SLIDE 1
FAIRNESS RISK MEASURES
Robert C. Williamson Aditya Menon
FAIRNESS RISK MEASURES FAIRNESS RISK MEASURES Robert C. Williamson - - PowerPoint PPT Presentation
FAIRNESS RISK MEASURES FAIRNESS RISK MEASURES Robert C. Williamson - - PowerPoint PPT Presentation
FAIRNESS RISK MEASURES FAIRNESS RISK MEASURES Robert C. Williamson Aditya Menon LOSS FUNCTIONS - OUTCOME CONTINGENT UTILITIES LOSS FUNCTIONS - OUTCOME CONTINGENT UTILITIES Walds abstraction: a loss function : Y A + {+
SLIDE 2
SLIDE 3
LOSS FUNCTIONS - OUTCOME CONTINGENT UTILITIES
SLIDE 4
LOSS FUNCTIONS - OUTCOME CONTINGENT UTILITIES
▸ Wald’s abstraction: a loss function
ℓ: Y × A → ℝ+ ∪ {+∞} =: ℝ
Label space Action space
SLIDE 5
LOSS FUNCTIONS - OUTCOME CONTINGENT UTILITIES
▸ Wald’s abstraction: a loss function ▸ is an outcome contingent utility
ℓ: Y × A → ℝ+ ∪ {+∞} =: ℝ
a ↦ ℓ(y, a)
Label space Action space
SLIDE 6
LOSS FUNCTIONS - OUTCOME CONTINGENT UTILITIES
▸ Wald’s abstraction: a loss function ▸ is an outcome contingent utility ▸ Learning goal: expected risk minimisation
ℓ: Y × A → ℝ+ ∪ {+∞} =: ℝ
min
f∈ℱ 𝔽(𝖸,𝖹)∼P ℓ(𝖹, f(𝖸))
a ↦ ℓ(y, a)
Label space Action space
SLIDE 7
LOSS FUNCTIONS - OUTCOME CONTINGENT UTILITIES
▸ Wald’s abstraction: a loss function ▸ is an outcome contingent utility ▸ Learning goal: expected risk minimisation ▸ In practice: empirical risk minimisation
ℓ: Y × A → ℝ+ ∪ {+∞} =: ℝ
min
f∈ℱ 𝔽(𝖸,𝖹)∼P ℓ(𝖹, f(𝖸))
min
f∈ℱ 𝔽(𝖸,𝖹)∼Pm ℓ(𝖹, f(𝖸))
= min
f∈ℱ 1 m m
∑
i=1
ℓ(yi, f(xi))
a ↦ ℓ(y, a)
Label space Action space
SLIDE 8
MINIMISING EMPIRICAL RISK
SLIDE 9
MINIMISING EMPIRICAL RISK
50 100 150 200 1 2 3 4 5 6 7 8 9 10 50 100 150 200 1 2 3 4 5 6 7 8 9 10
Data index
Loss HYPOTHESIS
SLIDE 10
MINIMISING EMPIRICAL RISK
F1 50 100 150 200 1 2 3 4 5 6 7 8 9 10 F1 50 100 150 200 1 2 3 4 5 6 7 8 9 10
Data index
Loss HYPOTHESIS
SLIDE 11
MINIMISING EMPIRICAL RISK
F2 50 100 150 200 1 2 3 4 5 6 7 8 9 10 F2 50 100 150 200 1 2 3 4 5 6 7 8 9 10
Data index
Loss HYPOTHESIS
SLIDE 12
MINIMISING EMPIRICAL RISK
F3 50 100 150 200 1 2 3 4 5 6 7 8 9 10 F3 50 100 150 200 1 2 3 4 5 6 7 8 9 10
Data index
Loss HYPOTHESIS
SLIDE 13
MINIMISING EMPIRICAL RISK
F4 50 100 150 200 1 2 3 4 5 6 7 8 9 10 F4 50 100 150 200 1 2 3 4 5 6 7 8 9 10
Data index
Loss HYPOTHESIS
SLIDE 14
MINIMISING EMPIRICAL RISK
F5 50 100 150 200 1 2 3 4 5 6 7 8 9 10 F5 50 100 150 200 1 2 3 4 5 6 7 8 9 10
Data index
Loss HYPOTHESIS
SLIDE 15
MINIMISING EMPIRICAL RISK
F5 50 100 150 200 1 2 3 4 5 6 7 8 9 10 F5 50 100 150 200 1 2 3 4 5 6 7 8 9 10
Data index
Loss HYPOTHESIS
Average loss of best hypothesis
SLIDE 16
MINIMISING EMPIRICAL RISK WITH SENSITIVE ATTRIBUTES VISIBLE
SLIDE 17
MINIMISING EMPIRICAL RISK WITH SENSITIVE ATTRIBUTES VISIBLE
50 100 150 200 1 2 3 4 5 6 7 8 9 10 50 100 150 200 1 2 3 4 5 6 7 8 9 10
Data index
Loss HYPOTHESIS
SLIDE 18
MINIMISING EMPIRICAL RISK WITH SENSITIVE ATTRIBUTES VISIBLE
F1 50 100 150 200 1 2 3 4 5 6 7 8 9 10 F1 50 100 150 200 1 2 3 4 5 6 7 8 9 10
Data index
Loss HYPOTHESIS
SLIDE 19
MINIMISING EMPIRICAL RISK WITH SENSITIVE ATTRIBUTES VISIBLE
F2 50 100 150 200 1 2 3 4 5 6 7 8 9 10 F2 50 100 150 200 1 2 3 4 5 6 7 8 9 10
Data index
Loss HYPOTHESIS
SLIDE 20
MINIMISING EMPIRICAL RISK WITH SENSITIVE ATTRIBUTES VISIBLE
F3 50 100 150 200 1 2 3 4 5 6 7 8 9 10 F3 50 100 150 200 1 2 3 4 5 6 7 8 9 10
Data index
Loss HYPOTHESIS
SLIDE 21
MINIMISING EMPIRICAL RISK WITH SENSITIVE ATTRIBUTES VISIBLE
F4 50 100 150 200 1 2 3 4 5 6 7 8 9 10 F4 50 100 150 200 1 2 3 4 5 6 7 8 9 10
Data index
Loss HYPOTHESIS
SLIDE 22
MINIMISING EMPIRICAL RISK WITH SENSITIVE ATTRIBUTES VISIBLE
F5 50 100 150 200 1 2 3 4 5 6 7 8 9 10 F5 50 100 150 200 1 2 3 4 5 6 7 8 9 10
Data index
Loss HYPOTHESIS
Average loss of best hypothesis
SLIDE 23
MINIMISING EMPIRICAL RISK REINDEXING PER SENSITIVE ATTRIBUTE
SLIDE 24
MINIMISING EMPIRICAL RISK REINDEXING PER SENSITIVE ATTRIBUTE
50 100 150 200 1 4 7 10 2 6 8 3 5 9 50 100 150 200 1 4 7 10 2 6 8 3 5 9
SLIDE 25
MINIMISING EMPIRICAL RISK REINDEXING PER SENSITIVE ATTRIBUTE
F1 50 100 150 200 1 4 7 10 2 6 8 3 5 9 F1 50 100 150 200 1 4 7 10 2 6 8 3 5 9
Loss HYPOTHESIS
SLIDE 26
MINIMISING EMPIRICAL RISK REINDEXING PER SENSITIVE ATTRIBUTE
F2 50 100 150 200 1 4 7 10 2 6 8 3 5 9 F2 50 100 150 200 1 4 7 10 2 6 8 3 5 9
Loss HYPOTHESIS
SLIDE 27
MINIMISING EMPIRICAL RISK REINDEXING PER SENSITIVE ATTRIBUTE
F3 50 100 150 200 1 4 7 10 2 6 8 3 5 9 F3 50 100 150 200 1 4 7 10 2 6 8 3 5 9
Loss HYPOTHESIS
SLIDE 28
MINIMISING EMPIRICAL RISK REINDEXING PER SENSITIVE ATTRIBUTE
F4 50 100 150 200 1 4 7 10 2 6 8 3 5 9 F4 50 100 150 200 1 4 7 10 2 6 8 3 5 9
Loss HYPOTHESIS
SLIDE 29
MINIMISING EMPIRICAL RISK REINDEXING PER SENSITIVE ATTRIBUTE
F5 50 100 150 200 1 4 7 10 2 6 8 3 5 9 F5 50 100 150 200 1 4 7 10 2 6 8 3 5 9
Loss HYPOTHESIS
Average loss of best hypothesis
SLIDE 30
MINIMISING EMPIRICAL RISK REINDEXING PER SENSITIVE ATTRIBUTE
F5 50 100 150 200 1 4 7 10 2 6 8 3 5 9 F5 50 100 150 200 1 4 7 10 2 6 8 3 5 9
Loss HYPOTHESIS
Average loss of best hypothesis
SLIDE 31
MINIMISING EMPIRICAL RISK REINDEXING PER SENSITIVE ATTRIBUTE
F5 50 100 150 200 1 4 7 10 2 6 8 3 5 9 F5 50 100 150 200 1 4 7 10 2 6 8 3 5 9
Loss HYPOTHESIS
Average loss of best hypothesis
SLIDE 32
MINIMISING EMPIRICAL RISK REINDEXING PER SENSITIVE ATTRIBUTE
F5 50 100 150 200 1 4 7 10 2 6 8 3 5 9 F5 50 100 150 200 1 4 7 10 2 6 8 3 5 9
Loss HYPOTHESIS
SLIDE 33
MINIMISING EMPIRICAL RISK REINDEXING PER SENSITIVE ATTRIBUTE
F5 50 100 150 200 1 4 7 10 2 6 8 3 5 9 F5 50 100 150 200 1 4 7 10 2 6 8 3 5 9
Loss HYPOTHESIS
1 2 3
Sensitive Feature index
SLIDE 34
MINIMISING AGGREGATED EMPIRICAL RISK
SLIDE 35
MINIMISING AGGREGATED EMPIRICAL RISK
50 100 150 200 1 2 3 50 100 150 200 1 2 3
Sensitive Feature index
HYPOTHESIS
SLIDE 36
MINIMISING AGGREGATED EMPIRICAL RISK
F1 50 100 150 200 1 2 3 F1 50 100 150 200 1 2 3
Sensitive Feature index
HYPOTHESIS
SLIDE 37
MINIMISING AGGREGATED EMPIRICAL RISK
F2 50 100 150 200 1 2 3 F2 50 100 150 200 1 2 3
Sensitive Feature index
HYPOTHESIS
SLIDE 38
MINIMISING AGGREGATED EMPIRICAL RISK
F3 50 100 150 200 1 2 3 F3 50 100 150 200 1 2 3
Sensitive Feature index
HYPOTHESIS
SLIDE 39
MINIMISING AGGREGATED EMPIRICAL RISK
F4 50 100 150 200 1 2 3 F4 50 100 150 200 1 2 3
Sensitive Feature index
HYPOTHESIS
SLIDE 40
MINIMISING AGGREGATED EMPIRICAL RISK
F5 50 100 150 200 1 2 3 F5 50 100 150 200 1 2 3
Sensitive Feature index
HYPOTHESIS
SLIDE 41
MINIMISING AGGREGATED EMPIRICAL RISK
▸ Standard problem: minimise average risk
F5 50 100 150 200 1 2 3 F5 50 100 150 200 1 2 3
Sensitive Feature index
HYPOTHESIS
SLIDE 42
MINIMISING AGGREGATED EMPIRICAL RISK
▸ Standard problem: minimise average risk ▸ Equity problem: also take account of variation
F5 50 100 150 200 1 2 3 F5 50 100 150 200 1 2 3
Sensitive Feature index
HYPOTHESIS
SLIDE 43
MINIMISING AGGREGATED EMPIRICAL RISK
▸ Standard problem: minimise average risk ▸ Equity problem: also take account of variation ▸ Fairness problem: mixture of both
F5 50 100 150 200 1 2 3 F5 50 100 150 200 1 2 3
Sensitive Feature index
HYPOTHESIS Loss
SLIDE 44
MINIMISING AGGREGATED EMPIRICAL RISK AND DEVIATION
SLIDE 45
MINIMISING AGGREGATED EMPIRICAL RISK AND DEVIATION
▸ Trade off low deviation against higher average
SLIDE 46
MINIMISING AGGREGATED EMPIRICAL RISK AND DEVIATION
▸ Trade off low deviation against higher average
20 40 60 80 1 2 3 20 40 60 80 1 2 3
Loss
SLIDE 47
MINIMISING AGGREGATED EMPIRICAL RISK AND DEVIATION
▸ Trade off low deviation against higher average
F5 20 40 60 80 1 2 3 F5 20 40 60 80 1 2 3
Loss
SLIDE 48
MINIMISING AGGREGATED EMPIRICAL RISK AND DEVIATION
▸ Trade off low deviation against higher average
F6 20 40 60 80 1 2 3 F6 20 40 60 80 1 2 3
Loss
SLIDE 49
MINIMISING AGGREGATED EMPIRICAL RISK AND DEVIATION
▸ Trade off low deviation against higher average ▸ Let be the sensitive feature space
F6 20 40 60 80 1 2 3 F6 20 40 60 80 1 2 3
Loss
S = {1,2,3}
SLIDE 50
MINIMISING AGGREGATED EMPIRICAL RISK AND DEVIATION
▸ Trade off low deviation against higher average ▸ Let be the sensitive feature space ▸ For let be a r.v. (taking as the
sample space, with a uniform base measure)
F6 20 40 60 80 1 2 3 F6 20 40 60 80 1 2 3
𝖲f : S → ℝ
S
𝖲f: S ∋ s ↦ 𝔽(𝖸,𝖹) [ℓ(𝖹, f(𝖸))|𝖳 = s]
f ∈ ℱ
Loss
S = {1,2,3}
SLIDE 51
MINIMISING AGGREGATED EMPIRICAL RISK AND DEVIATION
▸ Trade off low deviation against higher average ▸ Let be the sensitive feature space ▸ For let be a r.v. (taking as the
sample space, with a uniform base measure)
▸ Standard ERM:
F6 20 40 60 80 1 2 3 F6 20 40 60 80 1 2 3
𝖲f : S → ℝ
S
min
f∈ℱ 𝔽(𝖲f)
𝖲f: S ∋ s ↦ 𝔽(𝖸,𝖹) [ℓ(𝖹, f(𝖸))|𝖳 = s]
f ∈ ℱ
Loss
S = {1,2,3}
SLIDE 52
MINIMISING AGGREGATED EMPIRICAL RISK AND DEVIATION
▸ Trade off low deviation against higher average ▸ Let be the sensitive feature space ▸ For let be a r.v. (taking as the
sample space, with a uniform base measure)
▸ Standard ERM: ▸ Fairness Augmented ERM:
F6 20 40 60 80 1 2 3 F6 20 40 60 80 1 2 3
𝖲f : S → ℝ
S
min
f∈ℱ 𝔽(𝖲f)
min
f∈ℱ 𝔽(𝖲f) + (𝖲f) = min f∈ℱ ℛ(𝖲f)
𝖲f: S ∋ s ↦ 𝔽(𝖸,𝖹) [ℓ(𝖹, f(𝖸))|𝖳 = s]
f ∈ ℱ
Loss
S = {1,2,3}
SLIDE 53
FAIRNESS RISK MEASURES ARE “REGULAR MEASURES OF RISK”
SLIDE 54
FAIRNESS RISK MEASURES ARE “REGULAR MEASURES OF RISK”
▸ Instead can start with axioms for Paper lists and justifies them
ℛ
SLIDE 55
FAIRNESS RISK MEASURES ARE “REGULAR MEASURES OF RISK”
▸ Instead can start with axioms for Paper lists and justifies them ▸ Then show that such fairness risk measures are “regular measures of risk”
▸ (In fact they are “coherent measures of risk’’)
ℛ
SLIDE 56
FAIRNESS RISK MEASURES ARE “REGULAR MEASURES OF RISK”
▸ Instead can start with axioms for Paper lists and justifies them ▸ Then show that such fairness risk measures are “regular measures of risk”
▸ (In fact they are “coherent measures of risk’’)
▸ Such measures can always be written as
ℛ(𝖲) = 𝔽(𝖲) + (𝖲)
Fairness risk measure Deviation measure
ℛ
SLIDE 57
FAIRNESS RISK MEASURES ARE “REGULAR MEASURES OF RISK”
▸ Instead can start with axioms for Paper lists and justifies them ▸ Then show that such fairness risk measures are “regular measures of risk”
▸ (In fact they are “coherent measures of risk’’)
▸ Such measures can always be written as ▸ Here is a “regular measure of deviation”
(i.e. convex, positively homogeneous, zero only when R is constant, and lower semicontinuous)
ℛ(𝖲) = 𝔽(𝖲) + (𝖲)
Fairness risk measure Deviation measure
ℛ
SLIDE 58
EXAMPLE RISK MEASURE AND CORRESPONDING DEVIATION MEASURE
SLIDE 59
EXAMPLE RISK MEASURE AND CORRESPONDING DEVIATION MEASURE
ℛQ,α(𝖺) = CVaRα(𝖺) Q,α(𝖺) = CVaRα(𝖺 − 𝔽(𝖺))
SLIDE 60
EXAMPLE RISK MEASURE AND CORRESPONDING DEVIATION MEASURE
▸ CVaR is the “Conditional Value at Risk”. ▸ When Z is continuous random variable: ▸ where is the th quantile of Z
ℛQ,α(𝖺) = CVaRα(𝖺) Q,α(𝖺) = CVaRα(𝖺 − 𝔽(𝖺))
CVaRα(𝖺) = 𝔽(𝖺|𝖺 ≥ qα(𝖺))
qα(𝖺)
α
SLIDE 61
EXAMPLE RISK MEASURE AND CORRESPONDING DEVIATION MEASURE
▸ CVaR is the “Conditional Value at Risk”. ▸ When Z is continuous random variable: ▸ where is the th quantile of Z ▸ Have
ℛQ,α(𝖺) = CVaRα(𝖺) Q,α(𝖺) = CVaRα(𝖺 − 𝔽(𝖺))
CVaRα(𝖺) = 𝔽(𝖺|𝖺 ≥ qα(𝖺))
qα(𝖺)
CVaR0(𝖺) = 𝔽(𝖺) and CVaR1(𝖺) = max(𝖺)
α
SLIDE 62
EXAMPLE RISK MEASURE AND CORRESPONDING DEVIATION MEASURE
▸ CVaR is the “Conditional Value at Risk”. ▸ When Z is continuous random variable: ▸ where is the th quantile of Z ▸ Have ▸ Fairness objective becomes (see paper, eq (26)):
ℛQ,α(𝖺) = CVaRα(𝖺) Q,α(𝖺) = CVaRα(𝖺 − 𝔽(𝖺))
CVaRα(𝖺) = 𝔽(𝖺|𝖺 ≥ qα(𝖺))
qα(𝖺)
CVaR0(𝖺) = 𝔽(𝖺) and CVaR1(𝖺) = max(𝖺)
α
min
f∈ℱ,ρ∈ℝ {ρ +
1 1 − α ⋅ 𝔽[𝖬(f) − ρ]+} .
SLIDE 63
AN INTERESTING LIMITING CASE - EACH PERSON IS THEIR OWN CATEGORY!
SLIDE 64
AN INTERESTING LIMITING CASE - EACH PERSON IS THEIR OWN CATEGORY!
50 100 150 200
P1 P2 P3 P4 P5 P6 P7 P8 P9 P10 P11 P12 P13 P14 P15 P16 P17 P18 P19 P20 P21 P22
50 100 150 200
P1 P2 P3 P4 P5 P6 P7 P8 P9 P10 P11 P12 P13 P14 P15 P16 P17 P18 P19 P20 P21 P22
Loss
SLIDE 65
AN INTERESTING LIMITING CASE - EACH PERSON IS THEIR OWN CATEGORY!
F1 50 100 150 200
P1 P2 P3 P4 P5 P6 P7 P8 P9 P10 P11 P12 P13 P14 P15 P16 P17 P18 P19 P20 P21 P22
F1 50 100 150 200
P1 P2 P3 P4 P5 P6 P7 P8 P9 P10 P11 P12 P13 P14 P15 P16 P17 P18 P19 P20 P21 P22
Loss
SLIDE 66
AN INTERESTING LIMITING CASE - EACH PERSON IS THEIR OWN CATEGORY!
F2 50 100 150 200
P1 P2 P3 P4 P5 P6 P7 P8 P9 P10 P11 P12 P13 P14 P15 P16 P17 P18 P19 P20 P21 P22
F2 50 100 150 200
P1 P2 P3 P4 P5 P6 P7 P8 P9 P10 P11 P12 P13 P14 P15 P16 P17 P18 P19 P20 P21 P22
Loss
SLIDE 67
AN INTERESTING LIMITING CASE - EACH PERSON IS THEIR OWN CATEGORY!
F3 50 100 150 200
P1 P2 P3 P4 P5 P6 P7 P8 P9 P10 P11 P12 P13 P14 P15 P16 P17 P18 P19 P20 P21 P22
F3 50 100 150 200
P1 P2 P3 P4 P5 P6 P7 P8 P9 P10 P11 P12 P13 P14 P15 P16 P17 P18 P19 P20 P21 P22
Loss
SLIDE 68
AN INTERESTING LIMITING CASE - EACH PERSON IS THEIR OWN CATEGORY!
F4 50 100 150 200
P1 P2 P3 P4 P5 P6 P7 P8 P9 P10 P11 P12 P13 P14 P15 P16 P17 P18 P19 P20 P21 P22
F4 50 100 150 200
P1 P2 P3 P4 P5 P6 P7 P8 P9 P10 P11 P12 P13 P14 P15 P16 P17 P18 P19 P20 P21 P22
Loss
SLIDE 69
AN INTERESTING LIMITING CASE - EACH PERSON IS THEIR OWN CATEGORY!
F5 50 100 150 200
P1 P2 P3 P4 P5 P6 P7 P8 P9 P10 P11 P12 P13 P14 P15 P16 P17 P18 P19 P20 P21 P22
F5 50 100 150 200
P1 P2 P3 P4 P5 P6 P7 P8 P9 P10 P11 P12 P13 P14 P15 P16 P17 P18 P19 P20 P21 P22
Loss
SLIDE 70
AN INTERESTING LIMITING CASE - EACH PERSON IS THEIR OWN CATEGORY!
▸ Consistent with the principle that fundamental moral unit is the individual person
F5 50 100 150 200
P1 P2 P3 P4 P5 P6 P7 P8 P9 P10 P11 P12 P13 P14 P15 P16 P17 P18 P19 P20 P21 P22
F5 50 100 150 200
P1 P2 P3 P4 P5 P6 P7 P8 P9 P10 P11 P12 P13 P14 P15 P16 P17 P18 P19 P20 P21 P22
Loss
SLIDE 71
AN INTERESTING LIMITING CASE - EACH PERSON IS THEIR OWN CATEGORY!
▸ Consistent with the principle that fundamental moral unit is the individual person ▸ Avoids headaches with group boundaries and multiple group membership
F5 50 100 150 200
P1 P2 P3 P4 P5 P6 P7 P8 P9 P10 P11 P12 P13 P14 P15 P16 P17 P18 P19 P20 P21 P22
F5 50 100 150 200
P1 P2 P3 P4 P5 P6 P7 P8 P9 P10 P11 P12 P13 P14 P15 P16 P17 P18 P19 P20 P21 P22
Loss
SLIDE 72
AN INTERESTING LIMITING CASE - EACH PERSON IS THEIR OWN CATEGORY!
▸ Consistent with the principle that fundamental moral unit is the individual person ▸ Avoids headaches with group boundaries and multiple group membership ▸ Fairness risk measures automatically extend to this case (trivially)
F5 50 100 150 200
P1 P2 P3 P4 P5 P6 P7 P8 P9 P10 P11 P12 P13 P14 P15 P16 P17 P18 P19 P20 P21 P22
F5 50 100 150 200
P1 P2 P3 P4 P5 P6 P7 P8 P9 P10 P11 P12 P13 P14 P15 P16 P17 P18 P19 P20 P21 P22
Loss
SLIDE 73
CONCLUSION
SLIDE 74
CONCLUSION
▸ New and general approach to fairness in ML problems
𝖲f: S ∋ s ↦ 𝔽(𝖸,𝖹) [ℓ(𝖹, f(𝖸))|𝖳 = s]
min
f∈ℱ ℛ(𝖲f)
SLIDE 75
CONCLUSION
▸ New and general approach to fairness in ML problems ▸ Fairness only depends upon losses, not predictions
𝖲f: S ∋ s ↦ 𝔽(𝖸,𝖹) [ℓ(𝖹, f(𝖸))|𝖳 = s]
min
f∈ℱ ℛ(𝖲f)
SLIDE 76
CONCLUSION
▸ New and general approach to fairness in ML problems ▸ Fairness only depends upon losses, not predictions ▸ Fairness risk measures are symmetric coherent measures of risk
𝖲f: S ∋ s ↦ 𝔽(𝖸,𝖹) [ℓ(𝖹, f(𝖸))|𝖳 = s]
min
f∈ℱ ℛ(𝖲f)
SLIDE 77
CONCLUSION
▸ New and general approach to fairness in ML problems ▸ Fairness only depends upon losses, not predictions ▸ Fairness risk measures are symmetric coherent measures of risk ▸ Close connection to measures of inequality (see appendix)
𝖲f: S ∋ s ↦ 𝔽(𝖸,𝖹) [ℓ(𝖹, f(𝖸))|𝖳 = s]
min
f∈ℱ ℛ(𝖲f)
SLIDE 78
CONCLUSION
▸ New and general approach to fairness in ML problems ▸ Fairness only depends upon losses, not predictions ▸ Fairness risk measures are symmetric coherent measures of risk ▸ Close connection to measures of inequality (see appendix) ▸ Computationally tractable; related to SVM! (see paper / poster for experiments)
𝖲f: S ∋ s ↦ 𝔽(𝖸,𝖹) [ℓ(𝖹, f(𝖸))|𝖳 = s]
min
f∈ℱ ℛ(𝖲f)
SLIDE 79
Humanising Machine Intelligence
Machine Learning Postdoc position available
hmi.anu.edu.au