[読み会]Fair Adversarial Gradient Tree Boosting

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'BJS"EWFSTBSJBM (SBEJFOU5SFF#PPTUJOH ಡΈձ! ༶໌఩

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wஶऀ w7JODFOU(SBSJ 4PSCPOOF6OJWFSTJUZ w#PSJT3VG "9" w4ZMWBJO-BNQSJFS 4PSCPOOF6OJWFSTJUZ w.BSDJO%FUZOJFDLJ "9" wग़య*$%. ࿦จ৘ใ

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wܾఆ໦ͷϞσϧͰެฏͳϞσϧΛ֫ಘͰ͖ΔΑ͏ʹͨ͠ɽ w405"ͱಉ͘͡Β͍ͷੑೳΛୡ੒Ͱ͖ͨɽ wબΜͩཧ༝ wެฏͳϞσϧ֫ಘΛ໨తͱͯ͠ɼܾఆ໦ϕʔεͷख๏ΛఏҊ͍ͯͨͨ͠Ίɽ wޯ഑ϒʔεςΟϯάܾఆ໦͕ςʔϒϧσʔλʹରͯ͠ڧྗͰ͋Δ͔Βɽ ֓ཁ ͲΜͳ࿦จʁ

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wόΠΞεͷܰݮʹର͢ΔλεΫͰ͸Α͘χϡʔϥϧωοτϫʔΫ͕༻͍ΒΕ͍ͯ Δ͠ɼੑೳͱͯ͠΋͍͍ɽ wςʔϒϧσʔλʹରͯ͠ɼ9(#PPTU΍-JHIU(#.ͳͲޯ഑ϒʔεςΟϯά໦͕ඇ ৗʹڧྗͰΑ͘༻͍ΒΕ͍ͯΔɽ wͦ͜Ͱɼޯ഑ϒʔεςΟϯά໦ͰόΠΞεΛܰݮ͢Δ ެฏੑΛୡ੒͢Δ Α͏ͳख ๏ΛఏҊ͢Δɽ ֓ཁ ݚڀഎܠ

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wطଘݚڀͰ͸΄ͱΜͲ͕χϡʔϥϧωοτϫʔΫΛ༻͍ͯɼόΠΞεΛܰݮͯ͠ Δɽ wχϡʔϥϧωοτϫʔΫͰ͸ੑೳ͸ग़͍ͤͯΔ͕ɼͳΜͰ͜͏ͳ͔͕ͬͨ෼͔Γ ʹ͍͘ɽ wςʔϒϧσʔλͰ͸χϡʔϥϧωοτϫʔΫΑΓ΋ޯ഑ϒʔεςΟϯά໦͕޷·Ε ͯ࢖ΘΕ͍ͯΔɽ ֓ཁ طଘݚڀʹ͍ͭͯ

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wҰൠతͳ෼ྨϞσϧʹରͯ͠ɼܾఆ໦ΛؚΉఢରతֶशͰެฏΛ֫ಘ͢Δํ๏Λ ఏҊ͢Δɽ wҟͳΔެฏੑͷن४Ͱ405"ͳϞσϧͱಉ౳ͷੑೳΛୡ੒ͨ͠ɽ ֓ཁ ߩݙ

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w ࣍ݩͷಛ௃ྔʢඇηϯγςΟϒͳಛ௃ʣ wηϯγςΟϒͳଐੑɽࠓճ͸ೋ஋Ͱߟ͍͑ͯΔɽ w໨తม਺ɽࠓճ͸෼ྨ໰୊Λѻ͏ͷͰೋ஋Ͱߟ͑Δɽ wಛʹ؍ଌ஋͸ ༧ଌ஋͸ ͱ͢Δ wO͜ͷαϯϓϧͷσʔληοτ Λ༻͍ͯҰൠతͳڭࢣ͋ΓֶशΛߦ͏ɽ x ∈ ℝd d s y y ̂ y (xi , si , yi )n i=1 ެฏੑ഑ྀܕػցֶश දهͷఆٛ

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w%FNPHSBQIJD1BSJUZηϯγςΟϒଐੑʹ͔͔ΘΒͣ༧ଌ஋ͷൺ཰͸Ұக͢Δ w w%1Λ࢖ͬͨධՁ1SVMFΛ࣍ͷΑ͏ʹఆٛ͢Δ %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)) ެฏੑ഑ྀܕػցֶश ެฏੑͷఆٛ

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w΋͏Ұͭͷج४ͱͯ͠EJTQBSFJNQBDUʢ%*ʣΛఆٛ͢Δɽ w%*͸ʹͳΔ΄ͲެฏͰ͋Δɽ %* : |P( ̂ Y = 1|S = 1) − P( ̂ Y = 1|S = 0)| ެฏੑ഑ྀܕػցֶश ެฏੑͷఆٛ

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w؍ଌ஋ ΋৚݅ʹೖΕΔن४&RVBMJ[FE0EET͕͋Δɽ w w͜ͷ&0ʹΑͬͯٻΊΒΕΔ'13ͱ'/3ͷ஋͕ʹ͍ۙ΄Ͳެฏੑ͕֫ಘͰ͖Δɽ Y &0 : P( ̂ Y = 1|S = 0,Y = y) = P( ̂ Y = 1|S = 1,Y = y), ∀y ∈ 0,1 ެฏੑ഑ྀܕػցֶश ެฏੑͷن४ͦͷ

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wຊݚڀͰ͸ɼҰൠతͳޯ഑ϒʔεςΟϯά໦ͷ࿮૊ΈʹɼఢରతֶशΛ༻͍ͯɼ ެฏੑΛ֫ಘ͍ͯ͘͠ɽ ఏҊख๏

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wऑֶश໦ΛϒʔεςΟϯάͯ͠༧ଌੑೳͷ޲্Λ໨ࢦ͍ͯ͠Δɽ wֶश࣌ ؍ଌ஋ ͱ༧ଌ஋ ɹͱͷޡࠩΛݮΒ͢Α͏ʹܾఆ໦ͰֶशΛߦ͏ɽ ɽΛ܁Γฦͯ͠ɼޡࠩΛݮΒ͢ɽ w༧ଌ࣌ wֶशʹΑͬͯٻΊͨ࢒ᕓͱ࢖ͬͯ༧ଌΛߦ͏ɽ y ̂ y ఏҊख๏ ޯ഑ϒʔεςΟϯά໦ (5# ʹ͍ͭͯ

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w'"(5#ͰެฏੑΛ֫ಘ͢Δํ਑ͱͯ͠ɼ໨తม਺ͱηϯγςΟϒଐੑͷ༧ଌਫ਼౓Λ ఢରతʹֶशΛߦ͍ɼ໨ࢦ͍ͯ͘͠ɽ w໨తม਺ͷ༧ଌثͱఢରత༧ଌث ηϯγςΟϒଐੑͷ༧ଌ ΛϛχϚοΫε๏ͱͯ͠ ࠷దԽ͍ͯ͘͠ɽ w ͕ఢରֶशͷׂ߹Λௐ੔͢ΔϋΠύʔύϥϝʔλ w-͸ͦΕͧΕଛࣦؔ਺Ͱ͋Δɽࠓճ͸෼ྨ໰୊͔ͩΒɼෛͷର਺໬౓Λ࠾༻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#

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ఏҊख๏ '"(5#ͷΞϧΰϦζϜ

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ఏҊख๏ '"(5#ͷશମਤ

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w࣮ݧͰ͸ɼਓ޻σʔλͱ࣮σʔλͷ྆ํΛ࢖ͬͯݕূ͢Δɽ w·ͨ405"ͳख๏ͱൺ΂ͯɼ༗༻ੑΛ͍ࣔͯ͘͠ɽ wఢରతֶशͷϋΠύʔύϥϝʔλ ͕GBJSOFTTͱBDDVSBDZͰͲ͏͍͏ӨڹΛ༩͑Δ ͔ௐ΂Δ λ ࣮ݧ ࣮ݧ֓ཁ

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wঢ়گઃఆͱͯ͠ɼࣗಈंอݥͰΫϨʔϜΛड͚Δ͔Ͳ͏͔Λߟ͑Δɽ wಛ௃ྔͱͯ͠ɼंͷ৭ɼ೥ྸɼੑผɼڟ๫ੑɼෆ஫ҙ͞Λ࣋ͭɽ w໨తม਺ͱͯ͠ɼΫϨʔϜΛ͔ͨ͠Ͳ͏͔Λೋ஋Ͱද͢ɽ wηϯγςΟϒଐੑͱͯ͠ɼੑผΛ༻͍Δɽ wͦΕͧΕͷੜ੒ํ๏͸ӈͷ௨Γ ࣮ݧ ਓ޻σʔλΛ༻͍Δ

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࣮ݧ݁Ռ ਓ޻σʔλ

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wطଘͷ405"ͳख๏ͱൺ΂ΔͨΊɼ࣮σʔλͭΛ࢖͍ൺֱΛߦ͏ɽ w࢖༻͢Δσʔληοτ͸"EVMU $0.1"4 %FGBVMU #BOLͷ̐छྨ w ࣮ݧ ࣮σʔλ

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w%1Λߟ͍͑ͯΔͱ͖͸ɼ Λຬ͍ͨͯ͠Δঢ়گͷ΋ͱͰɼBDDVSBDZ Λ༻͍ͯൺֱΛߦ͏ɽ w·ͨ&0Λߟ͍͑ͯΔͱ͖͸ɼ\'13 '/3^͕ҎԼΛຬ͍ͨͯ͠Δ΋ͱͰͷ BDDVBSDZΛൺֱ͢Δɽ 1SVMF = 90 % ࣮ݧ ໰୊ઃఆ

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࣮ݧ݁Ռ %FNPHSBQIJD1BSJUZ

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࣮ݧ݁Ռ &RVBMJ[FE0EET

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࣮ݧ݁Ռ ϋΠύʔύϥϝʔλ ʹΑΔӨڹ λ

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wܾఆ໦Λ༻͍ͯɼެฏੑ഑ྀܕػցֶशΛߦ͏ख๏ΛఏҊͨ͠ɽ wຊख๏Ͱ͸طଘͷχϡʔϥϧωοτϫʔΫͷϞσϧͱಉ౳ͷੑೳ͕͋Δ͜ͱΛࣔ ͨ͠ɽ wܾఆ໦Λ༻͍Δ͜ͱͰ//ϞσϧΑΓ΋આ໌ੑ͕૿͍ͯ͠Δɽ ·ͱΊ

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wޯ഑ϒʔεςΟϯά໦ΛษڧͰ͖ͯΑ͔ͬͨ wϒʔεςΟϯάͩͱઆ໌ੑ͕͋Δͷ͔ٙ໰ʹࢥͬͨɽ wਓ޻σʔλͷ࡞Γํ͸͍͍ͳͬͯࢥͬͨɽ "9"Β͍͠ wਂ૚χϡʔϥϧωοτܾఆ໦ఢରֶशͰެฏੑΛ֫ಘͰ͖ͨΒࣗ෼ͷ΍Γͨ ͍͜ͱ ެฏੑͱઆ໌ੑ ΛຬͨͤΔ w%FFQ/FVSBM%FDJTJPO5SFFT IUUQTBSYJWPSHBCT ײ૝

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wޯ഑ܾఆϒʔεςΟϯά໦Ͱͱͯ΋෼͔Γ΍͔ͬͨ͢:PVUVCFS w4UBU2VFTUXJUI+PTI4UBSNFS͞Μ wIUUQTXXXZPVUVCFDPNXBUDI W$$/[(+D ͓·͚ ษڧʹͳͬͨಈը