɼಉ࣌ࣄޙ෼෍ΛٻΊΔࡍʹɼܭࢉෆՄ ೳͳೖΕࢠঢ়ଶ͕ൃੜ͢Δ w ͦͷͨΊɼۙࣅαϯϓϦϯάͰɼͲ͔͜ͷύϥϝʔλΛ؍ ଌͯ͠ɼೖΕࢠঢ়ଶΛղফ͢Δඞཁ͕͋Δɽ 16

Ͳ͏αϯϓϦϯά͢Δ͔ʁ w ͸͡Ίʹ4ʹରͯ͠ɼαϯϓϦϯά΍෼෍ΛۙࣅΛߦ͏ͱɼ ࢒ΓͷύϥϝʔλΛʢΨ΢γΞϯͷฏۉͱ෼ࢄΛআ͍ͯʣ ಠཱʹѻ͏͜ͱ͕Մೳ w ͦͷͨΊɼ4ͱͦͷଞͷύϥϝʔλΛผʑʹαϯϓϦϯά ͢Δͷ͕ྑ͍ 17

Ψ΢εࠞ߹Ϟσϧ (BVTTJBO.JYUVSF.PEFM

Ψ΢εࠞ߹Ϟσϧ w Ψ΢εࠞ߹Ϟσϧʹ͓͚Δ؍ଌ෼෍ w σʔλͷੜ੒աఔͦͷ·· w جຊతʹ͸ɼϙΞιϯࠞ߹Ϟσϧͱಉ͡ɽҧ͏ͷ͸ɼଟ࣍ ݩΨ΢ε෼෍͚ͩɽ 19 p(xn |sn, µ, ⇤) = K Y k=1 N(xn |µk, ⇤ 1 k )sn,k 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

ଟ࣍ݩΨ΢ε෼෍ w ਫ਼౓ߦྻʢڞ෼ࢄߦྻͷٯߦྻʣΛύϥϝʔλͱ͢Δ
 ଟ࣍ݩΨ΢ε෼෍͸ҎԼͷࣜͰද͞ΕΔ w ର਺όʔδϣϯ w ٯߦྻ͕ͳ͘ͳΔͷ͕ϙΠϯτ 20 N(x|µ, ⇤) = 1 p (2⇡)D|⇤ 1| exp{ 1 2 (x µ)T ⇤(x µ)} 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 lnN(x|µ, ⇤) = { 1 2 (x µ)T⇤(x µ) ln|⇤| + Dln2⇡} 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

ଟ࣍ݩΨ΢ε෼෍ͷର਺ͷಋग़ 21

ଟ࣍ݩΨ΢ε෼෍ͷڞ໾ࣄલ෼෍ w ڞ໾ࣄલ෼෍ʢΨ΢εɾ΢Ογϟʔτ෼෍ʣ w ٻΊ͍ͨಉ࣌ࣄޙ෼෍ w Ϋϥελม਺ͱͦͷύϥϝʔλɼ֤Ϋϥελͷ෼෍ͷύϥ ϝʔλͷಉ࣌ࣄޙ෼෍ 22 p(µk, ⇤k) = N(µk |m, ( ⇤k) 1)W(⇤k |⌫, W) 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 p(S, µ, ⇤, ⇡|X) AAACNXicbVBNS8MwGE7n15xfVY9egkOYIKNVQY9DLx52mOg+YB0jTdMtLG1Dkgqj9k958X940oMHRbz6F0y3Irr5QsiT53ne5M3jckalsqwXo7CwuLS8Ulwtra1vbG6Z2zstGcUCkyaOWCQ6LpKE0ZA0FVWMdLggKHAZabujy0xv3xEhaRTeqjEnvQANQupTjJSm+madV5wAqaHrJzfpEXTciHlyHOjNCWJ9zjWnrq/00IyDU3j/Y+mkh32zbFWtScF5YOegDPJq9M0nx4twHJBQYYak7NoWV70ECUUxI2nJiSXhCI/QgHQ1DFFAZC+Z/DqFB5rxoB8JvUIFJ+zvjgQFMhtUO7MR5ayWkf9p3Vj5572EhjxWJMTTh/yYQRXBLELoUUGwYmMNEBZUzwrxEAmElQ66pEOwZ788D1rHVfukal2flmsXeRxFsAf2QQXY4AzUwBVogCbA4AE8gzfwbjwar8aH8Tm1Foy8Zxf8KePrGxbhrDk=

Ψ΢εɾ΢Ογϟʔτ෼෍ w Ψ΢ε෼෍ͱ΢Ογϟʔτ෼෍ͷੵͰύϥϝʔλґଘ͋Γ w ΢Ογϟʔτ෼෍ w ର਺ 23 p(µ, ⇤) = N(µ|m, ( ⇤) 1)W(⇤|⌫, W) 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 W(⇤|⌫, W) = CW (⌫, W)|⇤|⌫ D 1 2 exp{ 1 2 Tr(W 1⇤)} 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 lnW(⇤|⌫, W) = ⌫ D 1 2 ln|⇤| 1 2 Tr(W 1⇤) + lnCW (⌫, W) 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

Α͘ग़ͯ͘Δର਺ࣜ w ଟ࣍ݩΨ΢ε෼෍ w ΢Ογϟʔτ෼෍ 24 lnW(⇤|⌫, W) = ⌫ D 1 2 ln|⇤| 1 2 Tr(W 1⇤) + lnCW (⌫, W) 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 lnN(x|µ, ⇤) = { 1 2 (x µ)T⇤(x µ) ln|⇤| + Dln2⇡} 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

جຊతͳํ਑ w αϯϓϦϯάͱۙࣅͷͲͪΒͷख๏ʹ͓͍ͯ΋ɼ
 જࡏม਺ͱύϥϝʔλ͸෼͚ͯߦ͏ w ྫ ΪϒεαϯϓϦϯάͷ৔߹ 25 S ⇠ p(S|X, , ⇡) AAACN3icbVBNS8NAEN3Ur1q/oh69LBahgpREBT0WvXiSivYDmlA2m027dDcJuxuhxP4rL/4Nb3rxoIhX/4GbNoJtHVj2zZsZZt7zYkalsqwXo7CwuLS8Ulwtra1vbG6Z2ztNGSUCkwaOWCTaHpKE0ZA0FFWMtGNBEPcYaXmDy6zeuidC0ii8U8OYuBz1QhpQjJSmuua1w5Hqe0F6O4KOpBzGlT/MA/xN2qMj6HgR8+WQ689heoWPprmYHnbNslW1xgHngZ2DMsij3jWfHT/CCSehwgxJ2bGtWLkpEopiRkYlJ5EkRniAeqSjYYg4kW461j2CB5rxYRAJ/UIFx+zfiRRxmd2mOzMZcraWkf/VOokKzt2UhnGiSIgni4KEQRXBzEToU0GwYkMNEBZU3wpxHwmElba6pE2wZyXPg+Zx1T6pWjen5dpFbkcR7IF9UAE2OAM1cAXqoAEweASv4B18GE/Gm/FpfE1aC0Y+swumwvj+AdSJrRs= µ, ⇤, ⇡ ⇠ p(µ, ⇤, ⇡|X, S) 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

ΪϒεαϯϓϦϯά (JCCT4BNQMJOH

ํ਑ w જࡏม਺ͱύϥϝʔλΛ෼͚ͯαϯϓϦϯά 27 S ⇠ p(S|X, , ⇡) AAACN3icbVBNS8NAEN3Ur1q/oh69LBahgpREBT0WvXiSivYDmlA2m027dDcJuxuhxP4rL/4Nb3rxoIhX/4GbNoJtHVj2zZsZZt7zYkalsqwXo7CwuLS8Ulwtra1vbG6Z2ztNGSUCkwaOWCTaHpKE0ZA0FFWMtGNBEPcYaXmDy6zeuidC0ii8U8OYuBz1QhpQjJSmuua1w5Hqe0F6O4KOpBzGlT/MA/xN2qMj6HgR8+WQ689heoWPprmYHnbNslW1xgHngZ2DMsij3jWfHT/CCSehwgxJ2bGtWLkpEopiRkYlJ5EkRniAeqSjYYg4kW461j2CB5rxYRAJ/UIFx+zfiRRxmd2mOzMZcraWkf/VOokKzt2UhnGiSIgni4KEQRXBzEToU0GwYkMNEBZU3wpxHwmElba6pE2wZyXPg+Zx1T6pWjen5dpFbkcR7IF9UAE2OAM1cAXqoAEweASv4B18GE/Gm/FpfE1aC0Y+swumwvj+AdSJrRs= µ, ⇤, ⇡ ⇠ p(µ, ⇤, ⇡|X, S) 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 w જࡏม਺ΛαϯϓϦϯά w Ж ϽͱК͕ಠཱʹͳΔ w ЖͱϽΛαϯϓϦϯά w КΛαϯϓϦϯά

Ϋϥελม਺4ͷΈαϯϓϦϯά w ύϥϝʔλ Ж Ͻ К ͸͢Ͱʹαϯϓϧ͞Ε͍ͯΔͱԾ ఆʢఆ਺ʣͱԾఆͯ͠ɼ4ʹؔ͢Δ͜͏ͷΈʹண໨ 28 S ⇠ p(S|X, µ, ⇤, ⇡) / p(X, S, µ, ⇤, S, ⇡) / p(X|S, µ, ⇤)p(S|⇡) = N Y n=1 p(xn |sn, µ, ⇤)p(sn |⇡) 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

ର਺Λͱͬͯܭࢉ 29

ΧςΰϦ෼෍ͱ߹Θͤͯ 30 MOК`

Ϋϥελ4ͷࣄޙ෼෍ w ύϥϝʔλ Ж Ͻ К ͕͢Ͱʹαϯϓϧ͞Ε͍ͯΔͱԾ ఆ͢Δͱɼ4ͷࣄޙ෼෍͸ҎԼͰදͤΔ w ͳͥࣄޙ෼෍ͷύϥϝʔλΛКϋοτͱ͔ʹ͠ͳ͍Μͩɽɽ 31

ύϥϝʔλͷαϯϓϦϯά w જࡏม਺4͸͢Ͱʹαϯϓϧ͞Ε͍ͯΔͱԾఆʢఆ਺ʣͱ͠ ͯɼύϥϝʔλ Ж Ͻ К ͷಉ࣌ࣄޙ෼෍Λܭࢉ w ЖͱϽ͸ଟ࣍ݩΨ΢εͷ৔߹͸ಠཱʹͳΒͳ͍ͷͰɼ
 ЖͱϽͷࣄޙ෼෍ͱɼКͷࣄޙ෼෍ΛผʑʹٻΊͯɼαϯ ϓϦϯά͢Δ 32 p(µ, ⇤, ⇡|X, S) / p(X, S, µ, ⇤, ⇡) / p(X|S, µ, ⇤)p(S|⇡)p(µ, ⇤)p(⇡) 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 4ͷ؍ଌʹΑΓಠཱʹͳͬͨ

Ж Ͻ Кͷࣄޙ෼෍ w ֤ύϥϝʔλʹؔ܎ͷ͋Δ߲͚ͩʹ஫໨ w ЖͱϽͷࣄޙ෼෍ w Кͷࣄޙ෼෍ 33 p(µ, ⇤|X, S) / p(X|S, µ, ⇤)p(µ, ⇤) 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 p(µ, ⇤, ⇡|X, S) / p(X, S, µ, ⇤, ⇡) / p(X|S, µ, ⇤)p(S|⇡)p(µ, ⇤)p(⇡) 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 p(⇡|X, S) / p(S|⇡)p(⇡) 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

ЖͱϽͷࣄޙ෼෍ w 4͕ఆ਺Ͱ͋Δ͜ͱʹ஫ҙ͢Ε͹ɼ୯ͳΔଟ࣍ݩΨ΢ε෼ ෍ͷࣄޙ෼෍ͱಉ౳ͱΈͳͤΔ 34 p(µ, ⇤|X, S) / p(X|S, µ, ⇤)p(µ, ⇤) 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 ଟ࣍ݩΨ΢ε෼෍ ʢ༧ଌ෼෍ʣ Ψ΢εɾ΢Ογϟʔτ෼෍ ʢࣄલ෼෍ʣ

ЖͱϽͷࣄޙ෼෍ͷܭࢉ w ର਺Λͱͬͯܭࢉ͠Α͏ʂ 35 lnN(x|µ, ⇤) = { 1 2 (x µ)T⇤(x µ) ln|⇤| + Dln2⇡} 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

ЖͱϽͷࣄޙ෼෍ͷܭࢉ w ষͷΨ΢εɾ΢Ογϟʔτ෼෍ͷϕΠζਪ࿦ͱಉ༷ʹٻ ΊΔ w Жͷࣄޙ෼෍ͷ෼ࢄ͕Ͻʹґଘ͢ΔͨΊɼϽ͕αϯϓϧ͞ Ε͍ͯΔલఏͰɼЖΛٻΊ͔ͯΒͦͷ݁ՌΛར༻ͯ͠ϽΛ ٻΊΔ 36

Α͘ग़ͯ͘Δର਺ࣜ w ଟ࣍ݩΨ΢ε෼෍ w ΢Ογϟʔτ෼෍ 37 lnW(⇤|⌫, W) = ⌫ D 1 2 ln|⇤| 1 2 Tr(W 1⇤) + lnCW (⌫, W) 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 lnN(x|µ, ⇤) = { 1 2 (x µ)T⇤(x µ) ln|⇤| + Dln2⇡} 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

Жͷࣄޙ෼෍ͷܭࢉ 38

Жͷࣄޙ෼෍ͷܭࢉ 39

w ࠷ऴతͳЖͷࣄޙ෼෍ Жͷࣄޙ෼෍ͷܭࢉ 40

Ͻͷࣄޙ෼෍ w ٻΊͨЖͷࣄޙ෼෍Λར༻ͯ͠ɼϽͷࣄޙ෼෍ΛٻΊΔ w ϕΠζͷఆཧΑΓ w ৚݅෇͖֬཰ͷఆٛΑΓ w ࿈ཱํఔࣜతʹͱ͘ͱ 41 Ψ΢εɾ΢Ογϟʔτ ͷಉ࣌ࣄલ෼෍ ଟ࣍ݩΨ΢εͷ ؍ଌ෼෍ ٻΊ͍ͨϽ ͷࣄޙ෼෍ Жͷࣄޙ෼෍ ʢ͖ͬ͞ٻΊͨʣ

w ର਺ΛऔΔ DPOTU๨Εͯͨʣ w ֤෼෍ͷࢦشʹม׵ʢແବͳՕॴ͸DPOTUͰٵऩʣ w શͯط஌ͷ߲ʹͳͬͨͷͰɼޙ͸ܭࢉ Ͻͷࣄޙ෼෍ͷܭࢉ 42

w ͔͜͜ΒϽʹؔ͢Δ߲Λ·ͱΊΔͷ͸ɼେมͳͷͰඈ͹͠ ·͢ɽɽɽ Ͻͷࣄޙ෼෍ͷܭࢉ 43

w ର਺ͷܭࢉ݁Ռ w ࣄલ෼෍ͷର਺ Ͻͷࣄޙ෼෍ͷܭࢉ 44 lnW(⇤|⌫, W) = ⌫ D 1 2 ln|⇤| 1 2 Tr(W 1⇤) + lnCW (⌫, W) 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

w Ͻͷࣄޙ෼෍ Ͻͷࣄޙ෼෍ͷܭࢉ 45

Ж Ͻ Кͷࣄޙ෼෍ w ֤ύϥϝʔλʹؔ܎ͷ͋Δ߲͚ͩʹ஫໨ w ЖͱϽͷࣄޙ෼෍ w Кͷࣄޙ෼෍ 46 p(µ, ⇤|X, S) / p(X|S, µ, ⇤)p(µ, ⇤) 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 p(µ, ⇤, ⇡|X, S) / p(X, S, µ, ⇤, ⇡) / p(X|S, µ, ⇤)p(S|⇡)p(µ, ⇤)p(⇡) 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 p(⇡|X, S) / p(S|⇡)p(⇡) 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

Кͷࣄޙ෼෍ w ࠞ߹ൺ཰Кͷࣄޙ෼෍͸ɼ؍ଌ෼෍ͱ͸ಠཱ w ϙΞιϯࠞ߹Ϟσϧͷ࣌ͱಉ͡Ͱ͋ΔͨΊɼ݁Ռ͚ͩ 47 p(⇡|X, S) / p(S|⇡)p(⇡) AAACTHicbVDLSgMxFM3UV62vUZdugkVoQcqMCrosunFZ0T6gM5RMmmlDM5OQZIQy9gPduHDnV7hxoYhgpi3Ftl4IOZxzT3LvCQSjSjvOm5VbWV1b38hvFra2d3b37P2DhuKJxKSOOeOyFSBFGI1JXVPNSEtIgqKAkWYwuMn05iORivL4QQ8F8SPUi2lIMdKG6thYlLyAs64aRubyBIVP0IuQ7gdh2hqdzvD9qFzwhORCc2gsMzZrn/OX4eKL5Y5ddCrOuOAycKegCKZV69ivXpfjJCKxxgwp1XYdof0USU0xI6OClygiEB6gHmkbGKOIKD8dhzGCJ4bpwpBLc2INx+xfR4oilc1mOrMt1KKWkf9p7USHV35KY5FoEuPJR2HCoEkkSxZ2qSRYs6EBCEtqZoW4jyTC2uRfMCG4iysvg8ZZxT2vOHcXxer1NI48OALHoARccAmq4BbUQB1g8AzewSf4sl6sD+vb+pm05qyp5xDMVW79Fxk3tIU=

-FU`TΪϒεαϯϓϦϯά w ٻΊͨࣄޙ෼෍͸ w ύϥϝʔλ͕αϯϓϧ͞Ε͍ͯΔͱԾఆͨ͠
 જࡏม਺ͷࣄޙ෼෍ w જࡏม਺͕αϯϓϧ͞Ε͍ͯΔͱԾఆͨ͠
 ύϥϝʔλͷࣄޙ෼෍ w ͲͪΒ͔Λαϯϓϧͯ͋͛͠ͳ͍ͱɼ෼෍Λܾఆ͢Δ͜ͱ͕Ͱ͖ ͳ͍ w ॳظ஋Λઃఆͯ͠ɼަޓʹαϯϓϦϯά͢Δ͜ͱͰ
 ྆ํͷ෼෍ͷਫ਼౓ΛߴΊ͍ͯ͘ 48

ΪϒεαϯϓϦϯάΞϧΰϦζϜ 49

ม෼ਪ࿦ 7BSJBUJPOBM*OGFSFODF

ม෼ਪ࿦ w ܗ͕ະ஌Ͱ͋Δ෼෍ͷܗঢ়΍ಛ௃Λ஌ΔͨΊʹɼܗ͕ط ஌ͷ෼෍Ͱۙࣅͯ͠ɼͦͷۙࣅ෼෍Ͱ୅༻͢Δख๏ w ਅͷ෼෍ͱۙࣅ෼෍ͷؒͷ,-%Λ࠷খԽ͢Δ
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ʢϏοάσʔλͱϕΠζֶश 
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