データドリブンな仮説検証のためのSelective Inference

TokyoR#82 で発表したLT

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1. σʔλυϦϒϯͳԾઆݕূͷͨΊͷ
   4FMFDUJWF*OGFSFODF
   !TBMUDPPLZ
   5PLZP3
   1
   

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2. ୭
   • !TBMUDPPLZ
   • 3ྺɿ೥͙Β͍͔ͳ
   • ۈઌɿݪ॓ʹ͋Δ*5ܥͷձࣾ
   • ࢓ࣄ಺༰ɿ3%తͳ෦ॺͰ3Λ࢖ͬͨ

   ɾσʔλ෼ੳ԰͞Μ

   ɾσʔλूܭ԰͞Μ
   • झຯɿ෰ϑΝογϣϯඒज़ؗ८Γ
   2
   

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3. ಺༰ΛҰݴͰ
   

   ࠷ۙษڧͨ͠4FMFDUJWF*OGFSFODFΛ঺հ

   3
   

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4. 4
   ౷ܭ෼ੳͷ࿩
   Ծઆݕఆ

   ؼແԾઆ͕غ٫Ͱ͖Δ͔
   ݁ՌධՁ

   ༗ҙͳ͕ࠩ͋Δͱ൑໌
   ஌ࣝܦݧ͔ΒͷԾઆܗ੒

   ʮҿञ͸ʹྑ͍ʯ
   ஌ࣝۦಈܕͳ౷ܭ෼ੳ
   σʔλ
   

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5. 5
   σʔλʹجͮ͘Ծઆܗ੒

   ʮҿञ͸ʹྑ͍ʯ
   σʔλۦಈܕͳ౷ܭ෼ੳ
   σʔλ
   Ծઆݕఆ

   ؼແԾઆ͕غ٫Ͱ͖Δ͔
   ݁ՌධՁ

   ༗ҙͳ͕ࠩ͋Δͱ൑໌
   ౷ܭ෼ੳͷ࿩
   

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6. 6
   σʔλʹجͮ͘Ծઆܗ੒

   ʮҿञ͸ʹྑ͍ʯ
   σʔλۦಈܕͳ౷ܭ෼ੳ
   ಘΒΕͯσʔλʹ

   ۮવͦͷΑ͏ͳ܏޲͕

   ͋ͬͨͷ͔΋͠Εͳ͍
   σʔλ
   Ծઆݕఆ

   ؼແԾઆ͕غ٫Ͱ͖Δ͔
   ݁ՌධՁ

   ༗ҙͳ͕ࠩ͋Δͱ൑໌
   ͦͷΑ͏ͳ܏޲͕͋ΔσʔλͰ

   ݕఆΛ͢Δͱ༗ҙʹͳΓ΍͍͢ʁ
   ౷ܭ෼ੳͷ࿩
   

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7. 7
   Ծઆબ୒όΠΞε
   σʔλʹجͮ͘Ծઆܗ੒

   ʮҿञ͸ʹྑ͍ʯ
   σʔλۦಈܕͳ౷ܭ෼ੳ
   σʔλ
   Ծઆݕఆ

   ؼແԾઆ͕غ٫Ͱ͖Δ͔
   ݁ՌධՁ

   ༗ҙͳ͕ࠩ͋Δͱ൑໌
   Ծઆબ୒όΠΞε
   σʔλΛجʹԾઆܗ੒Λ͓͜ͳͬͨͱ͖

   Ծઆݕఆʹੜͯ͡͠·͏όΠΞε
   

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8. Ծઆબ୒όΠΞεͷ֬ೝ
   ࣍ͷΑ͏ͳਅͷճؼϞσϧΛߟ͑Δ

   

   

   

   ͦͯ͠ɺ໨తม਺ʹӨڹ͕ͳ͍ม਺ͷܭม਺͕ಘΒΕ͍ͯΔͱԾఆ
   

   ҎԼΛճ܁Γ܁Γฦ͢
   w TUFQXJTFʹΑΔม਺બ୒Λߦ͍ճؼϞσϧΛಘΔ
   w ಘΒΕͨϞσϧʹ͓͚Δ܎਺ͷ༗ҙ͔Ͳ͏͔ݕఆ͢Δ Ћ
   
   w غ٫ׂ߹غ٫͞Εͨճ਺ݕఆΛߦͳͬͨճ਺
   8
   

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9. 9
   Ծઆબ୒όΠΞεͷ֬ೝ
   Ќ Ќ Ќ Ќ Ќ Ќ Ќ Ќ Ќ Ќ
   غ٫͞Εͨ਺
   غ٫͞Ε͔ͨ
   ͬͨ਺
   
   غ٫ൺ཰
   
   ʻม਺બ୒ΛߦΘͳ͍৔߹ʼ

   όΠΞε͕ͳ͍৔߹ɺ༗ҙਫ४ͱغ٫ׂ߹͸౳͘͠ͳΔ

   

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10. Ծઆબ୒όΠΞεͷ֬ೝ
    ؼແԾઆͷ΋ͱͰ͸Q஋͸Ұ༷෼෍ʹै͓ͬͯΓɺόΠΞε͕ͳ͍
    10
    

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11. 11
    Ծઆબ୒όΠΞεͷ֬ೝ
    Ќ Ќ Ќ Ќ Ќ Ќ Ќ Ќ Ќ Ќ
    غ٫͞Εͨ਺
    غ٫͞Ε͔ͨ
    ͬͨ਺
    
    غ٫ׂ߹
    
    ม਺બ୒Λߦ͏৔߹

    غ٫ׂ߹͸༗ҙਫ४ΑΓඇৗʹେ͖͘ͳ͍ͬͯΔ

    

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12. 12
    Ծઆબ୒όΠΞεͷ֬ೝ
    Q஋͸Ұ༷෼෍ʹै͓ͬͯΒͣɺόΠΞε͕৐͍ͬͯΔ

    ˠ༗ҙͰͳ͍ͷʹ༗ҙͳม਺Ͱ͋Δͱ͢ΔՄೳੑ͕ߴ͘ͳΔ
    

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13. 4FMFDUJWF*OGFSFODF
    Ծઆܗ੒ͷΠϕϯτͷٯ૾%Λ৚݅෇͚Δ͜ͱͰɺ

    Ծઆબ୒όΠΞεͷͳ͍ਪఆΛߦ͏͜ͱ͕Ͱ͖Δ
    13
    ɿԾઆ ಛ௃ྔ
    ू߹
    ɿԾઆબ୒Πϕϯτ

    ಛ௃બ୒ΞϧΰϦζϜ
    
    ɿબ୒͞ΕͨԾઆ ಛ௃ྔ
    
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14. 4FMFDUJWF*OGFSFODF
    "ճؼ෼ੳʹ͓͚Δಛ௃બ୒ΠϕϯτΛͲ͏දݱ͢Ε͹ྑ͍͔
    2ઢܗͳܗͰදݱ͢Ε͹ྑ͍ʢ-FFFUBM ʣ
    14
    ը૾ग़యIUUQTXXXJFJDFPSHdTJUBGPSVNBSUJDMFQEG
    
    

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15. 4FMFDUJWF*OGFSFODF
    ճؼ෼ੳʹ͓͚Δಛ௃બ୒Πϕϯτ
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    ɹϧʔϧఆٛʹج͍ͮͨม਺બ୒
    w MBTTP

    ɹ࠷దੑ৚݅ʹج͍ͮͨม਺બ୒
    w 4UFQXJTF

    ɹΞϧΰϦζϜʹج͍ͮͨม਺બ୒
    ͜ΕΒશͯઢܗͳಛ௃બ୒Πϕϯτ
    15
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16. 4FMFDUJWF*OGFSFODF
    ઢܗͳಛ௃બ୒ΠϕϯτΛ৚݅෇͚͜ͱͰɺؼແԾઆͷ෼෍͸

    ੾அਖ਼ن෼෍'ʹै͏
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17. 3Ͱ4FMFDUJWF*OGFSFODF
    3Ͱͷճؼ෼ੳͷ4FMFDUJWF*OGFSFODF͸

    TFMFDUJWF*OGFSFODFύοέʔδͰ࣮૷Մೳ
    17
    

    > # stepwiseʹ͓͚Δselective inferenceͷ࣮ߦྫ

    > library(selectiveInference)
    > gfit = fs(x,y) # x=આ໌ม਺ y=໨తม਺
    > out = fsInf(gfit,type = "aic",alpha = 0.05)

    > out # ݁Ռͷ֬ೝ

    

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18. 3Ͱ4FMFDUJWF*OGFSFODF
    3Ͱͷճؼ෼ੳͷ4FMFDUJWF*OGFSFODF͸

    TFMFDUJWF*OGFSFODFύοέʔδͰ࣮૷Մೳ
    18
    

    > # lassoʹ͓͚Δselective inferenceͷ࣮ߦྫ

    > gfit = glmnet(x,y)
    > lambda = .3
    > beta_ls = coef(gfit, s=lambda/n)[-1]
    > out = fixedLassoInf(x,y,beta_ls,lambda,sigma=sigma)
    

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19. 19
    3Ͱ4FMFDUJWF*OGFSFODF
    Ќ Ќ Ќ Ќ Ќ Ќ Ќ Ќ Ќ Ќ
    غ٫͞Εͨ਺
    غ٫͞Ε͔ͨ
    ͬͨ਺
    
    غ٫ׂ߹
    
    TUFQXJTFʹ͓͚Δ4*݁Ռ

    غ٫ׂ߹͸֓Ͷఔ౓ʹͳ͍ͬͯΔ
    

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20. 20
    3Ͱ4FMFDUJWF*OGFSFODF
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21. ΫϥελϦϯάʹ͓͚Δ4*
    ΫϥελϦϯάޙͷΫϥεؒʹ͕ࠩ͋Δ͔ͷݕఆ͢Δ࣌ʹ΋
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22. ΫϥελϦϯάʹ͓͚Δ4*
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23. ·ͱΊ
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24. ࢀߟ
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