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機械学習アルゴリズムに潜む不公平なバイアスとその理論

Kazuto Fukuchi
September 09, 2022

 機械学習アルゴリズムに潜む不公平なバイアスとその理論

2022年IEICEソサイエティ大会で発表した講演のスライドです.

Kazuto Fukuchi

September 09, 2022
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  1. ࣗݾ঺հ w ໊લ෱஍Ұే 'VLVDIJ,B[VUP  w ॴଐஜ೾େֶγεςϜ৘ใܥॿڭ w ܦྺ w

    ஜ೾େֶγεςϜ৘ใ޻ֶઐ߈Պത࢜ޙظ՝ఔमྃ w ཧݚ"*1ಛผݚڀһ w ݱࡏஜ೾େֶγεςϜ৘ใܥॿڭ w ݱࡏཧݚ"*1٬һݚڀһ w ݚڀڵຯ w ػցֶशʹ͓͚ΔެฏੑɼϓϥΠόγʔͷཧ࿦໘ w ਺ཧ౷ܭɼಛʹɼ൚ؔ਺ਪఆ
  2. ެฏੑͷ๏తཁٻ w 5JUMF7** w ਓछɼഽͷ৭ɼफڭɼੑผɼग़਎ࠃʹΑΔޏ༻ࠩผͷېࢭ w உঁޏ༻ػձۉ౳๏ w ৬৔ʹ͓͚Δஉঁࠩผͷېࢭ w

    (%13 w "SUJDMFݸਓσʔλॲཧʹؔ͢Δنఆ w lద๏ɺެฏ͔ͭಁ໌ੑͷ͋ΔखஈͰॲཧ͠ͳ͚Ε͹ͳΒͳ͍z 12 ޏ༻ʹػցֶशΛ࢖͏৔߹͸ରॲ͕ඞཁෆՄܽ (%13͸ͲΜͳλεΫͰ΋ެฏੑ͕ཁٻ͞ΕΔՄೳੑ͕͋Δ
  3. ෆެฏͷݪҼ ͳͥػցֶश͕ෆެฏͳग़ྗΛ͢Δͷ͔  w σʔλऩू͔Βֶशͷաఔʹ͓͍ͯόΠΞε͕৐Δ͜ͱ͕ݪҼ w ༷ʑͳόΠΞε͕ͷΔݪҼ͕ٞ࿦͞Ε͍ͯΔ<#BSPDBT > w େ͖ͭ͘ʹΘ͚Δ

    14 ෆެฏ σʔλऩूʹ͓͚Δ 
 όΠΞε w ࠩผతϥϕϧ෇͚ w αϯϓϦϯάόΠΞε ֶशʹ͓͚Δ 
 όΠΞε w ֶशϞσϧͷઃܭ w গ਺άϧʔϓͷແࢹ σʔλ ֶश
  4. "EVMUEBUB<$BMEFST > w 64ͷશ݅ௐࠪσʔλ w ݸਓͷऩೖ͕LҎ্͔ҎԼ͔༧ଌ͢Δ໰୊ 17 .BMF 'FNBMF )JHIJODPNF

      -PXJODPNF   ͕ ߴऩೖ ͕ ߴऩೖ σʔλʹஉঁؒͷόΠΞε͕͋Δ
  5. "EVMUEBUB<$BMEFST > w /BJWF#BZFTͰֶश͠෼ྨ͢Δ 19 .BMF 'FNBMF )JHIJODPNF  

    -PXJODPNF   ͕ ߴऩೖ ͕ ߴऩೖ ΑΓࠩผతͳ༧ଌ݁ՌʹͳΔ
  6. 3FEMJOJOHF ff FDU<$BMEFST > w௚઀உঁͷ஋Λ࢖Θͳͯ͘΋ࠩผ͕ى͜Δ w உঁ΍ਓछͳͲͱڧ͘ґଘͨ͠σʔλ Λ࢖͏͜ͱͰؒ઀తʹࠩผ͕ൃੜ w ྫ

    ֶྺΛ࢖ͬͯ࠾൱ΛܾΊΔͱ 
 ੑ͕ࠩੜ·ΕΔՄೳੑ͋Γ w ྫ ॅॴΛ࢖ͬͯ࠾൱ΛܾΊΔͱ 
 ਓछͷ͕ࠩੜ·ΕΔՄೳੑ͋Γ 21 'SPNXJLJQFEJB
  7. "EVMUEBUB<$BMEFST > w ੑผΛऔΓআ͍ͯ࠶౓/BJWF#BZFTͰֶश͠෼ྨ͢Δ 22 .BMF 'FNBMF )JHIJODPNF  

    -PXJODPNF   ͕ ߴऩೖ ͕ ߴऩೖ ΑΓࠩผతͳ༧ଌ݁ՌʹͳΔ
  8. ઃఆ w ؆୯ͷͨΊʹڭࢣ͋Γ෼ྨ໰୊ͷΈΛߟ͑Δ w ɹɹɹɹɹɹɹɹɹɹֶྺɼ৬ྺɼࢿ֨ͳͲ w ɹɹɹɹɹɹɹɹɹɹੑผɼਓछɼफڭɼ੓࣏ࢤ޲ɼ೥ྸͳͲ w ɹɹɹɹɹɹɹɹɹɹ༧ଌ͍ͨ͠΋ͷ FH

    ࠾൱  w ɹɹɹɹɹɹɹɹɹɹΞϧΰϦζϜʹΑͬͯ༧ଌ͞Εͨϥϕϧ ೖྗ X ϥϕϧ Y ༧ଌϥϕϧ ̂ Y ผͷೖྗ X S = உੑ S = ঁੑ ೖྗ X ϥϕϧ Y ηϯγςΟϒଐੑ S ༧ଌϥϕϧ ̂ Y ֶश
  9. ެฏੑج४ w ༷ʑͳެฏੑج४ w %FNPHSBQIJDQBSJUZ w &RVBMJ[FEPEET<)BSEU > w *OEJWJEVBMGBJSOFTT<%XPSL

    > w $BMJCSBUJPO<1MFJTT > w $PVOUFSGBDUVBMGBJSOFTT<,VTOFS > w 1BUITQFDJ fi DDPVOUFSGBDUVBMGBJSOFTT <$IJBQQB >
  10. %FNPHSBQIJDQBSJUZ w ηϯγςΟϒଐੑͰ৚͚݅ͮΒΕͨ༧ଌϥϕϧͷ෼෍͕Ұ க %FNPHSBQIJDQBSJUZ ℙ{ ̂ Y ∈ 𝒜

    |S = s} = ℙ{ ̂ Y ∈ 𝒜 |S = s′  } ೚ҙͷ 𝒜 , s, s′  ʹ͍ͭͯ ࠾༻ ඇ࠾༻ ࠾༻ ඇ࠾༻ உੑ ঁੑ = ̂ Y|S = உੑ ̂ Y|S = ঁੑ
  11. &RVBMJ[FEPEET<)BSEU > w ِཅੑͷΈͷҰகͷ৔߹&RVBM PQQPSUVOJUZͱݺͿ &RVBMJ[FEPEET ℙ{ ̂ Y ∈

    𝒜 |Y = y, S = s} = ℙ{ ̂ Y ∈ 𝒜 |Y = y, S = s′  } ೚ҙͷ 𝒜 , y, s, s′  ʹ͍ͭͯ ࠾༻ ඇ࠾༻ உੑ ࠾༻ ඇ࠾༻ ঁੑ ਅͷ࠾༻෼෍ ֶश ࠾༻ ඇ࠾༻ ࠾༻ ඇ࠾༻ ެฏ ֶशͷ݁ՌมԽͨ͠෦෼ ྘ͷ෦෼ ͷҰக
  12. *OEJWJEVBMGBJSOFTT<%XPSL > w ੑผҎ֎શ͘ಉ͡ਓ͕͍Ε͹࠾൱΋ಉ͡ʹ͢Δ΂͖ w ࣅͨΑ͏ͳਓ͸ࣅͨ݁ՌΛड͚औΔ΂͖ w ֬཰త༧ଌؔ਺ w -JQTDIJU[QSPQFSUZ

    ೚ҙͷx, x′  ʹ͍ͭͯ D( f(x), f(x′  )) ≤ d(x, x′  ) ≈ ⟹ f : 𝒳 → Δ( 𝒴 ) ݁Ռͷ෼෍ؒͷ ڑ཭
  13. ެฏͳֶशख๏ w1SPYZ"QQSPBDI<,BNJTIJNB  'VLVDIJ  ;BGBS > wඍ෼ෆՄೳ߲Λඍ෼Մೳͳؔ਺Ͱۙࣅ w3FEVDUJPO"QQSPBDI<"HBSXBM 

    $PUUFS  "HBSXBM > wެฏͳֶशͷ࠷దԽ໰୊Λஞ࣍తͳ੍໿ͳ͠࠷దԽʹॻ͖׵͑ Δ w'BJS3FQSFTFOUBUJPO<;BGBS  9JF  .PZFS   ;IBP  $SFBHFS > wηϯγςΟϒଐੑʹґଘ͠ͳ͍ਂ૚දݱΛֶश͠ɼͦͷදݱΛ ࢖ͬͯ༧ଌΛߦ͏
  14. ෼ྨʹ͓͚Δ#BZFTPQUJNBMDMBTTJ fi FS w ෼ྨ໰୊ w ɹɹɹɹɹɹɹɹɹɹɹɹֶྺɼ৬ྺɼࢿ֨ͳͲ w ɹɹɹɹɹɹɹɹɹɹɹɹੑผɼਓछɼफڭɼ੓࣏ࢤ޲ɼ೥ྸͳͲ w

    ɹɹɹɹɹɹɹɹɹɹɹɹ༧ଌ͍ͨ͠΋ͷ FH ࠾൱  w ɹɹɹɹɹɹɹɹɹɹɹɹΞϧΰϦζϜʹΑͬͯ༧ଌ͞Εͨϥϕϧ w ֬཰తͳ༧ଌث  w േଇϕʔεͷެฏͳֶश  w ֶशͷจ຺Ͱ͸໨తؔ਺ɾެฏੑ੍໿Λ௚઀ධՁͰ͖ͳ͍ w ͷ෼෍͕ಘΒΕΔ৔߹ͷ࠷దԽ໰୊ͷղ͸Կ͔ʁ w #BZFTPQUJNBMDMBTTJ fi FS f : ℝd × {0,1} → [0,1] minf 𝔼 [Y(1 − f(X, S)) + (1 − Y)f(X, S)] + λUnfair( f ) (Y, X, S) ೖྗ X ∈ ℝd ϥϕϧ Y ∈ {0,1} ηϯγςΟϒଐੑ S ∈ {0,1} ༧ଌϥϕϧ ̂ Y ∈ {0,1}
  15. ී௨ͷ෼ྨ໰୊ʹ͓͚Δ#BZFTPQUJNBM DMBTTJ fi FS<&MLBO> wެฏੑ੍໿͕ͳ͍৔߹ͷ#BZFTPQUJNBMDMBTTJ fi FS͸ʁ ଛࣦΛ࠷খʹ͢Δ֬཰తͳ#BZFTPQUJNBMDMBTTJ fi FS

    ͸೚ҙͷ ʹ͍ͭͯҎԼͷࣜͰ༩͑ΒΕΔɽ  f* α ∈ [0,1] f*(x) = Hα (η(x) − 1 2 ) ఆཧʢ؆қ൛ʣ<&MLBO> w  w ͸ࢦࣔؔ਺ w Hα (z) = 1{z > 0} + α1{z = 0} 1 η(x) = 𝔼 [Y|X = x]
  16. %FNPHSBQIJDQBSJUZ੍໿ʹ͓͚Δ#BZFT PQUJNBMDMBTTJ fi FS<.FOPO > wެฏੑΛ%FNPHSBQIJDQBSJUZͰଌΔͱ͢Δ w  w 

    Unfair(f ) = ℙ{ ̂ Y = 1|S = 0} − ℙ{ ̂ Y = 1|S = 1} η(x, s) = 𝔼 [Y = 1|X = x, S = s] π = ℙ{S = 0} %FNPHSBQIJDQBSJUZʹର͢Δേଇ෇͖ͷଛࣦΛ࠷খ ʹ͢Δ֬཰తͳ#BZFTPQUJNBMDMBTTJ fi FS ͸೚ҙͷ ʹ͍ͭͯҎԼͷࣜͰ༩͑ΒΕΔɽ  f* α ∈ [0,1] f*(x, s) = Hα (η(x, s) − (−1)s λ 2s(1 − π) + 2(1 − s)π − 1 2 ) ఆཧʢ؆қ൛ʣ<.FOPO >
  17. %FNPHSBQIJDQBSJUZ੍໿ʹ͓͚Δ#BZFT PQUJNBMDMBTTJ fi FS<.FOPO > wެฏੑΛ%FNPHSBQIJDQBSJUZͰଌΔͱ͢Δ w  w 

    Unfair(f ) = ℙ{ ̂ Y = 1|S = 0} − ℙ{ ̂ Y = 1|S = 1} η(x, s) = 𝔼 [Y = 1|X = x, S = s] π = ℙ{S = 0} %FNPHSBQIJDQBSJUZʹର͢Δേଇ෇͖ͷଛࣦΛ࠷খ ʹ͢Δ֬཰తͳ#BZFTPQUJNBMDMBTTJ fi FS ͸೚ҙͷ ʹ͍ͭͯҎԼͷࣜͰ༩͑ΒΕΔɽ  f* α ∈ [0,1] f*(x, s) = Hα (η(x, s) − (−1)s λ 2s(1 − π) + 2(1 − s)π − 1 2 ) ఆཧʢ؆қ൛ʣ<.FOPO > ͰͷΈมΘΔఆ਺ s
  18. &RVBMPQQPSUVOJUZ੍໿ʹ͓͚Δ#BZFT PQUJNBMDMBTTJ fi FS<.FOPO > wެฏੑΛ&RVBMPQQPSUVOJUZͰଌΔͱ͢Δ wUnfair(f ) = ℙ{

    ̂ Y = 1|Y = 1,S = 0} − ℙ{ ̂ Y = 1|Y = 1,S = 1} &RVBMPQQPSUVOJUZʹର͢Δേଇ෇͖ͷଛࣦΛ࠷খʹ ͢Δ֬཰తͳ#BZFTPQUJNBMDMBTTJ fi FS ͸೚ҙͷ ʹ͍ͭͯҎԼͷࣜͰ༩͑ΒΕΔɽ  f* α ∈ [0,1] f*(x, s) = Hα (η(x, s) − 1 2 ) ఆཧʢ؆қ൛ʣ<.FOPO > ੍໿ͳ͠ͱಉ͡ʂ
  19. &RVBMPQQPSUVOJUZ੍໿ʹ͓͚Δܾఆత #BZFTPQUJNBMDMBTTJ fi FS<$I[IFO > w׬શͳ&RVBMPQQPSUVOJUZ੍໿Λߟ͑Δ wേଇͰ͸ͳ͘ ͷ੍໿ͱ͢Δ w 

    w Unfair(f ) = 0 Unfair(f ) = ℙ{ ̂ Y = 1|Y = 1,S = 0} − ℙ{ ̂ Y = 1|Y = 1,S = 1} πs = ℙ{Y = 1,S = s} &RVBMPQQPSUVOJUZʹର͢Δേଇ෇͖ͷଛࣦΛ࠷খʹ ͢Δܾఆతͳ#BZFTPQUJNBMDMBTTJ fi FS ͸೚ҙͷ ʹ͍ͭͯҎԼͷࣜͰ༩͑ΒΕΔɽ  f* α ∈ [0,1] f*(x, s) = 1 {η(x, s)(1 + (−1)s θ πs ) ≥ 1 2 } ఆཧʢ؆қ൛ʣ<$I[IFO > ຖʹᮢ஋Λม͍͑ͯΔ s
  20. ճؼʹ͓͚Δ#BZFTPQUJNBMSFHSFTTPS w ύϥϝτϦοΫճؼϞσϧ  w ͸ฏۉͷϊΠζ w ܾఆతͳ༧ଌث  w

    %FNPHSBQIJDQBSJUZ੍໿ͷެฏͳֶश  Y = f*(X, S) + ξ ξ f : ℝd × [M] → ℝ minf 𝔼 [(Y − f(X, S))2] sub to ∀s ∈ [M], E, ℙ{f(X, S) ∈ E|S = s} = ℙ{f(X, S) ∈ E}
  21. 8BTTFSTUFJOCBSZDFOUFSʹΑΔ 
 #BZFTPQUJNBMFSSPSͷಛ௃͚ͮ<$I[IFO > w %FNPHSBQIJDQBSJUZ੍໿ͷެฏͳֶश͸8BTTFSTUFJO CBSZDFOUFSͰಛ௃͚ͮͰ͖Δ w 8BTTFSTUFJOڑ཭ 

    w ͷ Ͱ৚͚݅ͭͨ෼෍  w W2 (ν0 , ν1 ) = infπ∈Π(ν0 ,ν1 ) ∫ |x − y|2 π(dx, dy) f*(X, S) S = s νf*|s ps = ℙ{S = s} minf:DP 𝔼 [(f*(X, S) − f(X, S))2] = minν ∑ s∈[M] ps W2 2 (νf*|s , ν) ఆཧ<$I[IFO > 8BTTFSTUFJOCBSZDFOUFS
  22. ճؼʹ͓͚Δ#BZFTPQUJNBMSFHSFTTPS <$I[IFO > w %FNPHSBQIJDQBSJUZ੍໿ͷ#BZFTPQUJNBMSFHSFTTPS͸ҎԼͷఆཧͰٻ·Δ w ͸ ͷ Ͱ৚݅෇͚ͨ࣌͠ͷ$%'ͱٖࣅ*$%' Fs

    , F−1 s f*(X, S) S = s g*(x, s) = ∑ s∈[M] ps F−1 s (Fs (f*(x, s))) ఆཧ<$I[IFO > ੨ͱ྘ͷ໘ੵ͸౳͍͠ ੺͸੨ͱ྘ͷฏۉ
  23. ճؼʹ͓͚Δ#BZFTPQUJNBMSFHSFTTPS <$I[IFOBOE4DISFVEFS> w%FNPHSBQIJDQBSJUZͷެฏੑ੍໿Λ؇࿨ͨ࣌͠ͷ#BZFT PQUJNBMSFHSFTTPS w  w U(f ) =

    infν ∑ s∈[M] ps W2 2 (νf|s , ν) U(f ) ≤ αU(f*) g* α (x, s) = (1 − α)g* 0 (x, s) + αf*(x, s) ఆཧ<$I[IFOBOE4DISFVEFS> લϖʔδͷ#BZFTPQUJNBM SFHSFTTPS
  24. Ճ๏తόΠΞεઢܗϞσϧʹ͓͚Δճؼͷ NJOJNBY࠷దੑ<$I[IFOBOE4DISFVEFS> wଛࣦ  wެฏͳΞϧΰϦζϜ೚ҙͷαϯϓϧαΠζ ʹ͍ͭͯ  w ͸ΞϧΰϦζϜ͕ग़ྗ͢Δ༧ଌث w

    ͜ͷ໰୊ʹ͓͚ΔNJOJNBY࠷దͳΞϧΰϦζϜͱ͸ʁ Err( f; P) = 𝔼 P [( f*(X, S) − f(X, S))2] n ℙ{U( ̂ f ) ≤ αU( f*)} ≥ 1 − δ ̂ f w  w ͸ฏۉͷ෼ࢄ ͷਖ਼ن෼෍ʹै͏ w ͸ฏۉ ͷڞ෼ࢄߦྻ ͷଟมྔਖ਼ن෼෍ʹै͏ Y = f*(X, S) + ξ = ⟨β, X⟩ + bS + ξ ξ σξ X μ Σ Ճ๏తόΠΞεઢܗϞσϧ
  25. Ճ๏తόΠΞεઢܗϞσϧʹ͓͚Δճؼͷ NJOJNBY࠷దੑ<$I[IFOBOE4DISFVEFS> wଛࣦ  wެฏͳΞϧΰϦζϜ೚ҙͷαϯϓϧαΠζ ʹ͍ͭͯ  w ͸ΞϧΰϦζϜ͕ग़ྗ͢Δ༧ଌث w

    ͜ͷ໰୊ʹ͓͚ΔNJOJNBY࠷దͳΞϧΰϦζϜͱ͸ʁ Err( f; P) = 𝔼 P [( f*(X, S) − f(X, S))2] n ℙ{U( ̂ f ) ≤ αU( f*)} ≥ 1 − δ ̂ f w  w ͸ฏۉͷ෼ࢄ ͷਖ਼ن෼෍ʹै͏ w ͸ฏۉ ͷڞ෼ࢄߦྻ ͷଟมྔਖ਼ن෼෍ʹै͏ Y = f*(X, S) + ξ = ⟨β, X⟩ + bS + ξ ξ σξ X μ Σ Ճ๏తόΠΞεઢܗϞσϧ ʹґଘ͢Δ߲͸Ճ๏తͳఆ਺ S
  26. ઢܗϞσϧʹ͓͚ΔNJOJNBY࠷దੑ <'VLVDIJ > w EFNPHSBQIJDQBSJUZ੍໿ԼͰͷ#BZFTPQUJNBMSFHSFTTPS w%1੍໿  wଛࣦ  wެฏͳΞϧΰϦζϜ೚ҙͷαϯϓϧαΠζ

    ʹ͍ͭͯ  w͜ͷϞσϧͰͷNJOJNBY࠷దͳΞϧΰϦζϜ͸ʁ f* DP ∀s ∈ [M], E, ℙ{f(X, S) ∈ E|S = s} = ℙ{f(X, S) ∈ E} Err( f; P) = 𝔼 P [( f* DP (X, S) − f(X, S))2] n ℙ{maxs,s′  ∈[M] W2 (ν ̂ f|s , ν ̂ f|s′  ) ≤ Cn−α} ≥ 1 − δ w  w ͸ฏۉͷ෼ࢄ ͷਖ਼ن෼෍ʹै͏ w ͸ฏۉ ͷڞ෼ࢄߦྻ ͷଟมྔਖ਼ن෼෍ʹै͏ Y = f*(X, S) + ξ = ⟨βs , X⟩ + ξ ξ σξ X μS σX I ઢܗϞσϧ
  27. ઢܗϞσϧʹ͓͚ΔNJOJNBY࠷దੑ <'VLVDIJ > w EFNPHSBQIJDQBSJUZ੍໿ԼͰͷ#BZFTPQUJNBMSFHSFTTPS w%1੍໿  wଛࣦ  wެฏͳΞϧΰϦζϜ೚ҙͷαϯϓϧαΠζ

    ʹ͍ͭͯ  w͜ͷϞσϧͰͷNJOJNBY࠷దͳΞϧΰϦζϜ͸ʁ f* DP ∀s ∈ [M], E, ℙ{f(X, S) ∈ E|S = s} = ℙ{f(X, S) ∈ E} Err( f; P) = 𝔼 P [( f* DP (X, S) − f(X, S))2] n ℙ{maxs,s′  ∈[M] W2 (ν ̂ f|s , ν ̂ f|s′  ) ≤ Cn−α} ≥ 1 − δ w  w ͸ฏۉͷ෼ࢄ ͷਖ਼ن෼෍ʹै͏ w ͸ฏۉ ͷڞ෼ࢄߦྻ ͷଟมྔਖ਼ن෼෍ʹै͏ Y = f*(X, S) + ξ = ⟨βs , X⟩ + ξ ξ σξ X μS σX I ઢܗϞσϧ ઢܗύϥϝʔλͱ ͷฏۉ͕ ʹΑΓมΘΔ X S ଛࣦΛެฏͰ࠷దͳ༧ଌثͱͷ 
 ޡࠩͰఆٛʢҰகੑ͕੒Γཱͭʣ ࠷ѱέʔεͷެฏੑΛධՁ ʢ ͸ฏۉతͳެฏੑʣ U
  28. ઢܗϞσϧʹ͓͚ΔNJOJNBY࠷దੑ <'VLVDIJ > w ͱ Λఆ਺ͱݟΕ͹࠷దଛࣦ͸  w ͸ฏۉ ͷ࠷େϊϧϜ

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  29. ·ͱΊ wެฏੑͷ஫໨ͱࣾձతͳඞཁੑ wݱ࣮ͷΞϓϦέʔγϣϯͰ໰୊ʹͳ͓ͬͯΓɼࣾձతɾ๏తʹඞཁੑ͕ग़͖ͯ ͍ͯΔ wػցֶशʹ͓͚ΔෆެฏͷݪҼ wσʔλऩूʹ͓͚ΔόΠΞεɾֶशʹ͓͚ΔόΠΞε wެฏͳֶशͷ࢓૊Έ wެฏੑج४EFNPHSBQIJDQBSJUZ FRVBMJ[FEPEET ʜ

    wެฏੑͷ੍໿ɾേଇ෇͖ͷଛࣦ࠷খԽ wެฏͳֶशͷ#BZFTPQUJNBMͳ෼ྨɾճؼ wᮢ஋Λม͑ΔΑ͏ͳΠϝʔδͰா৲߹ΘͤΛߦ͏ wެฏͳֶशͷNJOJNBY࠷దͳճؼ wՃ๏తϞσϧͰͷ࠷దੑ<$I[IFOBOE4DISFVEFS>ɼઢܗϞσϧͰͷ࠷ద ੑ<'VLVDIJ >
  30. ࢀߟจݙ w<#VPMBNXJOJ `>#VPMBNXJOJ +PZ BOE5JNOJU(FCSV(FOEFSTIBEFT*OUFSTFDUJPOBM BDDVSBDZEJTQBSJUJFTJODPNNFSDJBMHFOEFSDMBTTJ fi DBUJPO$POGFSFODFPOGBJSOFTT  BDDPVOUBCJMJUZBOEUSBOTQBSFODZ1.-3

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  31. ࢀߟจݙ w<#BSPDBT >#BSPDBT 4PMPO BOE"OESFX%4FMCTU#JHEBUBTEJTQBSBUFJNQBDU$BMJG- 3FW   w<$BMEFST >$BMEFST

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  32. ࢀߟจݙ w<,BNJTIJNB >,BNJTIJNB 5PTIJIJSP 4IPUBSP"LBIP )JEFLJ"TPI BOE+VO4BLVNBl'BJSOFTT"XBSF $MBTTJ fi FSXJUI1SFKVEJDF3FNPWFS3FHVMBSJ[FSz*O.BDIJOF-FBSOJOHBOE,OPXMFEHF%JTDPWFSZJO

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