不確実性と上手く付き合う意思決定の手法

 不確実性と上手く付き合う意思決定の手法

予測モデルの不確実性を減らすActive Learning,
モデルの不確実性を予測結果に反映するThompson Sampling,
オンライン最適化など

D77e6b2d469947a4792ab062d466350b?s=128

Takashi Nishibayashi

April 04, 2019
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  1. ༧ଌͷෆ࣮֬ੑͱ্ख͘෇͖߹͏
 ҙࢥܾఆͷख๏ ެ։൛ 5BLBTIJ/JTIJCBZBTIJ  3FQSP5FDI

  2. ͓લͩΕΑ Name: Takashi Nishibayashi twitter.com/@hagino3000 Job: Software Engineer VOYAGE GROUPͰωοτ޿ࠂ഑৴αʔϏε࡞ͬͯ

    ·͢ɻओʹ഑৴ϩδοΫ͔Βσʔλ෼ੳج൫·Ͱɻ
 ࠷ۙͷڵຯ͸ΦϯϥΠϯҙࢥܾఆͱϝΧχζϜσβ Πϯɻ  
  3. ࠷ۙͷ׆ಈ ਓ޻஌ೳֶձࢽ Vol. 32 No. 4 (2017/07) ͷʮ޿ࠂͱ AI ಛूʯʹʮΞυωοτϫʔΫʹ͓͚Δ޿ࠂ഑৴ܭ

    ըͷ࠷దԽʯ͕ܝࡌ͞Ε·ͨ͠ɻ   ΦϥΠϦʔ͔Βʮ࢓ࣄͰ͸͡ΊΔػցֶशʯ͕ग़· ͨ͠ɻ @chezou, @tokorotenͱڞஶ ࢴ൛ɾిࢠॻ੶྆ํ͋Γ·͢
  4. ࠓ೔ͷ࿩ w ༧ଌγεςϜͱҙࢥܾఆ w Ϗδωεʹ͓͚Δ࠷దԽ w ϥϕϧແ͠σʔλͷ୳ࠪ w ༧ଌϞσϧͷෆ͔֬͞Λߦಈʹ൓ө͢Δ w

    ΦϯϥΠϯ࠷దԽ ػցֶशͰಘͨ༧ଌ஋ΛͲͷΑ͏ʹͯ͠࢖͏͔ɺ༧ଌͷ࣍ͷҙࢥܾ ఆͷϑΣʔζʹ஫໨͠·͢ɻ࣮ࡍͷΞϓϦέʔγϣϯ΋঺հͭͭ͠ ࿩ΛਐΊ·͢ɻ
  5. ༧ଌγεςϜͱҙࢥܾఆ

  6. ༧ଌͱҙࢥܾఆͷྫ ༧ଌλεΫ ҙࢥܾఆ ԿͷͨΊʹ धཁ༧ଌ ੜ࢈ܭը ҆શࡏݿ֬อɾࡏݿίετ࡟ݮ ނোՕॴͷ༧ଌ ϝϯςφϯεܭը ϝϯςφϯεඅ༻࡟ݮ

    Ձ஋ͷ༧ଌ ചΓ஋ങ͍஋ͷܾఆ औҾ͕ੜΉརӹͷ࠷େԽ ޿ࠂޮՌͷਪఆ ޿ࠂΛදࣔ͢΂͖͔Ͳ͏͔ ༧ࢉ಺Ͱͷ޿ࠂޮՌ࠷େԽ Ͱ͖Ε͹ࣗಈͰܾΊ͍ͨɺͰ͸Ͳ͏͢Ε͹  Ή͠ΖΞϓϦέʔγϣϯΤϯδχΞͷ࢓ࣄ͸ࣗಈԽ͕ϝΠϯ
  7. ਺ཧ࠷దԽ ͋Δ੍໿ͷݩͰ໨తؔ਺Λ࠷େ ࠷খ Խ͢ΔύϥϝʔλΛٻΊΔ ෆ࣮֬ੑͷແ͍໰୊ͱ͸

  8. *1"ಠཱߦ੓๏ਓ৘ใॲཧਪਐػߏɿ໰୊࡭ࢠɾ഑఺ׂ߹ɾղ౴ྫɾ࠾఺ߨධʢɺฏ੒೥ʣ
 IUUQTXXXKJUFDJQBHPKQ@IBOOJ@TVLJSVNPOEBJ@LBJUPV@IIUNMBLJ ͋Δ޻৔Ͱ͸දʹࣔ͢੡඼Λ੡଄͍ͯ͠Δɻ࣮ݱՄೳͳ࠷େརӹ͸Կԁ͔ɻ͜͜Ͱɺ ֤੡඼ͷ݄ؒधཁྔʹ͸্ݶ͕͋Γɺ·ͨɺ੡଄޻ఔʹ࢖͑Δ޻৔ͷ࣌ؒ͸݄ؒ࣌ ؒ·ͰͰɺෳ਺छྨͷ੡඼Λಉ࣌ʹฒߦͯ͠੡଄͢Δ͜ͱ͸Ͱ͖ͳ͍΋ͷͱ͢Δɻ جຊ৘ใॲཧٕज़ऀࢼݧ)ळق໰୊ΑΓ ੡඼9 ੡඼: ੡඼; ݸ౰ͨΓͷརӹ

    ԁ       ݸ͋ͨΓͷ੡଄ॴ༻࣌ؒ ෼    ݄ؒधཁ࠷্ݶ     ྫੜ࢈ܭը ֬ఆͨ͠஋
  9. ެ։൛ࢿྉʹ͖ͭิ଍ ҎԼͷ௨Γ੔਺ܭը໰୊ͱͯ͠ఆࣜԽͯ͠ղ͚͹
 Yݸ Zݸ [ݸΛ࡞Ε͹རӹ͕࠷େʹͳΔͷ͕Θ͔Δɻ࣮຿Ͱखܭࢉ͸͠ͳ͍

  10. ༧ଌΛར༻ͨ͠࠷దԽ ੡඼9 ੡඼: ੡඼; ݸ౰ͨΓͷརӹ ԁ  ʙ  ݸ͋ͨΓͷ੡଄ॴ༻࣌ؒ

    ෼ ʙ ݄ؒधཁ࠷্ݶ   ࣮ࡍʹ࡞ͬͨΓചͬͯΈΔ·ͰΘ͔Βͳ͍෦෼ ༧ଌΛར༻͍ͯ͠Δ࣌఺ͰɺԿΒ͔ͷෆ࣮֬ੑΛ಺แ͍ͯ͠Δ ͦΕͳΓʹ༧ଌͰ͖Δ෦෼ ͜Μͳঢ়ଶ͔Βελʔτ͢Δʹ͸Ͳ͏ͨ͠Β͍͍͔
  11. ࠓ೔঺հ͢Δओͳํࡦ wҎԼͷ܁Γฦ͠  ༧ଌ  ҙࢥܾఆɾߦಈ  ݁Ռͷ؍ଌ  ༧ଌثͷߋ৽

  12. ༨ஊ࠷దͱ͸Կ͔ w ඇࣗ໌Ͱ͋Δࣄ͕ଟ͍ͱײ͡Δ w ࠗ׆ϚονϯάΞϓϦ w Ϛονϯά͕଎͗͢Δͱࢢ৔͕ബ͘ͳΔδϨϯϚ w ࢓ೖΕՁ֨ w

    ʮ࢓ೖΕՁ֨Λ্͍͛ͨʯʮརӹ૬൓Ͱ͸ ʯ w ࢓ೖΕ஋ʹϚʔδϯ ཰ Λ৐ͤͯച͍ͬͯͨˠ࢓ೖΕ஋্͕͕Δͱૈར૿ w ஋෇͚ϧʔϧΛม͑Δॴ͔Β΍ͬͨ w ۀ຿ͦͷ΋ͷΛม͑ΒΕΔ༨஍͕ͲΕ͚ͩ͋Δ͔
  13. 'MJOUࢢͷਫಓ؅ަ׵ࣄۀ

  14. 5IF4FBSDIGPS-FBE1JQFT JO'MJOU .JDIJHBO<> w Ԗڅਫ؅ -FBE1JQFT ͷަ׵Λ͢ΔͨΊʹػցֶश༧ଌϞσϧΛར༻ͨ͠ࣄྫ w ,%%ʹ࠾୒͞Εͨ࿦จʹख๏͕ࡌ͍ͬͯΔ w

    എܠ w Ԗڅਫ؅͸Ԗ༹͕ग़͠ͳ͍Α͏ʹද໘͕ίʔςΟϯά͞Ε͍ͯΔ w 'MJOUࢢʹ͓͍ͯ͸ਫݯΛม͑ͨ࣌ʹਫ࣭͕มΘͬͯίʔςΟϯά͕ണ͛ͨ w ਫಓਫ΁ͷԖͷ༹ग़ʹΑΔ݈߁ඃ֐͕ൃੜ w ߦ੓ͷه࿥͸ෆਖ਼֬
  15. 5IF4FBSDIGPS-FBE1JQFT JO'MJOU .JDIJHBO ଓ͖ w ໰୊ w ͲͷՈʹԖڅਫ؅͕࢖ΘΕ͍ͯͯɺͦΕ͸Ͳ͜ʹ͋Δͷ͔ w ݶΒΕͨ༧ࢉΛͲͷΑ͏ʹͯ͠Ԗڅਫ؅ͷަ׵ʹׂΓ౰ͯΕ͹͍͍ͷ͔

    w ঢ়گɾ੍໿ w ਫಓ؅Λ۷Γىͯ֬͠ೝ͢Δίετ͕ߴ͍ ϥϕϧ෇͚ίετ  w ܇࿅σʔλ͸ݶΒΕ͓ͯΓɺภ͍ͬͯΔ
  16. 'MJOUMFBEQJQFSFQMBDFNFOUQSPHSBNUPTXJUDIIBOETJONMJWFDPN IUUQTXXXNMJWFDPNOFXTqJOUqJOU@MFBE@QJQF@SFQMBDFNFOU@QSIUNM

  17. "CFSOFUIZ +BDPC FUBM"DUJWF3FNFEJBUJPO5IF4FBSDIGPS-FBE1JQFTJO'MJOU .JDIJHBO1SPDFFEJOHTPGUIFUI "$.4*(,%%*OUFSOBUJPOBM$POGFSFODFPO,OPXMFEHF%JTDPWFSZ%BUB.JOJOH"$.  ༧ଌ݁ՌΛݩʹௐࠪϙΠϯτΛܾΊΔϧʔϧ ༧ଌ݁ՌΛݩʹύΠϓަ׵ϙΠϯτΛܾΊΔϧʔϧ ༧ଌϞσϧ

  18. 5IF4FBSDIGPS-FBE1JQFT JO'MJOU .JDIJHBO ଓ͖ w ௐࠪϙΠϯτܾఆϧʔϧ w ৘ใΛऔಘͯ͠༧ଌੑೳΛ্͛Δͷ͕໨త w ೳಈֶश

    "DUJWF-FBSOJOH  w ύΠϓަ׵ϙΠϯτܾఆϧʔϧ w ޡ۷࡟ίετΛ࠷খԽ͍ͨ͠ w ࠷΋֬཰ͷߴ͍ϙΠϯτΛબͿɺᩦཉ๏ (SFFEZ"MHPSJUIN
  19. ೳಈֶश "DUJWF-FBSOJOH w എܠ w ڭࢣ͋Γֶश͸܇࿅σʔλ͕ଟ͍ఔਫ਼౓্͕͕Δ w ͨͩ͠ϥϕϧ෇͚ Ξϊςʔγϣϯ ʹίετ͕͔͔Δ

    w Ξϓϩʔν w ༧ଌثͷਫ਼౓޲্ʹد༩͢ΔσʔλΛ౎౓બͿ w ํࡦͷྫ࠷΋ෆ͔֬ͳσʔλΛબ୒͢Δ w 'MJOUͰ͸*NQPSUBODF8FJHIUFE"DUJWF-FBOJOHΛ࠾༻
  20. ᩦཉ๏ (SFFEZ"MHPSJUIN w ࢼߦຖʹͦͷ࣌఺Ͱ࠷΋ظ଴ใु͕େ͖ͳߦಈΛऔΔํࡦ w FHμΠΫετϥ๏ w ۙࣅղ͕ಘΒΕΔ w ໰୊ʹΑͬͯ͸ϫʔετέʔεͷۙࣅ཰ʹཧ࿦อূ͕͋Δ

    w FHφοϓαοΫ໰୊ w େମ্ख͍࣮͘͘͠૷͕༰қͳͷͰΑ͘࢖ΘΕΔ
  21. ͞ΒͳΔࠔ೉ w ࢪࡦͷධՁ͸ύΠϓަ׵݅͋ͨΓͷίετ࡟ݮྔ w  ˠ  w .ͷઅ໿ w

    ੒Ռ͸ग़ͨ΋ͷͷࢢຽ͕൓ൃ w ਓؒͷ໋Λٹ͏͸ͣͩͬͨ"*͕੓࣏ͱແ஌ʹΑͬͯແࢹ͞Εͯ͠·ͬͨ࿩
 IUUQTOPUFNVEBUBTDJFODFOOEFCEEBGF w ΞϧΰϦζϜΛݟΕ͹Θ͔Δ௨Γɺे෼ͳ༧ࢉ͕͋Ε͹શॅ୐Λ۷Γฦ͠ ͯݕࠪ͢ΔࣄʹͳΔɻௐࠪ͢Δॱ൪͕ૣ͍͔஗͍͔ͷҧ͍ɻ w ࠷దͱ͸ҰମԿͳͷ͔
  22. ༧ଌϞσϧͷෆ͔֬͞Λ
 ൓өͨ͠ߦಈ

  23. ྦྷੵใुΛ࠷େԽ͍ͨ͠ ࢼߦճ਺ ͋ͨΓճ਺ Q ㅟ εϩοτϚγϯ"    εϩοτϚγϯ#

       ֬཰QͰ౰ͨΓ͕ग़ΔϕϧψʔΠࢼߦΛߟ͑Δɺ͜ͷޙ͸Ͳ͏͢΂͖͔ ෳ਺͋Δબ୒ࢶͦΕͧΕ͔Β֬཰త JJE ʹใु͕ಘΒΕΔઃఆͰγʔέϯγϟϧʹ ߦಈΛܾΊͯྦྷੵใु࠷େԽΛ໨ࢦ͢໰୊Λʮ֬཰తόϯσΟοτ໰୊ʯɺ͜ͷ࣌ ͷબ୒ࢶΛʮΞʔϜʯͱݺͿɻ
  24. Qͷࣄޙ෼෍ΛݟΔ ύϥϝʔλQͷ໬౓ #FUB ੒ޭճ਺ ࣦഊճ਺ #͕"ΑΓ΋ྑ͍ͱ൑அ͢Δʹ͸·ͩϦεΫ͕͋Δ

  25. Qͷࣄޙ෼෍ΛݟΔ ύϥϝʔλQͷ໬౓ #FUB ੒ޭճ਺ ࣦഊճ਺ ෼཭͍ͯͨ͠Β#ͷΈΛબ΂͹ྑ͍

  26. ֬཰తόϯσΟοτ໰୊ͷํࡦ w ֬཰Ұக๏ w ΞʔϜa ͷظ଴஋͕࠷େͰ͋Δ֬཰ͰaΛબ୒͢Δ w ͲͷΑ͏ʹ  w

    ϥ΢ϯυຖʹ w ΞʔϜͦΕͧΕͷظ଴஋ͷࣄޙ෼෍͔ΒЖaΛੜ੒ ㅟ w Жa ͕࠷େͷΞʔϜΛબ୒͢Δ ㅟ w ݁Ռͷ؍ଌΛͯ͠બ୒ͨ͠ΞʔϜͷه࿥Λߋ৽ w 㱺5IPNQTPO4BNQMJOH
  27. ઢܗϞσϧͷ৔߹ ύϥϝʔλͷਪఆ஋ͦΕͧΕ͸ҟͳΔޡࠩΛ࣋ͭ ස౓ओٛͰ͸࠷໬ਪఆྔwΛݻఆͨ͠ύϥϝʔλͱͯ͠࢖͏͕

  28. Results: Ordinary least squares ================================================================== Model: OLS Adj. R-squared: 0.946

    Dependent Variable: y AIC: 3196.9303 Date: 2019-04-04 00:32 BIC: 3230.7426 No. Observations: 506 Log-Likelihood: -1590.5 Df Model: 8 F-statistic: 1110. Df Residuals: 498 Prob (F-statistic): 8.68e-312 R-squared: 0.947 Scale: 31.960 -------------------------------------------------------------------- Coef. Std.Err. t P>|t| [0.025 0.975] -------------------------------------------------------------------- CRIM -0.1858 0.0380 -4.8884 0.0000 -0.2605 -0.1111 ZN 0.0833 0.0146 5.7100 0.0000 0.0546 0.1119 CHAS 3.8725 1.0130 3.8227 0.0001 1.8821 5.8629 NOX -18.5928 3.0070 -6.1833 0.0000 -24.5007 -12.6849 RM 6.8287 0.2539 26.8931 0.0000 6.3298 7.3276 DIS -1.3713 0.1736 -7.8985 0.0000 -1.7124 -1.0302 RAD 0.2022 0.0711 2.8420 0.0047 0.0624 0.3420 TAX -0.0180 0.0038 -4.7172 0.0000 -0.0255 -0.0105 ------------------------------------------------------------------ ྫ#PTUPOෆಈ࢈Ձ֨σʔλͷઢܗճؼ ஫#PTUPOIPVTFQSJDFTEBUBTFUΛલॲཧແ͠Ͱ0-4ͨ݁͠Ռ
  29. ਪఆ஋ʹ༧ଌͷෆ͔֬͞Λ൓ө͢Δ w wͷࣄޙ෼෍͔Βੜ੒ͨ͠wΛ࢖ͬͯਪఆ஋ΛٻΊΔ ㅟ w ใु͕ઢܗϞσϧ͔Βੜ੒͞ΕΔઃఆͷόϯσΟοτ໰୊ͷղ๏<> w 5IPNQTPO4BNQMJOHGPS$POUFYUVBM#BOEJUTXJUI-JOFBS1BZP⒎T<> w ϕΠδΞϯϒʔτετϥοϓͰࣄޙ෼෍Λੜ੒͢ΔҊ<>

    w ิ଍$POUFYUVBM#BOEJU w ϥ΢ϯυຖʹίϯςΩετ৘ใ͕༩͑ΒΕΔઃఆ w ޿ࠂ഑৴͸ΞʔϜ͚ͩͰใु͕JJEʹੜ੒͞ΕΔͱ͸ݴ͑ͳ͍ͷͰίϯςΩ ετΛ࢖͏
  30. "HSBXBM 4IJQSB BOE/BWJO(PZBM5IPNQTPOTBNQMJOHGPSDPOUFYUVBMCBOEJUTXJUIMJOFBSQBZP⒎T *OUFSOBUJPOBM$POGFSFODFPO.BDIJOF-FBSOJOH ଟมྔਖ਼ن෼෍͔Βαϯϓϧ͍ͯ͠Δ ޡ͕ࠩਖ਼ن෼෍ΛԾఆ

  31. 5IPNQTPO4BNQMJOH w ࣄޙ֬཰෼෍͔ΒͷαϯϓϧΛར༻͢Δ w ଟ࿹όϯσΟοτ໰୊ͷ༷ͳ׆༻ͱ୳ࡧ͕ඞཁͳ࣌ʹڧ͍ w ใुͷ৴པ্ݶʹجͮ͘બ୒Λߦͳ͏ख๏ 6$# ΑΓ΋ੑೳ͕ྑ͍ w

    όϯσΟοτ໰୊ʹద༻͢Δͱڧ͍ࣄ͸஌ΒΕ͍͕ͯͨɺੑೳͷཧ࿦ղੳ͕ ͞Εͨͷ͸೥
  32. *ODSFNFOUBMJUZ#JEEJOH"UUSJCVUJPO<> w /FUqJYͷਓͷ35#ೖࡳઓུ w 35#޿ࠂදࣔݖརͷϦΞϧλΠϜΦʔΫγϣϯ w ޿ࠂͷҼՌޮՌ͕࠷େʹͳΔೖࡳΛ͍ͨ͠ w ༧ଌ͸ೖࡳϦΫΤετຖ ԯճEBZ

     w ༧ଌͷෆ͔֬͞Λදݱ͢ΔͷʹύϥϝʔλΛࣄޙ෼෍͔Βੜ੒ w ಺༰੝Γ΋Γͷ8PSLJOH1BQFSͰݟॴ͕ଟ͍ w ޿ࠂͷϥϯμϜԽൺֱࢼݧ (IPTU"ET ɺޮՌͷݮਰϞσϧ
  33. ΦϯϥΠϯ࠷దԽ

  34. ΦϯϥΠϯ࠷దԽ w ΍Γ௚͕͠Ͱ͖ͳ͍ઃఆͰ໨తؔ਺ͷ࠷େԽΛૂ͏ w ࠓ೔͸੍໿෇͖ΦϯϥΠϯತ࠷దԽͷ঺հ w ·ͣ͸ΦϑϥΠϯઃఆ͔Β

  35. ತ࠷దԽ w ੍໿ɾ໨తؔ਺͍ͣΕ΋ತؔ਺ w ղ͕ತू߹Ͱ͋Δඞཁ w ྫ͑͹޿ࠂબ୒ํ๏ΛٻΊΔ໰୊ͩͱ
 /ݸ͋Δ޿ࠂͷͲΕΛબ୒͢Δ͔x㱨\ ^/ͷ୅ΘΓʹ
 ͦΕͧΕͷ޿ࠂΛબ୒͢Δ֬཰x㱨<

    >/ΛٻΊΔ
  36. ΦϯϥΠϯͰ΍Γ͍ͨ w ੍໿ΛͲΕ͚ͩҧ൓͢Δ͔ɺ΍ͬͯΈͳ͍ͱΘ͔Βͳ͍ w ੍໿Λҧ൓ͯͨͩͪ͠ʹఀࢭ͢Δͷ΋ࠔΔ ؇੍͍໿  w 0OMJOF$POWFY0QUJNJ[BUJPOXJUI4UPDIBTUJD$POTUSBJOUT<> w

    G Y H Y ͦΕͧΕඍ෼Ͱ͖Ε͹ྑ͍ w ࣮ݧσʔληϯλʔͷফඅిྗΛ࠷খԽ͢ΔόονδϣϒͷׂΓ͋ͯ
  37. ·ͱΊ w "DUJWF-FBSOJOH w ᩦཉ๏ w ༧ଌͷෆ࣮֬ੑΛߦಈʹ൓ө͢Δͱڧ͍ w ΦϯϥΠϯͰ΋࠷దԽͰ͖Δ w

    Կ͕࠷ద͔ܾΊΔͷ͕೉͍͠
  38. ࢀߟจݙ <>"CFSOFUIZ +BDPC FUBM"DUJWF3FNFEJBUJPO5IF4FBSDIGPS-FBE 1JQFTJO'MJOU .JDIJHBO1SPDFFEJOHTPGUIFUI"$.4*(,%% *OUFSOBUJPOBM$POGFSFODFPO,OPXMFEHF%JTDPWFSZ%BUB.JOJOH"$.   <>"HSBXBM

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