Fairness is still an actively studied & disputed concept!

Fairness: Definitions

• Anti-classification (fairness through blindness)
• Independence (group fairness)
• Separation (equalized odds)
• ...and numerous others!

Anti-Classification

• Also called fairness through blindness
• Ignore/eliminate sensitive attributes from dataset
• Example: Remove gender or race from a credit card scoring system
• Q. Advantages and limitations?

Recall: Proxies

Features correlate with protected attributes

Recall: Not all discrimination is harmful

• Loan lending: Gender discrimination is illegal.
• Medical diagnosis: Gender-specific diagnosis may be desirable.
• Discrimination is a domain-specific concept!

Other examples?

Anti-Classification

• Ignore/eliminate sensitive attributes from dataset
• Limitations
  • Sensitive attributes may be correlated with other features
  • Some ML tasks need sensitive attributes (e.g., medical diagnosis)

Testing Anti-Classification

How do we test that an ML model achieves anti-classification?

Testing Anti-Classification

Straightforward invariant for classifier $f$ and protected attribute $p$:

$\forall x. f(x[p\leftarrow 0]) = f(x[p\leftarrow 1])$

(does not account for correlated attributes)

Test with random input data or on any test data

Any single inconsistency shows that the protected attribute was used. Can also report percentage of inconsistencies.

Notations

• $X$: Feature set (e.g., age, race, education, region, income, etc.,)
• $A \in X$: Sensitive attribute (e.g., gender)
• $R$: Regression score (e.g., predicted likelihood of loan default)
• $Y'$: Classifier output
  • $Y' = 1$ if and only if $R > T$ for some threshold $T$
  • e.g., Deny the loan ($Y' = 1$) if the likelihood of default > 30%
• $Y$: Target variable being predicted ($Y = 1$ if the person actually defaults on loan)

Independence

$P[Y' = 1 | A = a] = P[Y' = 1 | A = b]$

• Also called group fairness or demographic parity
• Mathematically, $Y' \perp A$
  • Prediction ($Y'$) must be independent of the sensitive attribute ($A$)
• Examples:
  • The predicted rate of recidivism is the same across all races
  • Both women and men have the equal probability of being promoted
  • i.e., P[promote = 1 | gender = M] = P[promote = 1 | gender = F]

Independence

• Q. What are limitations of independence?
  • Ignores possible correlation between $Y$ and $A$
    • Rules out perfect predictor $Y' = Y$ when $Y$ & $A$ are correlated
  • Permits abuse and laziness: Can be satisfied by randomly assigning a positive outcome ($Y' = 1$) to protected groups
    • e.g., Randomly promote people (regardless of their job performance) to match the rate across all groups

Recall: Equality vs Equity

Calibration to Achieve Independence

Select different thresholds for different groups to achieve prediction parity:

$P[R > t_0 | A = 0] = P[R > t_1 | A = 1]$

Lowers bar for some groups -- equity, not equality

Testing Independence

• Separate validation/telemetry data by protected attribute
  • Or generate realistic test data, e.g. from probability distribution of population
• Separately measure rate of positive predictions
• Report issue if rate differs beyond $\epsilon$ across groups

Separation

$P[Y'=1∣Y=0,A=a] = P[Y'=1∣Y=0,A=b]$ $P[Y'=0∣Y=1,A=a] = P[Y'=0∣Y=1,A=b]$

• Also called equalized odds
• $Y' \perp A | Y$
  • Prediction must be independent of the sensitive attribute conditional on the target variable

Review: Confusion Matrix

Can we explain separation in terms of model errors?

$P[Y'=1∣Y=0,A=a] = P[Y'=1∣Y=0,A=b]$ $P[Y'=0∣Y=1,A=a] = P[Y'=0∣Y=1,A=b]$

Separation

$P[Y'=1∣Y=0,A=a] = P[Y'=1∣Y=0,A=b]$ (FPR parity) $P[Y'=0∣Y=1,A=a] = P[Y'=0∣Y=1,A=b]$ (FNR parity)

• $Y' \perp A | Y$
  • Prediction must be independent of the sensitive attribute conditional on the target variable
• i.e., All groups are susceptible to the same false positive/negative rates
• Example: Promotion
  • Y': Promotion decision, A: Gender of applicant: Y: Actual job performance
  • Separation w/ FNR: Probability of being incorrectly denied promotion is equal across both male & female employees

Testing Separation

• Generate separate validation sets for each group
• Separate validation/telemetry data by protected attribute
  • Or generate realistic test data, e.g. from probability distribution of population
• Separately measure false positive and false negative rates

Case Study: Cancer Diagnosis

Exercise: Cancer Diagnosis

• 1000 data samples (500 male & 500 female patients)
• Does the model achieve independence? Separation w/ FPR or FNR?
• What can we conclude about the model & its usage?

Review of Criteria so far:

Recidivism scenario: Should a defendant be detained?

• Anti-classification: Race and gender should not be considered for the decision at all
• Independence: Detention rates should be equal across gender and race groups
• Separation: Among defendants who would not have gone on to commit a violent crime if released, detention rates are equal across gender and race groups

Can we achieve fairness during the learning process?

• Data acquisition:
  • Collect additional data if performance is poor on some groups
• Pre-processing:
  • Clean the dataset to reduce correlation between the feature set and sensitive attributes
• Training time constraint
  • ML is a constraint optimization problem (i.e., minimize errors)
  • Impose additional parity constraint into ML optimization process (as part of the loss function)
• Post-processing
  • Adjust thresholds to achieve a desired fairness metric
• (Still active area of research! Many new techniques published each year)

Trade-offs: Accuracy vs Fairness

• In general, accuracy is at odds with fairness
  • e.g., Impossible to achieve perfect accuracy ($R = Y$) while ensuring independence
• Determine how much compromise in accuracy or fairness is acceptable to your stakeholders