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[読み会]Fair Adversarial Gradient Tree Boosting
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mei28
November 10, 2020
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[読み会]Fair Adversarial Gradient Tree Boosting
読み会資料.
Fair Adversarial Gradient Tree Boosting(ICDM2019)
mei28
November 10, 2020
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Transcript
'BJS"EWFSTBSJBM (SBEJFOU5SFF#PPTUJOH ಡΈձ! ༶໌
wஶऀ w7JODFOU(SBSJ 4PSCPOOF6OJWFSTJUZ w#PSJT3VG "9" w4ZMWBJO-BNQSJFS 4PSCPOOF6OJWFSTJUZ
w.BSDJO%FUZOJFDLJ "9" wग़య*$%. จใ
wܾఆͷϞσϧͰެฏͳϞσϧΛ֫ಘͰ͖ΔΑ͏ʹͨ͠ɽ w405"ͱಉ͘͡Β͍ͷੑೳΛୡͰ͖ͨɽ wબΜͩཧ༝ wެฏͳϞσϧ֫ಘΛతͱͯ͠ɼܾఆϕʔεͷख๏ΛఏҊ͍ͯͨͨ͠Ίɽ wޯϒʔεςΟϯάܾఆ͕ςʔϒϧσʔλʹରͯ͠ڧྗͰ͋Δ͔Βɽ ֓ཁ ͲΜͳจʁ
wόΠΞεͷܰݮʹର͢ΔλεΫͰΑ͘χϡʔϥϧωοτϫʔΫ͕༻͍ΒΕ͍ͯ Δ͠ɼੑೳͱ͍͍ͯ͠ɽ wςʔϒϧσʔλʹରͯ͠ɼ9(#PPTU-JHIU(#.ͳͲޯϒʔεςΟϯά͕ඇ ৗʹڧྗͰΑ͘༻͍ΒΕ͍ͯΔɽ wͦ͜ͰɼޯϒʔεςΟϯάͰόΠΞεΛܰݮ͢Δ ެฏੑΛୡ͢Δ Α͏ͳख ๏ΛఏҊ͢Δɽ ֓ཁ
ݚڀഎܠ
wطଘݚڀͰ΄ͱΜͲ͕χϡʔϥϧωοτϫʔΫΛ༻͍ͯɼόΠΞεΛܰݮͯ͠ Δɽ wχϡʔϥϧωοτϫʔΫͰੑೳग़͍ͤͯΔ͕ɼͳΜͰ͜͏ͳ͔͕͔ͬͨΓ ʹ͍͘ɽ wςʔϒϧσʔλͰχϡʔϥϧωοτϫʔΫΑΓޯϒʔεςΟϯά͕·Ε ͯΘΕ͍ͯΔɽ ֓ཁ طଘݚڀʹ͍ͭͯ
wҰൠతͳྨϞσϧʹରͯ͠ɼܾఆΛؚΉఢରతֶशͰެฏΛ֫ಘ͢Δํ๏Λ ఏҊ͢Δɽ wҟͳΔެฏੑͷن४Ͱ405"ͳϞσϧͱಉͷੑೳΛୡͨ͠ɽ ֓ཁ ߩݙ
w ࣍ݩͷಛྔʢඇηϯγςΟϒͳಛʣ wηϯγςΟϒͳଐੑɽࠓճೋͰߟ͍͑ͯΔɽ wతมɽࠓճྨΛѻ͏ͷͰೋͰߟ͑Δɽ wಛʹ؍ଌ ༧ଌ ͱ͢Δ wO͜ͷαϯϓϧͷσʔληοτ
Λ༻͍ͯҰൠతͳڭࢣ͋ΓֶशΛߦ͏ɽ x ∈ ℝd d s y y ̂ y (xi , si , yi )n i=1 ެฏੑྀܕػցֶश දهͷఆٛ
w%FNPHSBQIJD1BSJUZηϯγςΟϒଐੑʹ͔͔ΘΒͣ༧ଌͷൺҰக͢Δ w w%1ΛͬͨධՁ1SVMFΛ࣍ͷΑ͏ʹఆٛ͢Δ %1P( ̂ Y =
1|S = 0) = P( ̂ Y = 1|S = 1) 1SVMF = min ( P( ̂ Y = 1|S = 0) P( ̂ Y = 1|S = 1) , P( ̂ Y = 1|S = 1) P( ̂ Y = 1|S = 0)) ެฏੑྀܕػցֶश ެฏੑͷఆٛ
w͏Ұͭͷج४ͱͯ͠EJTQBSFJNQBDUʢ%*ʣΛఆٛ͢Δɽ w%*ʹͳΔ΄ͲެฏͰ͋Δɽ %* : |P( ̂ Y
= 1|S = 1) − P( ̂ Y = 1|S = 0)| ެฏੑྀܕػցֶश ެฏੑͷఆٛ
w؍ଌ ݅ʹೖΕΔن४&RVBMJ[FE0EET͕͋Δɽ w w͜ͷ&0ʹΑͬͯٻΊΒΕΔ'13ͱ'/3ͷ͕ʹ͍ۙ΄Ͳެฏੑ͕֫ಘͰ͖Δɽ Y &0 : P(
̂ Y = 1|S = 0,Y = y) = P( ̂ Y = 1|S = 1,Y = y), ∀y ∈ 0,1 ެฏੑྀܕػցֶश ެฏੑͷن४ͦͷ
wຊݚڀͰɼҰൠతͳޯϒʔεςΟϯάͷΈʹɼఢରతֶशΛ༻͍ͯɼ ެฏੑΛ֫ಘ͍ͯ͘͠ɽ ఏҊख๏
wऑֶशΛϒʔεςΟϯάͯ͠༧ଌੑೳͷ্Λࢦ͍ͯ͠Δɽ wֶश࣌ ؍ଌ ͱ༧ଌ ɹͱͷޡࠩΛݮΒ͢Α͏ʹܾఆͰֶशΛߦ͏ɽ ɽΛ܁Γฦͯ͠ɼޡࠩΛݮΒ͢ɽ w༧ଌ࣌
wֶशʹΑͬͯٻΊͨᕓͱͬͯ༧ଌΛߦ͏ɽ y ̂ y ఏҊख๏ ޯϒʔεςΟϯά (5# ʹ͍ͭͯ
w'"(5#ͰެฏੑΛ֫ಘ͢Δํͱͯ͠ɼతมͱηϯγςΟϒଐੑͷ༧ଌਫ਼Λ ఢରతʹֶशΛߦ͍ɼࢦ͍ͯ͘͠ɽ wతมͷ༧ଌثͱఢରత༧ଌث ηϯγςΟϒଐੑͷ༧ଌ ΛϛχϚοΫε๏ͱͯ͠ ࠷దԽ͍ͯ͘͠ɽ w ͕ఢରֶशͷׂ߹Λௐ͢ΔϋΠύʔύϥϝʔλ
w-ͦΕͧΕଛࣦؔͰ͋Δɽࠓճྨ͔ͩΒɼෛͷରΛ࠾༻ɽ arg min F max θA n ∑ i=1 LFi (F (xi)) − λ n ∑ i=1 LAi (F (xi); θA) λ ఏҊख๏ 'BJS"EWFSTBSJBM(SBEJFOU5SFF#PPTUJOH '"(5#
ఏҊख๏ '"(5#ͷΞϧΰϦζϜ
ఏҊख๏ '"(5#ͷશମਤ
w࣮ݧͰɼਓσʔλͱ࣮σʔλͷ྆ํΛͬͯݕূ͢Δɽ w·ͨ405"ͳख๏ͱൺͯɼ༗༻ੑΛ͍ࣔͯ͘͠ɽ wఢରతֶशͷϋΠύʔύϥϝʔλ ͕GBJSOFTTͱBDDVSBDZͰͲ͏͍͏ӨڹΛ༩͑Δ ͔ௐΔ λ ࣮ݧ ࣮ݧ֓ཁ
wঢ়گઃఆͱͯ͠ɼࣗಈंอݥͰΫϨʔϜΛड͚Δ͔Ͳ͏͔Λߟ͑Δɽ wಛྔͱͯ͠ɼंͷ৭ɼྸɼੑผɼڟੑɼෆҙ͞Λ࣋ͭɽ wతมͱͯ͠ɼΫϨʔϜΛ͔ͨ͠Ͳ͏͔ΛೋͰද͢ɽ wηϯγςΟϒଐੑͱͯ͠ɼੑผΛ༻͍Δɽ wͦΕͧΕͷੜํ๏ӈͷ௨Γ ࣮ݧ ਓσʔλΛ༻͍Δ
࣮ݧ݁Ռ ਓσʔλ
wطଘͷ405"ͳख๏ͱൺΔͨΊɼ࣮σʔλͭΛ͍ൺֱΛߦ͏ɽ w༻͢Δσʔληοτ"EVMU $0.1"4 %FGBVMU #BOLͷ̐छྨ w ࣮ݧ ࣮σʔλ
w%1Λߟ͍͑ͯΔͱ͖ɼ Λຬ͍ͨͯ͠Δঢ়گͷͱͰɼBDDVSBDZ Λ༻͍ͯൺֱΛߦ͏ɽ w·ͨ&0Λߟ͍͑ͯΔͱ͖ɼ\'13 '/3^͕ҎԼΛຬ͍ͨͯ͠ΔͱͰͷ BDDVBSDZΛൺֱ͢Δɽ 1SVMF = 90
% ࣮ݧ ઃఆ
࣮ݧ݁Ռ %FNPHSBQIJD1BSJUZ
࣮ݧ݁Ռ &RVBMJ[FE0EET
࣮ݧ݁Ռ ϋΠύʔύϥϝʔλ ʹΑΔӨڹ λ
wܾఆΛ༻͍ͯɼެฏੑྀܕػցֶशΛߦ͏ख๏ΛఏҊͨ͠ɽ wຊख๏ͰطଘͷχϡʔϥϧωοτϫʔΫͷϞσϧͱಉͷੑೳ͕͋Δ͜ͱΛࣔ ͨ͠ɽ wܾఆΛ༻͍Δ͜ͱͰ//ϞσϧΑΓઆ໌ੑ͕૿͍ͯ͠Δɽ ·ͱΊ
wޯϒʔεςΟϯάΛษڧͰ͖ͯΑ͔ͬͨ wϒʔεςΟϯάͩͱઆ໌ੑ͕͋Δͷ͔ٙʹࢥͬͨɽ wਓσʔλͷ࡞Γํ͍͍ͳͬͯࢥͬͨɽ "9"Β͍͠ wਂχϡʔϥϧωοτܾఆ ఢରֶशͰެฏੑΛ֫ಘͰ͖ͨΒࣗͷΓͨ ͍͜ͱ ެฏੑͱઆ໌ੑ
ΛຬͨͤΔ w%FFQ/FVSBM%FDJTJPO5SFFT IUUQTBSYJWPSHBCT ײ
wޯܾఆϒʔεςΟϯάͰͱ͔ͯΓ͔ͬͨ͢:PVUVCFS w4UBU2VFTUXJUI+PTI4UBSNFS͞Μ wIUUQTXXXZPVUVCFDPNXBUDI W$$/[(+D ͓·͚ ษڧʹͳͬͨಈը