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[読み会] Individually Fair Gradient Boosting

mei28
April 13, 2021
26

[読み会] Individually Fair Gradient Boosting

読み会資料
Individually Fair Gradient Boosting (ICLR 2021)

mei28

April 13, 2021
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  1.  •ஶऀ৘ใ •Alexander Vargo, Fan Zhang, Mikhail Yurochkin, Yuekai Sun

    •ϛγΨϯେֶɼ্ւՊٕେֶɼMIT-IBM Watson AI Lab •ग़య: ICLR2021 •ͳΜͰબΜ͔ͩʁ •ݸผެฏੑ+ܾఆ໦Λߟ͍͑ͯΔͷ͸ҙ֎ʹগͳ͍ɽˠ͜Ε͕ॳΊͯΒ͍͠ ࿦จ৘ใ ݸผެฏੑ + GBDTʹ஫໨ͨ͠ݚڀ
  2.  •ೖྗ: , ग़ྗ: •อޢ͢Δଐੑ: ͍ΘΏΔηϯγςΟϒଐੑ •αϯϓϧ͝ͱެฏࢦඪ: ͜Ε͸αϯϓϧ͕͍ۙ΄Ͳࣅ͍ͯΔ •໨ඪ: 


    ɹαϯϓϧ͝ͱʹެฏͳϞσϧ Λ֫ಘ͢Δ͜ͱ 𝒳 ∈ ℝd 𝒴 = {0,1} 𝒵 = 𝒳 × {0,1} dx f : 𝒳 → {0,1} ४උ ࢖͏ه߸Λఆٛ͢Δ
  3.  •Transport cost function: ݸผͷαϯϓϧ͕͍ۙ΄Ͳখ͍͞ •Zͷ֬཰෼෍্ͷ࠷ద༌ૹڑ཭ : ෼෍ͷۙ͞Λߟ͍͑ͯΔ c ((x1

    , y1), (x2 , y2)) ≜ d2 x (x1 , x2) + ∞ ⋅ 1 {y1 ≠y2} W W (P1 , P2) ≜ inf Π∈C(P1 , P2) ∫ 𝒵×𝒵 c (z1 , z2) dΠ (z1 , z2) ४උ αϯϓϧ͝ͱʹެฏͳϞσϧΛֶश͍ͨ͠
  4.  •σʔληοτΛ֦ு͢Δ: •࠷ద༌ૹؔ਺ʹ੍ݶΛՃ͑Δ: ҧ͍͸্ͷσʔληοτ͔Ͳ͏͔ 𝒟0 ≜ {(xi , yi), (xi

    ,1 − yi)} n i=1 W𝒟 (P1 , P2) ≜ inf Π∈C0(P1 , P2) ∫ 𝒵×𝒵 c (z1 , z2) dΠ (z1 , z2) ఏҊख๏ ੍ݶΛՃ͑ͯnon-smoothͷͨΊʹ޻෉͢Δɽ
  5.  ޯ഑ϒʔεςΟϯάͰ͸ ΛٻΊΔඞཁ͕͋Δɽ μϯεΩϯͷఆཧΛ༻͍Δͱޯ഑͸ɼ ∂L ∂ ̂ y ∂L ∂

    ̂ yi = ∂ ∂f (xi) [ sup P:W𝒟(P, Pn)≤ϵ 𝔼P [ℓ (f (xi), yi)]] = ∑ y∈𝒴 ∂ ∂f (xi) [ℓ (f (xi), y)) P* (xi , y) ఏҊख๏ ޯ഑ϒʔεςΟϯά໦Ͱ΋࢖͑ΔΑ͏ʹ͢Δ
  6.  • ʹΑΔ೚ҙͷ෼෍ ʹରͯ͠ɼ ͱ͢Δͱ ͸࣍ͷΑ͏ͳߦྻ ͰදͤΔɽ 1. 2. D0

    P Pi,k = P({(xi , k}), k ∈ {0,1} WD (P, Pn ) ≤ ϵ Π Π ∈ Γ with Γ = {Π ∣ Π ∈ ℝn×n + , ⟨C, Π⟩ ≤ ϵ, ΠT ⋅ 1n = 1 n 1n} Π ⋅ y1 = (P1,1 , …, Pn,1), and Π ⋅ y0 = (P1,0 , …, Pn,0) ఏҊख๏ Λઢܗܭը๏ͰٻΊΔ P⋆
  7.  •ߦྻ ɹˠ ϥϕϧjͰ͋Δαϯϓϧj͕αϯϓϧiʹ ͳͬͨͱ͖ͷଛࣦ •ٻΊ͍ͨߦྻ ͸࣍ͷΑ͏ʹͳΔ Ri,j = l(f(xi

    ), yj ) Π⋆ Π⋆ ∈ arg max Π∈Γ ⟨R, Π⟩ ఏҊख๏ ͞Βʹఆ͍ٛͯ͘͠Α