fairness, part iii - course.ece.cmu.edu
TRANSCRIPT
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Fairness, Part IIIGiulia Fanti
Fall 2019Based in part on slides by Anupam Datta
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Administrative
• HW4 due Nov. 22 (2.5 weeks from now)• Fairness + anonymous communication
• Recitation on Friday (Sruti)• Creating fair classifiers
• Feedback included on presentations, please read!
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In-class Quiz
• On Canvas
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Last time
• Group fairness vs Individual Fairness• When does one imply the other?
• Equalized odds vs equal opportunity• How do we transform an unfair classifier into a fair one?• What is the effect of fairness on classifier accuracy?
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Today
• Review of equalized odds vs equal opportunity• Revisit geometric interpretation
• Disparate impact• Metric for measuring• How to prevent it
• Overview of fairness techniques & how they relate to each other
• Wrap up Unit 2
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Last time: Another definition of fair classifiers
• NeurIPS 2016
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Individual’sData
True label
x 𝑌𝑥 =
𝑥$…𝑥&
Protected attribute 𝐴
(𝑌
LearnedClassifier
)𝑌
New (fair)Classifier
S𝑨 = 𝟏
T𝑨 = 𝟎
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Equalized odds
• Consider binary classifiers• We say a classifier (𝑌 has equalized odds if for all true labels 𝑦,
𝑃 (𝑌 = 1|𝐴 = 0, 𝑌 = 𝑦 = 𝑃 (𝑌 = 1|𝐴 = 1, 𝑌 = 𝑦
Q: How would this definition look if we only wanted to enforce group fairness?A: 𝑃 (𝑌 = 1|𝐴 = 0 = 𝑃 (𝑌 = 1|𝐴 = 1
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Exercise
Come up with an example classifier that exhibits group fairness but not equalized odds.Equalized Odds: 𝑃 (𝑌 = 1|𝐴 = 0, 𝑌 = 𝑦 = 𝑃 (𝑌 = 1|𝐴 = 1, 𝑌 = 𝑦Group Fairness: 𝑃 (𝑌 = 1|𝐴 = 0 = 𝑃 (𝑌 = 1|𝐴 = 1
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Equal opportunity
• Suppose 𝑌 = 1 is the desirable outcome• E.g., getting a loan
• We say a classifier (𝑌 has equal opportunity if
𝑃 (𝑌 = 1|𝐴 = 0, 𝑌 = 1 = 𝑃 (𝑌 = 1|𝐴 = 1, 𝑌 = 1
Interpretation: True positive rate is the same for both classes
Weaker notion of fairness à can enable better utility
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So how do we enforce fairness?
Classifier𝑋
𝐴(𝑌
What was originally trained What we
see
Fairness Module )𝑌 Finaloutput
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How is the fairness module defined?
0 1
0 𝑝55 = 𝑃( )𝑌 = 1|𝐴 = 0, (𝑌 = 0) 𝑝5$ = 𝑃( )𝑌 = 1|𝐴 = 1, (𝑌 = 0)
1 𝑝$5 = 𝑃( )𝑌 = 1|𝐴 = 0, (𝑌 = 1) 𝑝$$ = 𝑃( )𝑌 = 1|𝐴 = 1, (𝑌 = 1)
Protected attribute 𝐴
Predicted Label (𝑌
Note: These four numbers are decoupled!
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Geometric Interpretation via ROC curves
• False positive rate for 𝐴 = 0:
𝑃 )𝑌 = 1 𝐴 = 0, 𝑌 = 0 = 𝑃 (𝑌 = 1 𝐴 = 0, 𝑌 = 0 𝑝$5 +𝑃 (𝑌 = 0 𝐴 = 0, 𝑌 = 0 𝑝55
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Case study: FICO Scores
Baseline fairness techniques• Max profit – no fairness constraint (output (𝑌)• Race blind – uses same FICO threshold for all groups• Group fairness – picks for each group a threshold such that the fraction of
group members that qualify for loans is the same• Equal opportunity – picks a threshold for each group s.t. fraction of non-
defaulting group members is the same• Equalized odds –fraction of non-defaulters that qualify for loans and the
fraction of defaulters that qualify for loans constant across groups
Regular Classifier𝑋 = 𝐹𝐼𝐶𝑂𝐴 = race
(𝑌 = pay loan? Fairness Module GY
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Profit Results
Method Profit (% relative to max profit)
Max profit 100
Race blind 99.3
Equal opportunity 92.8
Equalized odds 80.2
Group fairness (demographic parity) 69.8
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To summarize…
• Equalized odds and equal opportunity are more practical than individual fairness
• Equal opportunity doesn’t hurt utility too much
• Still requires access to original output labels to evaluate fairness• This is also clear from the definition of equalized odds/equal opportunity
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Yet another definition, this time based on “Disparate Impact”
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Disparate impact
• Griggs v. Duke Power Co (1971)• US Supreme Court: business hiring decision illegal if it results in disparate
impact by race
• Leading technique today for determining unintended discrimination in court system• … but how do we define this?
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Formal definition (80% rule)Suppose𝐴 = 1 istheminority(protected)class,asbefore.WesaymechanismMhasdisparateimpact if
𝑃𝑟 𝑌 = 1 𝐴 = 1𝑃𝑟 𝑌 = 1 𝐴 = 0
≤ 𝜏 = 0.8
Q: What does this look like? A: Group fairness
Q: More or less stringent?A: Less stringent, group fairness requires ratio to be 1
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How do you estimate this?
• Can we predict sensitive attribute 𝐴 from non-sensitive attributes 𝑋? • Balanced error rate:
𝐵𝐸𝑅 𝑓 𝑋 , 𝐴 =𝑃 𝑓 𝑋 = 0 𝐴 = 1 + 𝑃 𝑓 𝑋 = 1|𝐴 = 0
2
A dataset is 𝜖-predictable iff there exists classification algorithm 𝑓(𝑋), 𝐵𝐸𝑅 𝑓 𝑋 , 𝐴 ≤ 𝜖
What does this mean?
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How does all this relate to disparate impact?
• Theorem: A dataset with fraction 𝛽 minority samples receiving outcome 𝑌 = 1 has disparate impact iff if is $
b− d
e-predictable.
Idea: Look for classifier with low BER!(authors use SVMs)
If BER < $b− d
ethen we have
disparate impact.
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How do we get rid of disparate impact?
• Dataset:• SAT score: 𝑋• Gender: 𝐴 ß sensitive• Admission status: 𝑌
• Idea: change 𝑋 while keeping 𝐴 fixed• Ensure that 95th percentile in
original remains 95th
percentile in the new distribution
Female
Male
Modified
Conditioned on new SAT score, what is the distribution over sensitive attribute?
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Spot the mistakes
𝐴 = 0 | 𝐴 = 1
𝑌 = 0𝑌 = 1 Just because 𝐴 = 1 doesn’t
mean that 𝑌 should equal 1!
This is a misunderstanding of true positive rates.
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Disparate impact
Individual Fairness
Fairness: High-Level View
Metrics Enforcement Algorithms
Group Fairness
Equal Opportunity
Equalized Odds