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

Transcript

1. σʔλυϦϒϯͳԾઆݕূͷͨΊͷ 4FMFDUJWF
   *OGFSFODF !TBMUDPPLZ
   
   
   5PLZP3
   
    1
2. ୭ • !TBMUDPPLZ
   • 3ྺɿ೥͙Β͍͔ͳ
   • ۈઌɿݪ॓ʹ͋Δ*5ܥͷձࣾ
   • ࢓ࣄ಺༰ɿ3%తͳ෦ॺͰ3Λ࢖ͬͨ

   
   
   
   ɾσʔλ෼ੳ԰͞Μ

   
   
   
   ɾσʔλूܭ԰͞Μ
   • झຯɿ෰ϑΝογϣϯඒज़ؗ८Γ 2
3. ಺༰ΛҰݴͰ 
 ࠷ۙษڧͨ͠4FMFDUJWF
   *OGFSFODFΛ঺հ
 3
4. 4 ౷ܭ෼ੳͷ࿩ Ծઆݕఆ
 ؼແԾઆ͕غ٫Ͱ͖Δ͔ ݁ՌධՁ
 ༗ҙͳ͕ࠩ͋Δͱ൑໌ ஌ࣝܦݧ͔ΒͷԾઆܗ੒
 ʮҿञ͸ ʹྑ͍ʯ ஌ࣝۦಈܕͳ౷ܭ෼ੳ σʔλ
5. 5 σʔλʹجͮ͘Ծઆܗ੒
 ʮҿञ͸ ʹྑ͍ʯ σʔλۦಈܕͳ౷ܭ෼ੳ σʔλ Ծઆݕఆ
 ؼແԾઆ͕غ٫Ͱ͖Δ͔ ݁ՌධՁ
 ༗ҙͳ͕ࠩ͋Δͱ൑໌ ౷ܭ෼ੳͷ࿩
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࿩
7. 7 Ծઆબ୒όΠΞε σʔλʹجͮ͘Ծઆܗ੒
 ʮҿञ͸ ʹྑ͍ʯ σʔλۦಈܕͳ౷ܭ෼ੳ σʔλ Ծઆݕఆ
 ؼແԾઆ͕غ٫Ͱ͖Δ͔ ݁ՌධՁ
 ༗ҙͳ͕ࠩ͋Δͱ൑໌ Ծઆબ୒όΠΞε
   σʔλΛجʹԾઆܗ੒Λ͓͜ͳͬͨͱ͖
 Ծઆݕఆʹੜͯ͡͠·͏όΠΞε
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
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

10. Ծઆબ୒όΠΞεͷ֬ೝ ؼແԾઆͷ΋ͱͰ͸Q஋͸Ұ༷෼෍ʹै͓ͬͯΓɺόΠΞε͕ͳ͍ 10
11. 11 Ծઆબ୒όΠΞεͷ֬ೝ Ќ Ќ Ќ Ќ Ќ Ќ Ќ Ќ Ќ Ќ غ٫͞Εͨ਺           غ٫͞Ε͔ͨ ͬͨ਺           غ٫ׂ߹            ม਺બ୒Λߦ͏৔߹
 غ٫ׂ߹͸༗ҙਫ४ΑΓඇৗʹେ͖͘ͳ͍ͬͯΔ

12. 12 Ծઆબ୒όΠΞεͷ֬ೝ Q஋͸Ұ༷෼෍ʹै͓ͬͯΒͣɺόΠΞε͕৐͍ͬͯΔ
 ˠ
    ༗ҙͰͳ͍ͷʹ༗ҙͳม਺Ͱ͋Δͱ͢ΔՄೳੑ͕ߴ͘ͳΔ
13. 4FMFDUJWF
    *OGFSFODF Ծઆܗ੒ͷΠϕϯτͷٯ૾%Λ৚݅෇͚Δ͜ͱͰɺ
 Ծઆબ୒όΠΞεͷͳ͍ਪఆΛߦ͏͜ͱ͕Ͱ͖Δ 13 ɿԾઆ ಛ௃ྔ ू߹ ɿԾઆબ୒Πϕϯτ

    
    
    ಛ௃બ୒ΞϧΰϦζϜ ɿબ୒͞ΕͨԾઆ ಛ௃ྔ ը૾ग़య
    
    IUUQTXXXJFJDFPSHdTJUBGPSVNBSUJDMFQEG
14. 4FMFDUJWF
    *OGFSFODF "
    ճؼ෼ੳʹ͓͚Δಛ௃બ୒ΠϕϯτΛͲ͏දݱ͢Ε͹ྑ͍͔
    2
    ઢܗͳܗͰදݱ͢Ε͹ྑ͍ʢ-FF
    FU
    BM
    ʣ 14 ը૾ग़య
    
    IUUQTXXXJFJDFPSHdTJUBGPSVNBSUJDMFQEG
15. 4FMFDUJWF
    *OGFSFODF ճؼ෼ੳʹ͓͚Δಛ௃બ୒Πϕϯτ
    w .BSHJOBM
    4DSFBOJOH
 ɹϧʔϧఆٛʹج͍ͮͨม਺બ୒
    w MBTTP
 ɹ࠷దੑ৚݅ʹج͍ͮͨม਺બ୒
    w 4UFQXJTF
 ɹΞϧΰϦζϜʹج͍ͮͨม਺બ୒
    ͜ΕΒશͯઢܗͳಛ௃બ୒Πϕϯτ 15 ը૾ग़య
    
    IUUQTXXXJFJDFPSHdTJUBGPSVNBSUJDMFQEG
16. 4FMFDUJWF
    *OGFSFODF ઢܗͳಛ௃બ୒ΠϕϯτΛ৚݅෇͚͜ͱͰɺؼແԾઆͷ෼෍͸
 ੾அਖ਼ن෼෍'ʹै͏ 16 w 4FMFDUJWF
    QWBMVF w 4FMFDUJWF
    DPOpEFODF
    JOUFSWBMT ը૾ग़య
    
    IUUQTXXXJFJDFPSHdTJUBGPSVNBSUJDMFQEG
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

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

    
    غ٫ׂ߹͸֓Ͷఔ౓ʹͳ͍ͬͯΔ
20. 20 3Ͱ4FMFDUJWF
    *OGFSFODF Q஋ͷ෼෍΋֓ͶҰ༷෼෍ʹै͓ͬͯΓɺόΠΞεͷͳ͍ਪఆ ͕Ͱ͖͍ͯΔͱߟ͑ΒΕΔ
21. ΫϥελϦϯάʹ͓͚Δ4* ΫϥελϦϯάޙͷΫϥεؒʹ͕ࠩ͋Δ͔ͷݕఆ͢Δ࣌ʹ΋ 4FMFDUJWF
    JOGFSFODFΛߦΘͳ͍ͱ͍͚ͳ͍
 Ϋϥεͷܗ੒ʹ͸ར༻͍ͯ͠Δσʔλʹґଘ͍ͯ͠ΔͨΊ
    21 ը૾ग़య
    
    IUUQTXXXJFJDFPSHdTJUBGPSVNBSUJDMFQEG
22. ΫϥελϦϯάʹ͓͚Δ4* ֊૚ΫϥελϦϯάʹ͓͚ΔTFMFDUJWF
    JOGFSFODF͸ɺ QWDMVTU 㱢W ͱTDBMFCPPU 㱢W ύοέʔδͰ࣮૷Մೳ

    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
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    22
23. ·ͱΊ w ม਺બ୒ΛߦͳͬͨճؼϞσϧʹ͓͚Δ܎਺ͷݕఆʹ͸ɺ
 Ծઆબ୒όΠΞε͕৐͍ͬͯΔ
    w TFMFDUJWF
    JOGFSFODFΛߦ͏͜ͱʹΑΓόΠΞεͷͳ͍ਪఆ Λߦ͏͜ͱ͕Ͱ͖Δ
    w TFMFDUJWF*OGFSFODFύοέʔδΛ࢖͍·͠ΐ͏
    w ΫϥελϦϯάʹ͓͚ΔTFMFDUJWF
    JOGFSFODF΋͋Γ·͢ 23
24. ࢀߟ w &YBDU
    QPTUTFMFDUJPO
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    %
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    BM
    
 IUUQTBSYJWPSHBCT
    w 4FMFDUJWF
    JOGFSFODF
    BGUFS
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    TFMFDUJPO
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    CPPUTUSBQ
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 IUUQTBSYJWPSHBCT
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    QWBMVFT
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    DMVTUFST
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 IUUQTUBUTZTJLZPUPVBDKQQSPHTDBMFCPPUQWDMVTUQEG
    w σʔλۦಈܕՊֶͷͨΊͷ
    બ୒తਪ࿦ʢ4FMFDUJWF
    *OGFSFODFʣ
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    w Ծઆݕఆʹ͓͚Δม਺બ୒ͷӨڹΛߟ͑Δ4FMFDUJWF
    *OGFSFODFೖ໳
    XJUI
    3
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