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Equality Of OddsSummary

Reading time: ~5 min

One page to revise from — the ideas first, then every formula you need.

  • A model can be accurate overall and still be unfair: its mistakes can fall more often on one group, usually because of the data it learned from rather than anyone's intention.
  • A fairness audit works out the error rates group by group. Real audits compare groups defined by protected attributes.
  • Equal opportunity: the same true positive rate in every group, so every qualified person has the same chance.
  • Equalized odds: the same true positive rate and the same false positive rate in every group.
  • One threshold for everyone can treat groups very differently. Post-processing gives each group its own threshold; a fairness rule can also be built into training.
  • On an ROC plot, equalized odds holds where the groups' curves cross. The corners, where everyone or no one is shortlisted, are lazy solutions.
  • Fairness usually costs some accuracy. Which rule to use is a human decision, to be made openly.

Rates
\text{TPR} = \dfrac{\text{TP}}{\text{TP} + \text{FN}}, \qquad \text{FPR} = \dfrac{\text{FP}}{\text{FP} + \text{TN}}

Fairness rules
equal opportunity: \text{TPR}_A = \text{TPR}_B
equalized odds: also \text{FPR}_A = \text{FPR}_B

Sina