差分プライバシー入門

差分プライバシーが求められている背景と、差分プライバシーの概要についてご紹介します。

Transcript

1. ˜
   -:
   $PSQPSBUJPO ࠩ෼ϓϥΠόγʔೖ໳ ٻΊΒΕΔഎܠͱϓϥΠόγʔอޢͷ࢓૊Έ ∁ڮ
   ཌྷ c
   5TVCBTB 5",")"4)* -*/&Ϡϑʔݚڀॴ ্੮ݚڀһ 
   "*
   4FDVSJUZ
   
   1SJWBDZਪਐࣨ ࣨ௕ 
2. ˜
   -:
   $PSQPSBUJPO  5TVCBTB 5",")"4)*
   1I% IUUQTXXXOFDTPMVUJPOJOOPWBUPSTDPKQTMEBOPOZ /&$ -*/& -*/&Ϡϑʔ 4#
   *OUVJUJPOT d d /&$σʔλಗ໊ԽιϦϡʔγϣϯ ʮ-*/&ʯΞϓϦͷελϯϓαδΣετ ࿈߹ֶश ࠩ෼ϓϥΠόγʔ IUUQTMJOFDPSQDPNKB TFDVSJUZBSUJDMF ੜ੒"* ετϨε ςετ"* ҙਤతͳ߈ܸతΫΤϦ 8BUFSNBSL
   %JGGVTJPO
   .PEFM --.ͷετϨεςετ ఢରతಁ͔͠ʹΑΔஶ࡞ݖอޢ $.6d ໦ߋ௡ߴઐ ஜ೾େֶ
3. ˜
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   $PSQPSBUJPO ࠩ෼ϓϥΠόγʔͱ͸ʢ֓ཁʣ ౷ܭ։ࣔʹ͓͚ΔϓϥΠόγʔϦεΫ ࠩ෼ϓϥΠόγʔͷ࢓૊Έ     ຊߨٛͷίϯςϯπ ࠩ෼ϓϥΠόγʔͷৄࡉͳཧ࿦΍Ԡ༻ΑΓ΋ɺͳͥࠩ෼ϓϥΠόγʔ͕ඞཁͱ͞Ε͍ͯΔ͔ʹয఺Λ౰ͯ·͢
4. ˜
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   $PSQPSBUJPO  1SJWBDZ
   &OIBODJOH
   5FDIOPMPHJFT
   1&5T 1&5Tʹ͸ɺ
   ҉߸౳ʹΑΔΞΫηε੍ޚٕज़ͱ 
   ৘ใͦͷ΋ͷΛՃ޻͢Δٕज़ ͕͋Δ ࿈߹ֶशɾ ہॴࠩ෼ϓϥΠόγʔ ಗ໊Խɾσʔλ߹੒ ࠩ෼ϓϥΠόγʔ ੺͍఺ઢΑΓࠨଆ͕ϓϥΠόγʔอޢͷൣғ FH
   ಗ໊Խ΍ࠩ෼ϓϥΠόγʔ FH
   ࿈߹ֶश΍ൿີܭࢉ
5. ˜
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   $PSQPSBUJPO  ࠩ෼ϓϥΠόγʔͱ͸ ϊΠζʢ ʣ͕Ճࢉ͞Ε͍ͯΔͱϓϥΠόγʔอޢ͞Ε͍ͯΔΑ͏ʹײ͡·ͤΜ͔ʁ ౷ܭత ͳग़ྗ ϊΠζ ΛՃࢉ 𝜖  ∞    TUSPOH XFBL   ʜ ࠩ෼ϓϥΠόγʔ͕ఏڙ͢Δ΋ͷ • ϊΠζͷՃࢉʹର͢Δ ཧ࿦తͳϓϥΠόγʔอޢͷई౓ • ॴఆͷϓϥΠόγʔڧ౓ 𝜖 ͷ ୡ੒ʹඞཁͳϊΠζͷಋग़
6. ˜
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   $PSQPSBUJPO  ͭͷओཁͳϓϥΠόγʔϞσϧ $FOUSBM
   %JGGFSFOUJBM
   1SJWBDZ -PDBM
   %JGGFSFOUJBM
   1SJWBDZ ୈࡾऀ΁ͷ ౷ܭ஋ͷެ։ ػඍͳ ౷ܭͷऩू αʔόʔΛ ৴༻͠ͳ͍ αʔόʔΛ ৴༻͢Δ ಋೖࣄྫ • $ISPNFϒϥ΢βͰͷ౷ܭऩू (PPHMF • J04σόΠεͰͷ౷ܭऩू "QQMF • ελϯϓαδΣετͷ࿈߹ֶश -*/&Ϡϑʔ ಋೖࣄྫ • ೥౓ถࠃࠃ੎ௐࠪ 64
   $FOTVT
   • 'VMM
   63-T
   EBUB
   TFU
   .FUB • /FYU
   XPSE
   QSFEJDUJPO
   JO
   (CPBSE (PPHMF • "VEJFODF
   &OHBHFNFOU
   "1*
   -JOLFE*O ʢ͝ࢀߟʣ"
   MJTU
   PG
   SFBMXPSME
   VTF
   PG
   EJGGFSFOUJBM
   QSJWBDZ
   IUUQTEFTGPOUBJOFTQSJWBDZSFBMXPSMEEJGGFSFOUJBMQSJWBDZIUNM
7. ˜
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   $PSQPSBUJPO  64
   $FOTVT
   Ͱࠩ෼ϓϥΠόγʔΛར༻ͨ͠ཧ༝ • ࠩ෼ϓϥΠόγʔ͸ɺࠓ೔ͷϓϥΠόγʔڴҖʹର͢Δ ࠷৽ͷηʔϑΨʔυͰ͋Δ • εύίϯ͸ɺݸਓ৘ใΛಛఆ͢ΔͨΊʹෳ਺ͷ%#͔Β σʔλΛݟ͚ͭग़͠ɺর߹͢Δ͜ͱͰɺ܈ऺͷத͔Β͋ ͳͨΛ༰қʹબͼग़͢ʢڱ͍஍ҬʹॅΜͰ͍ͯɺྡਓͱ ਓछ΍ຽ଒͕ҟͳΔ৔߹͸ಛʹʣ • ϓϥΠόγʔʹର͢ΔਂࠁͳڴҖ͸ɺ೥લͷࠃ੎ௐࠪ ͷ࣌ʹ͸ଘࡏ͠ͳ͔ͬͨ΋ͷͰ͋Δ • ࢲͨͪ͸ɺਓʑͷϓϥΠόγʔΛอޢ͠ଓ͚ΔͨΊʹɺ ৽͍ٕ͠ज़Λ࢖Θͳ͚Ε͹ͳΒͳ͍ • ࠓ೔ͷϓϥΠόγʔͷڴҖͷن໛Λߟ͑Δͱɺաڈͷํ ๏͸ɺެද͞Εͨσʔλʹஶ͘͠େ͖ͳ࿪ΈΛੜͤ͡͞ɺ σʔλͷଟ͘Λ࢖༻Ͱ͖ͳͯ͘͠͠·͏ͩΖ͏ IUUQTXXXDFOTVTHPWDPOUFOUEBN$FOTVTMJCSBSZGBDUTIFFUTEJGGFSFOUJBMQSJWBDZBOEUIFDFOTVTQEG
8. ˜
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   $PSQPSBUJPO  Ҏ߱ͷύʔτͷૂ͍ • աڈʹى͖ͨϓϥΠόγʔ৵֐ͷࣄྫͱɺͦ͜Ͱར༻͞ΕͨϓϥΠόγʔอޢٕज़ʹ͍ͭͯ ঺հ͠·͢ • աڈࣄྫΛ௨ͯ͠ɺͳͥࠩ෼ϓϥΠόγʔ͕ඞཁͳͷ͔ɺΛղઆ͍͖ͯ͠·͢ • ݫີͳఆٛΑΓ΋ɺΘ͔Γ΍͢͞Λ༏ઌͨ͠આ໌Λ͠·͢
9. ˜
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   $PSQPSBUJPO ౷ܭ։ࣔʹ͓͚ΔϓϥΠόγʔϦεΫ 
10. ˜
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    $PSQPSBUJPO  ถࠃ."भʹ͓͚Δ࠶ࣝผͷ໰୊
    ೥୅ • ถࠃ."भͰ͸ɺभͷ৬һͷ௨Ӄه࿥ " Λر๬͢Δݚڀऀʹެ։ ໊લ͸࡟আ • έϯϒϦοδࢢͷ༗ݖऀσʔλϕʔε # ͸υϧͰߪೖͰ͖ͨ • " ͱ # ͷ૊Έ߹Θ͔ͤΒ8FME஌ࣄͷϨίʔυ͕؆୯ʹಛఆͰ͖ͨ (FOEFS ;JQ #JSUI %JTFBTF ' B YYBBCC "#$ . C YYZZ[[ %&' . D BCXXUU ()* ' E NOQQRR +,- /BNF (FOEFS ;JQ #JSUI ʜ ' B YYBBCC 8JMMJBN
    8FME . C YYZZ[[ . D BCXXUU ' E NOQQRR /BNF (FOEFS ;JQ #JSUI %JTFBTF ' B YYBBCC "#$ 8JMMJBN
    8FME . C YYZZ[[ %&' . D BCXXUU ()* ' E NOQQRR +,- +0*/ ४ࣝผࢠ 2VBTJ*EFOUJGJFS
    2*%
11. ˜
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    $PSQPSBUJPO  /FUGMJY
    1SJ[Fͷ࠶ࣝผͷ໰୊  • ಗ໊Խ͞Ε͍ͯͳ͍֎෦ͷσʔλϕʔε
    *.%#
    ͱͷಥ߹ʹΑͬͯɺಗ໊Խ͞Ε͍ͯͨίϝ ϯτͱϢʔβ͕ରԠ෇͍ͯ͠·ͬͨ • ίϝϯτʹ͸੓࣏৴৚͕Θ͔Δ΋ͷ΋͋ͬͨ • ݸͷධՁͱ೔෇
    िؒҎ಺ͷਫ਼౓
    ͕෼͔Ε͹ͷਫ਼౓ͰݸਓΛಛఆͰ͖ͨ 6TFSOBNF 5JUMF 3BUF "MJDF """  ###  %%%  #PC """  999  1TFVEP
    *% 5JUMF 3BUF $PNNFOU Y """  ###  %%%  *U
    TFFNT
    YYY B :::  999  "OPOZNJ[FE
    /FUGMJY
    .PWJF
    SBOLJOH
    EBUB /POBOPOZNPVT
    *.%#
    NPWJF
    SBUJOH +0*/
12. ˜
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    $PSQPSBUJPO  Lಗ໊Խ • ಗ໊Խɿσʔλͷಛఆ΍ࣝผΛࠔ೉ʹ͢ΔͨΊʹߦ͏σʔλͷՃ޻ॲཧ • Lಗ໊Խɿ%#಺ʹɺ೚ҙͷϨίʔυͱಉ͡४ࣝผࢠͷ૊Λ࣋ͭଞͷϨίʔυ͕Lݸଘࡏ • ४ࣝผࢠ
    2VBTJ
    *EFOUJGJFS ɿ૊߹ͤʹΑͬͯݸਓΛࣝผ͠ಘΔଐੑͷू߹ɻࣄલʹఆٛ "HF (FOEFS 4BMBSZ "MJDF  'FNBMF 
    . #PC  .BMF 
    . $IBSMJF  .BMF 
    . %BWJE  .BMF 
    , &NNB  'FNBMF 
    . 'SBOD  .BMF 
    . (FPSHF  .BMF 
    , )BOB  'FNBMF 
    , "HF (FOEFS 4BMBSZ  
    .  
    .  
    .  
    ,  
    .  
    .  
    ,  
    , Lಗ໊Խ L
13. ˜
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    $PSQPSBUJPO  Lಗ໊Խͷݶք • ४ࣝผࢠҎ֎ͷଐੑʹର͢Δ֎෦஌ࣝͷಥ߹ʹΑΓɺLಗ໊ԽΛഁΒΕΔ͜ͱ͕͋Δ • è ߈ܸऀͷഎܠ஌ࣝʹΑͬͯ͸ಗ໊ੑ͕े෼Ͱͳ͍ "HF (FOEFS 4BMBSZ  
    .  
    .  
    .  
    ,  
    .  
    .  
    ,  
    , Lಗ໊Խ L "HF (FOEFS 1IPOF "MJDF  'FNBMF  #PC  .BMF  $IBSMJF  .BMF  %BWJE  .BMF  &NNB  'FNBMF  'SBOD  .BMF  (FPSHF  .BMF  )BOB  'FNBMF  (FOEFS 4BMBSZ #PC .BMF 
    . &NNB 'FNBMF 
    . (FPSHF .BMF 
    , ᶃ ᶃ ᶄ 'SBOD
    à 4BMBSZ. ΛಛఆͰ͖ͯ͠·͏ ఢରऀͷ֎෦஌ࣝ
14. ˜
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    $PSQPSBUJPO  ࠩ෼߈ܸ • ෳ਺ͷ౷ܭ৘ใͷʮࠩ෼ʯ͔Βಛఆͷݸਓʹؔ͢Δ৘ใΛਪఆ • ಉ͡ϢʔβΛؚΉσʔλϕʔε͔Βੜ੒ͨ͠ෳ਺ͷ౷ܭ৘ใ͕ର৅ BWH
    TBMBSZ 
    ສԁ BWH
    TBMBSZ 
    ສԁ ʲ2VJ[ʳ"MJDFͷ೥ऩ͸ʁ ʜ ʜ ʜ ʜ "MJDF "MJDF͕ୀ৬ 
    FOHJOFFST 
    FOHJOFFST ೥ ೥
15. ˜
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    $PSQPSBUJPO  2VJ[ͷճ౴ BWH
    TBMBSZ 
    ສԁ BWH
    TBMBSZ 
    ສԁ ʲ2VJ[ʳ"MJDFͷ೥ऩ͸ʁ ʜ ʜ ʜ ʜ "MJDF "MJDF͕ୀ৬ 
    FOHJOFFST 
    FOHJOFFST ೥ ೥ 
    Y
    
    r 
    Y
     
    ສԁ ౴͑
16. ˜
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    $PSQPSBUJPO  ࠩ෼߈ܸͷࣄྫ • 'BDFCPPLͷ1**CBTFE
    5BSHFUJOH
    ݱࡏ͸मਖ਼ࡁΈ • ޿ࠂλʔήςΟϯάͷޮՌΛܭଌ͢ΔͨΊͷ౷ܭ෼ੳ"1* • ։੍ࣔޚͷͨΊʹᮢ஋ʹΑΔอޢΛಋೖ͍͕ͯͨ͠ɺόΠύε͞Εͨ • ి࿩൪߸΍ϝʔϧΞυϨεɺ8FCӾཡཤྺ͕࿙Ӯ IUUQTXXXZPVUVCFDPNXBUDI W-Q *X:WY(QL IUUQTXXXGUDHPWTZTUFNGJMFTEPDVNFOUTQVCMJD@FWFO UTQQSJWBDZDPONJTMPWF@QEG
17. ˜
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    $PSQPSBUJPO  σʔλϕʔε࠶ߏங߈ܸ • ౷ܭ৘ใͷݩʹͳͬͨϨίʔυΛ༷ʑͳެ։৘ใΛۦ࢖ͯ͠෮ݩ l਺ಠzΛղ͘Πϝʔδ "O
    &YBNQMF IUUQTXXXDFOTVTHPWBCPVUUSBJOJOHXPSLTIPQTEBTQSFTFOUBUJPOQEG ౷ܭ৘ใͷಋग़աఔʹ͸ɺ ϧʔϧɺΞϧΰϦζϜɺґଘؔ܎͕͋Δ
18. ˜
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    $PSQPSBUJPO  σʔλϕʔε࠶ߏங߈ܸͷࣄྫ • ถࠃͷ೥ͷࠃ੎ௐࠪ • Ҏ্ͷݸਓͷϨίʔυ͕෮ݩ͞ΕಘΔ͜ͱ͕ใࠂ͞Ε͍ͯΔ IUUQTXXXDFOTVTHPWBCPVUUSBJOJOHXPSLTIPQTEBTQSFTFOUBUJPOQEG ೥ͷถࠃͷࠃ੎ௐࠪͰ͸ࠩ෼ϓϥΠόγʔ͕ಋೖ͞Ε͍ͯΔ
19. ˜
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    $PSQPSBUJPO  ౷ܭͷ҆શͳ։ࣔ r ස౓ͱࠩ෼ͷ͖͍͠஋ॲཧ  • ݪཧతʹ͸Մೳ͕ͩɺ͋Γͱ͋ΒΏΔࠩ෼ΛຖճνΣοΫ͢Δ͜ͱ͸༰қͰ͸ͳ͍ • ͖͍͠஋ॲཧʹΑͬͯɺར༻ෆՄೳʹͳΔσʔλ͕ଟ਺ੜ͡ΔڪΕ ೥୅ ੑผ ਓ਺ ୅ உ   ୅ ঁ  ୅ உ   ୅ ঁ   ೥୅ ੑผ ਓ਺ ୅ உ   ୅ ঁ  ୅ உ   ୅ ঁ   ೥୅ ੑผ ਓ਺ ୅ உ   ୅ ঁ  ୅ உ   ୅ ঁ   ਓ਺ͷ͖͍͠஋ɿ ࠩ෼ͷ͖͍͠஋ɿ /( 0, ࣌ࠁ 5 ࣌ࠁ 5 𝜏 ݁ୗऀΛूΊΒΕͳ͍ఔ౓ʹ େ͖͍͖͍͠஋Λઃఆ ྫ
20. ˜
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    $PSQPSBUJPO  ࠩ෼ϓϥΠόγʔ͕ٻΊΒΕ͍ͯΔഎܠ L ಗ໊Խͷݶք • ֎෦஌ࣝʹ੬ऑ ɿ֎෦஌ࣝͱͷಥ߹ʹΑͬͯɺಗ໊Խ͕ഁΒΕΔڪΕ • ෳ਺ެ։ʹඇରԠɿෳ਺ͷಗ໊Խσʔλͷಥ߹ʹΑͬͯ΋ɺಗ໊Խ͕ഁΒΕΔڪΕ • ༗༻ੑҡ͕࣋ࠔ೉ɿσʔλͷෳࡶ౓ɺڴҖͷڧ͞ʹԠͯ͡༗༻ੑͷҡ͕࣋ΑΓࠔ೉ʹ ৽͍͠ڴҖͷొ৔ • ࠩ෼߈ܸ • σʔλϕʔε࠶ߏங߈ܸ ౷ܭσʔλ΍ػցֶशϞσϧʹର͢ΔϓϥΠόγʔई౓ͷඞཁੑ
21. ˜
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    $PSQPSBUJPO ࠩ෼ϓϥΠόγʔͷ࢓૊Έ 
22. ˜
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    $PSQPSBUJPO  ࠩ෼ϓϥΠόγʔͱ͸ ϊΠζʢ ʣ͕Ճࢉ͞Ε͍ͯΔͱϓϥΠόγʔอޢ͞Ε͍ͯΔΑ͏ʹײ͡·ͤΜ͔ʁ ౷ܭత ͳग़ྗ ϊΠζ ΛՃࢉ 𝜖  ∞    TUSPOH XFBL   ʜ ࠩ෼ϓϥΠόγʔ͕ఏڙ͢Δ΋ͷ • ϊΠζͷՃࢉʹର͢Δ ཧ࿦తͳϓϥΠόγʔอޢͷई౓ • ॴఆͷϓϥΠόγʔڧ౓ 𝜖 ͷ ୡ੒ʹඞཁͳϊΠζͷಋग़
23. ˜
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    $PSQPSBUJPO  %1ʹ౷ܭॲཧͱϊΠζՃࢉʹΑΔग़ྗͷࣝผࠔ೉ੑ • ग़ྗͷࣝผࠔ೉ੑɿೖྗͷΘ͔ͣͳࠩҟʹґΒͣग़ྗ͕΄ͱΜͲมΘΒͳ͍ • ˞
    Ұൠతͳʮಗ໊Խʯͱ͸ҟͳΔϓϥΠόγʔͷߟ͑ํ • ॴఆͷࣝผࠔ೉ੑΛୡ੒͢ΔΑ͏ʹϝΧχζϜℳʢ౷ܭॲཧͱϊΠζՃࢉʣΛઃܭ ℳ ℳ ग़ྗ஋ ग़ ྗ ֬ ཰
24. ˜
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    $PSQPSBUJPO  ࠩ෼ϓϥΠόγʔͷ࢓૊Έ • %1ʹΑΔϓϥΠόγʔอޢʹϢʔβʔͷߩݙ˞Λ੍ݶ͠ɺϊΠζͰߩݙͷ༗ແΛ෴͍Ӆ͢ • ˞Ϣʔβʔͷߩݙɿग़ྗʢ౷ܭ৘ใʣʹର͢Δ̍ݸਓʢσʔλʣͷد༩ͷେ͖͞ ߩݙͷ੍ݶ ʢ&ODPEFʣ ू໿ ʢ"HHSFHBUFʣ "MJDF #PC $IBSMJF ઁಈ ʢ1FSUVSCʣ   ສԁ  ສԁ   ສԁ   ສԁ  ສԁ   ສԁ   ສԁ 0 1000 2000 3000 4000 5000
25. ˜
    -:
    $PSQPSBUJPO  𝝐, 𝜹 %JGGFSFOUJBM
    1SJWBDZ ϝΧχζϜ ℳ: 𝒟 → 𝒮 ͕ 𝜖, 𝛿 %1
    Λຬͨ͢ͱ͸ɺྡ઀σʔλϕʔε 𝐷, 𝐷" ∈ 𝒟 ͓Αͼ೚ҙͷग़ྗͷू߹ 𝑆 ⊆ 𝒮 ʹରͯ͠ҎԼ͕੒Γཱͭͱ͖Ͱ͋Δ %BUBCBTF
    𝑫 0VUQVU 𝜖  ∞    TUSPOH XFBL   ʜ Pr ℳ 𝐷 ∈ 𝑆 ≤ exp 𝜖 Pr ℳ 𝐷! ∈ 𝑆 + 𝛿 ℳ 𝑫′ɿ BEKBDFOU
    PG
    𝑫 ℳ 𝜖 ≥ 0, 𝛿 ∈ 0,1 ) ೖྗ͕มԽͯ͠΋ग़ྗʹ͸΄ͱΜͲʢexp 𝜖 ఔ౓͔͠ʣӨڹ͕ͳ͍ %XPSL
    %JGGFSFOUJBM
    QSJWBDZ
    *$"-1
    
26. ˜
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    $PSQPSBUJPO  -BQMBDFϝΧχζϜ ࠷΋Α͘஌ΒΕͨϥϯμϜԽॲཧΛ࣮ݱ͢ΔϝΧχζϜʢ𝛿 = 0Λ૝ఆʣ ℳ 𝐷 = 𝑓 𝐷 + Lap 0, Δ. 𝜖 -BQMBDF
    .FDIBOJTN 𝜖 = 10, Δ! = 1 𝜖 = 1, Δ! = 1 ฏۉɿ
    ඪ४ภࠩɿ 2 "! # ͷ ϥϓϥε෼෍͔ΒϊΠζΛαϯϓϦϯά Δ' = sup (,(!∈𝒟 𝑓 𝐷 − 𝑓 𝐷" , ℓ𝟏 TFOTJUJWJUZ Δ-./01 = 1 Δ2340 = 1 𝑛 ˞
    ૝ఆ͢Δྡ઀%#ʹґଘ &Y 4FOTJUJWJUZ
    𝚫𝒇 ೚ҙͷҰϨίʔυͷมԽ˞͕ؔ਺ͷग़ྗʹӨڹΛ༩͑Δ౓߹͍ %XPSL
    %JGGFSFOUJBM
    QSJWBDZ
    *$"-1
    
27. ˜
    -:
    $PSQPSBUJPO  ࠩ෼ϓϥΠόγʔͷ࣮૷ ώετάϥϜʹ-BQMBDFϝΧχζϜΛద༻͢Δྫ ϓϥΠόγʔϞσϧ • อޢ୯Ґɿ6TFSMFWFM
    Ϩίʔυਓ • ྡ઀%#ɿBEESFNPWBM
28. ˜
    -:
    $PSQPSBUJPO  -BQMBDFϝΧχζϜͷڍಈ ϥϯμϜੑΛ࣋ͬͨڍಈΛ͢ΔͨΊɺಉ͡ઃఆͰ΋ຖճग़ྗ͕ҟͳΔ 𝜖 = 1, Δ# = 1 𝜖 = 1, Δ# = 1 𝜖 = 1, Δ# = 1
29. ˜
    -:
    $PSQPSBUJPO  -BQMBDFϝΧχζϜͷڍಈ ϓϥΠόγʔύϥϝʔλ𝜖Λมಈʢ𝜖
    খ à ϓϥΠόγʔอޢ
    ڧʣ 𝜖 = 0.1 𝜖 = 0.5 𝜖 = 2 𝜖 = 0.05 𝜖 = 10 Δ# = 1
30. ˜
    -:
    $PSQPSBUJPO  ࠩ෼ϓϥΠόγʔͷ՝୊ • ಁ໌ੑͷܽ೗ • ग़ྗʢ౷ܭɾػցֶशϞσϧʣ͚ͩΛݟͯ΋ࠩ෼ϓϥΠόγʔ͕อূ͞Ε͍ͯΔ͔Ͳ͏͔ෆ໌֬ • ؔ਺ʢ౷ܭॲཧ΍ػցֶशϓϩηεʣͷ҆શੑΛଌΔई౓Ͱ͋ΔͨΊɺσʔλͦͷ΋ͷʹԿΒ͔ͷอূΛ ༩͑Δ΋ͷͰ͸ͳ͍ɻ͜ͷ఺͕͜Ε·Ͱͷʮಗ໊Խʯʮ౷ܭԽʯͰ࿦͡ΒΕ͖ͯͨ҆શੑͱ؍఺͕ҟͳΔ • ͦ΋ͦ΋Θ͔ΓͮΒ͍ • ೝূ੍౓ͷΑ͏ͳऔΓ૊Έ͕ඞཁ͔΋͠Εͳ͍͕ɺͦ΋ͦ΋ਖ਼͘͠ཧղ͍ͯ͠Δٕज़ऀ͕ࠃ಺Ͱ͸ رগͳଘࡏͰ͋Δ఺͕࠷େͷ՝୊ • ٕज़ऀͷෆ଍ • ࠃ಺Ͱࠩ෼ϓϥΠόγʔΛ஌͍ͬͯΔਓ͕গͳ͍͠ɺਖ਼͘͠ཧղ͍ͯ͠Δਓ͸ҰѲΓ • ۙ೥͸ɺൿີܭࢉͱͷϋΠϒϦου͕૿Ճɻٕज़త೉қ౓͕ߋʹߴ·͍ͬͯΔ • 64ͷϏοάςοΫ͕ٕज़ऀΛಠ઎ • ڭҭ͕ඞཁ
31. ˜
    -:
    $PSQPSBUJPO  ·ͱΊ • աڈͷϓϥΠόγʔ৵֐ͷࣄྫͱطଘͷϓϥΠόγʔอޢٕज़ʹ͍ͭͯ঺հ • աڈࣄྫΛ௨ͯ͠ɺͳͥࠩ෼ϓϥΠόγʔ͕ඞཁͳͷ͔ɺΛղઆ • ࠩ෼ϓϥΠόγʔͷಋೖɾਁಁɾීٴʹ͓͚Δ՝୊Λ঺հ • ݫີͳఆٛΑΓ΋ɺΘ͔Γ΍͢͞Λ༏ઌͨ͠આ໌Λ͠·ͨ͠ • ػցֶशʹؔ͢Δ࿩୊ʹ͍ͭͯ͸࣌ؒͷؔ܎ͰׂѪ͠·ͨ͠
32. ˜
    -:
    $PSQPSBUJPO