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# 公平性を保証したAI/機械学習 アルゴリズムの最新理論

2019.11.26 第38回AIセミナー「機械学習／人工知能の公平性」

2019.11.26 第38回AIセミナー「機械学習／人工知能の公平性」

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### 公平性を保証したAI/機械学習 アルゴリズムの最新理論

1. 1.
2. 2. ACM FAT*
3. 3. f
4. 4. f( )=A
5. 5. f( )=A   f
6. 6. f( )=A f
7. 7. f( )=A   f f
8. 8. f( )=A f f
9. 9. X Y ̂YX S = S = X Y S ̂Y
10. 10. ℙ{ ̂Y ∈ 𝒜|S = s} = ℙ{ ̂Y ∈ 𝒜|S = s′} 𝒜, s, s′ = ̂Y|S = ̂Y|S =
11. 11. ℙ{ ̂Y ∈ 𝒜|Y = y, S = s} = ℙ{ ̂Y ∈ 𝒜|Y = y, S = s′} 𝒜, y, s, s′ Y ̂Y
12. 12. Y = 1 ̂p Y = 1 ̂p ℙ{Y = 1| ̂p = p, S = s} = p p, s p ̂p = p|S =
13. 13. x, x′ D( f(x), f(x′)) ≤ d(x, x′) ≈ ⟹ f : 𝒳 → Δ(𝒴)
14. 14. f( )=A f
15. 15. minf Err(f ) + ηUnfair(f ) minf Err(f ) Unfair(f ) ≤ η
16. 16. Q Q f minQ 𝔼f∼Qℙ{f(X) ≠ Y} M𝔼f∼Q[μ(f )] ≤ c 𝔼{f(X)|S = 0} = 𝔼{f(X)} 𝔼{f(X)|S = 1} = 𝔼{f(X)}
17. 17. minQ 𝔼f∼Qℙ{f(X) ≠ Y} M𝔼f∼Q[μ(f )] ≤ c maxλ∈ℝK +,∥λ∥≤B minQ 𝔼f∼Qℙ{f(X) ≠ Y} + λ⊤ (M𝔼f∼Q[μ(f )] − c)
18. 18. minf ∑ n i=1 (h(Xi)C1 i + (1 − h(Xi))C0 i )
19. 19. λ Q μ
20. 20. Q λ
21. 21.
22. 22. g( )= z f( )=A zz
23. 23. g( ) g( ) z
24. 24. g( ) g( ) z
25. 25. g( ) g( ) z f( )=A z
26. 26. g( ) g( ) z
27. 27. g( )= f( )=A d( )=z z z
28. 28.
29. 29.   minf Likelihood(f(X), Y) + ηI(f(X), S)
30. 30. f( )=A
31. 31. f( )=A
32. 32. f( )=A
33. 33. f( )=A
34. 34.   ̂Y = 1
35. 35. maxy,s (VC(ℱ) + ln(1/δ))/(nPy,s) maxy,s ln(1/δ)/(nPy,s)
36. 36. maxy,s (VC(ℱ) + ln(1/δ))/(nPy,s) maxy,s ln(1/δ)/(nPy,s) (y, s)
37. 37. minθ 𝔼[ℓ0(X, θ)] 𝔼[ℓi(X, θ)] ≤ 0
38. 38. ϵ m Rn(ℱ) ϵ + Rn(ℱ) + ln(1/δ)/n (m ln(1/ϵ) + ln(m/δ))/n
39. 39. ϵ + Rn(ℱ) + ln(1/δ)/n (m ln(1/ϵ) + ln(m/δ))/n ϵ m Rn(ℱ)
40. 40. ̂Y = 1 h : 𝒳 → [0,1] h ℓ0 ℙx,x′{|h(x) − h(x′)| > d(x, x′) + γ} ≤ α (γ, α)
41. 41. maxi,j max(0,|h(x) − h(x′)| − d(xi, xj)) ≤ γ m = O(poly(1/ϵα,1/ϵγ,1/ϵ)) ϵ (α + ϵα, γ + ϵγ) h
42. 42.
43. 43. ∑ T t=1 r(t) x(t) 1 , . . . , x(t) K i r(t) = fi(x(t) i ) x(t) i(t) r(t)
44. 44. πi(t) > πj(t) fi(x(t) i ) > fj(x(t) j ) fi(x(t) i )
45. 45. K3 T ln(Tk/δ) T4/5 K6/5 d3/5 ∨ k3 ln(k/δ) Ω( T) Ω( K3 ln(1/δ))   TKd ln(T)
46. 46. πi(t) ≠ ℙ{i = arg maxj rj} D(π(t) i , π(t) j ) ≤ ϵ1D(ri, rj) + ϵ2
47. 47.
48. 48.     (KT)2/3 1 − δ D(π(t) i , π(t) j ) ≤ 2D(ri, rj) + ϵ2
49. 49. |πi(t) − πj(t)| ≤ d(x(t) i , x(t) j ) x(t) i π(t) r(t) O(t)    ϵ
50. 50. r(t) maxπ∈ΔK ∑ K i=1 riπi |πi − πj | ≤ dij
51. 51. K, d T d T ln(T/δ) K2 d2 ln(TKd) K2 d2 ln(kdT/ϵ) + K3 ϵT + d T ln(T/δ) K2 d2 ln(d/ϵ) ϵ = 1/K3 T T
52. 52. ∑ ∞ t=τ γt−τ r(t) s(t) a(t) r(t)
53. 53. ϵ 1/(1 − γ) πi(t) > πj(t) fi(s(t) i ) > fj(s(t) j )
54. 54.
55. 55. f
56. 56. f
57. 57. • [Hardt+16] Moritz Hardt, Eric Price, and Nathan Srebro. Equality of Opportunity in Supervised Learning. In: NeurIPS, pp. 3315-3323, 2016. https://arxiv.org/abs/1610.02413 • [Pleiss+17] Geoff Pleiss, Manish Raghavan, Felix Wu, Jon Kleinberg, and Kilian Q. Weinberger. On Fairness and Calibration. In: NeurIPS, pp. 5680-5689, 2017. https://arxiv.org/ abs/1709.02012 • [Dwork+12] Cynthia Dwork, Moritz Hardt, Toniann Pitassi, Omer Reingold, Rich Zemel. Fairness Through Awareness. In: the 3rd innovations in theoretical computer science conference, pp. 214-226, 2012. https://arxiv.org/abs/ 1104.3913
58. 58. • [Agarwal+18] Alekh Agarwal, Alina Beygelzimer, Miroslav Dudík, John Langford, and Hanna Wallach. A Reductions Approach to Fair Classification. In: ICML, PMLR 80, pp. 60-69, 2018. https://arxiv.org/abs/1803.02453 • [Agarwal+19] Alekh Agarwal, Miroslav Dudík, and Zhiwei Steven Wu. Fair Regression: Quantitative Definitions and Reduction-based Algorithms. In: ICML, PMLR 97, pp. 120-129, 2019. https://arxiv.org/abs/1905.12843 • [Zafar+13] Rich Zemel, Yu Wu, Kevin Swersky, Toni Pitassi, and Cynthia Dwork. Learning Fair Representations. In: ICML, PMLR 28, pp. 325-333, 2013.
59. 59. • [Zhao+19] Han Zhao, Geoffrey J. Gordon. Inherent Tradeoffs in Learning Fair Representations. In: NeurIPS, 2019, to appear. https://arxiv.org/abs/1906.08386 • [Xie+16] Qizhe Xie, Zihang Dai, Yulun Du, Eduard Hovy, Graham Neubig. Controllable Invariance through Adversarial Feature Learning. In: NeurIPS, pp. 585-596, 2016. https://arxiv.org/abs/1705.11122 • [Moyer+18] Daniel Moyer, Shuyang Gao, Rob Brekelmans, Greg Ver Steeg, and Aram Galstyan. Invariant Representations without Adversarial Training. In: NeurIPS, pp. 9084-9893, 2018. https://arxiv.org/abs/1805.09458
60. 60. • [Woodworth+18] Blake Woodworth, Suriya Gunasekar, Mesrob I. Ohannessian, Nathan Srebro. Learning Non-Discriminatory Predictors. In: COLT, pp. 1920-1953, 2017. https://arxiv.org/abs/ 1702.06081 • [Cotter+19] Andrew Cotter, Maya Gupta, Heinrich Jiang, Nathan Srebro, Karthik Sridharan, Serena Wang, Blake Woodworth, Seungil You. Training Well-Generalizing Classifiers for Fairness Metrics and Other Data-Dependent Constraints. In: ICML, PMLR 97, pp. 1397-1405, 2019. https:// arxiv.org/abs/1807.00028 • [Rothblum+18] Guy N. Rothblum, Gal Yona. Probably Approximately Metric-Fair Learning. In: ICML, PMLR 80, pp. 5680-5688, 2018. https://arxiv.org/abs/1803.03242
61. 61. • [Joseph+16] Matthew Joseph, Michael Kearns, Jamie Morgenstern, Aaron Roth. Fairness in Learning: Classic and Contextual Bandits. In: NeurIPS, pp. 325-333, 2016. • [Liu+17] Yang Liu, Goran Radanovic, Christos Dimitrakakis, Debmalya Mandal, David C. Parkes. Calibrated Fairness in Bandits. In: 4th Workshop on Fairness, Accountability, and Transparency in Machine Learning (FATML), 2017. https://arxiv.org/abs/1707.01875 • [Gillen+18] Stephen Gillen, Christopher Jung, Michael Kearns, Aaron Roth. Online Learning with an Unknown Fairness Metric. In: NeurIPS, pp. 2600-2609, 2018. https:// arxiv.org/abs/1802.06936
62. 62. • [Jabbari+17] Shahin Jabbari, Matthew Joseph, Michael Kearns, Jamie Morgenstern, Aaron Roth. Fairness in Reinforcement Learning. In: ICML, PMLR 70, pp. 1617-1626, 2017. https://arxiv.org/abs/1611.03071 • [Liu+18] Lydia T. Liu, Sarah Dean, Esther Rolf, Max Simchowitz, Moritz Hardt. Delayed Impact of Fair Machine Learning. In: ICML, PMLR 80, pp. 3150-3158, 2018. https://arxiv.org/abs/ 1803.04383 • [Aivodji+19] Ulrich Aïvodji, Hiromi Arai, Olivier Fortineau, Sébastien Gambs, Satoshi Hara, Alain Tapp. Fairwashing: the risk of rationalization. In: ICML, 2019. https://arxiv.org/abs/1901.09749 • [Fukuchi+20] Kazuto Fukuchi, Satoshi Hara, Takanori Maehara. Faking Fairness via Stealthily Biased Sampling. In: AAAI, Special Track on AI for Social Impact (AISI), 2020, to appear. https://arxiv.org/abs/ 1901.08291